Agilent PSA Performance Spectrum Analyzer Series

Optimizing Dynamic Range forDistortion Measurements

Product Note

Its wide dynamic range makes the spectrum analyzer the testinstrument of choice for measuringharmonic distortion, intermodulationdistortion, adjacent channel powerratio, spurious-free dynamic range,gain compression, etc. Distortionmeasurements such as these arebounded on one side by the noisefloor of the spectrum analyzer andon the other side by the signal powerstrength at which the spectrum analyzer’s internally generated distortion masks the distortion beingmeasured. The simultaneous lownoise floor and low internally gener-ated distortion products uniquelyqualify the spectrum analyzer formaking distortion measurements.

Having wide dynamic range andaccessing this dynamic range are two different things. Unless the useris given enough information on howto optimize the spectrum analyzer tomake distortion measurements, itsdynamic range performance cannotfully be exploited. Many distortionmeasurements are very straightfor-ward: measure the fundamental tonepower, measure the distortion prod-uct power, and compute the differ-ence. Problems arise when the deviceunder test has distortion product

levels that approach the internallygenerated distortion product levels of the spectrum analyzer. Furthercomplications arise when trying to maximize speed and minimizemeasurement uncertainty. In thesecases more care in the measurementtechnique is required.

The search for information on making distortion measurementsbegins with the spectrum analyzerdata sheet. The data sheet is mostuseful for comparing one spectrumanalyzer against another in itsdynamic range capability and the relevant measurement uncertaintiesin the distortion measurement. Whatthe data sheet fails to convey is howto configure the spectrum analyzer to achieve the specified dynamicrange performance.

Primers are another source of infor-mation. Two excellent references are[1] and [2] listed on page 39 of thisdocument. Primers such as theseprovide the necessary fundamentalknowledge for making distortionmeasurements. Yet, primers treatspectrum analyzers as a general classof test instrumentation. In order to

make truly demanding distortionmeasurements accurately or lessdemanding measurements morequickly, the user needs product specific information.

This product note bridges the gapbetween primers and data sheets,focusing on distortion measurementsusing the Agilent Technologies performance spectrum analyzer(PSA) series (model E4440A). Part I is a self-contained section for making the less demanding distortion measurement quicklyusing the auto-coupled settings found in the PSA. Part II guides theuser in setting the appropriate powerat the input mixer in order to maxi-mize the dynamic range for carrierwave or continuous wave (CW) measurements. Part III explains themeasurement of distortion measure-ments on digitally modulated signals.Part IV details some of the internalarchitecture of the PSA as it relatesto distortion measurements. Finally,Part V describes some measurementtechniques, both internal and external to the PSA, that yield more accuracy in certain kinds of distortion measurements.

2

Table of Contents

Part I: Distortion Measurement Examples 4

Harmonic Distortion 4

Intermodulation Distortion 6

Small Signal Desensitization 9

Spectral Regrowth of a Digitally Modulated Signal 11

Part II: Mixer Level Optimization 12

Signal-to-Noise versus Mixer Level 12

Signal-to-Noise with Excess Noise 15

Signal-to-Distortion versus Mixer Level 15

The Dynamic Range Chart 17

Adding Phase Noise to the Dynamic Range Chart 18

Noise Adding to the Distortion Product 19

SA Distortion Adding to DUT Distortion 21

Part III: Distortion Measurements on Digitally Modulated Signals 23

Choice of Averaging Scale and Display Detector 23

Maximizing Spectrum Analyzer Dynamic Range 24

Signal-to-Noise of Digitally Modulated Signals 24

Spectral Regrowth Due to Spectrum Analyzer Intermodulation Distortion 25

Phase Noise Contribution 27

Dynamic Range Chart for Digitally Modulated Signals 28

Measurement Error Due to SA Spectral Regrowth Adding to DUT Spectral Regrowth 30

Part IV: PSA Architectural Effects on Distortion Measurements 31

Input Attenuator Resolution 31

Internal Filtering 32

Internal Preamplifier 33

Part V: Enhancing Distortion Measurements 34

Reducing Source Intermodulation Distortion 34

Effects of Harmonics on Intermodulation Distortion 35

Noise Subtraction Techniques 36

Conclusions 38

Glossary of Terms 38

References 39

3

The Agilent PSA series are high-per-formance radio frequency (RF) andmicrowave spectrum analyzers thatoffer an exceptional combination of dynamic range, accuracy andmeasurement speed. The PSA series deliver the highest level ofmeasurement performance availablein Agilent Technologies’ spectrumanalyzers. An all-digital IF sectionincludes fast Fourier transform (FFT)analysis and a digital implementationof a swept IF. The digital IF andinnovative analog design providemuch higher measurement accuracyand improved dynamic range com-pared to traditional spectrum analyz-ers. This performance is combinedwith measurement speed typically 2 to 50 times faster than spectrumanalyzers using analog IF filters.

The PSA series complement Agilent’sother spectrum analyzers such as the ESA series, a family of mid-levelanalyzers that cover a variety of RFand microwave frequency rangeswhile offering a great combination of features, performance and value.

Specifications:

Frequency coverage 3 Hz to 26.5 GHz

DANL -153 dBm (10 MHz to 3 GHz)

Absolute accuracy ±0.27 dB (50 MHz)

Frequency response ±0.40 dB (3 Hz to 3 GHz)

Display scale fidelity ±0.07 dB total (below -20 dBm)

TOI (mixer level -30 dBm) +16 dBm (400 MHz to 2 GHz)+17 dBm (2–2.7 GHz)+16 dBm (2.7–3 GHz)

Noise sidebands (10 kHz offset) -113 dBc/Hz (CF = 1 GHz)

1 dB gain compression +3 dBm (200 MHz to 6.6 GHz)

Attenuator 0–70 dB in 2 dB steps

About the Agilent PSA Performance Spectrum Analyzer Series

4

In this first part we offer quick methods of making some commondistortion measurements using aPSA series spectrum analyzer (model E4440A). Measurementsin this section emphasize the auto-coupled features of the PSAseries that serve the occasional user or the user who must quicklymake distortion measurements andjust does not have the time to learnthe intricacies of the analyzer.Techniques outlined in this sectionpurposely place the analyzer instates such that the measurement is noise-limited rather than distor-tion-limited. The user does not needto worry if the distortion generatedwithin the analyzer is interferingwith the distortion generated by the device under test (DUT).

The measurement procedures outlined in this section place thespectrum analyzer in narrow spanswhere only the fundamental tone or only the distortion product is displayed at any given time. Thistechnique is in opposition to themore intuitive approach of using a span wide enough to view the fun-damental tones and the distortionproducts in one sweep. In order toincrease the signal-to-noise-ratio ofthe spectrum analyzer, the resolutionbandwidth (RBW) filter setting mustbe reduced. Furthermore, to reducethe variance of the measured distor-tion products that appear close tothe noise floor, the video bandwidth(VBW) filter setting must be reduced.The combination of wide span,

narrow RBW and narrow VBW, ingeneral, increases the sweep time. By reducing the span, more dynamicrange is available without sacrificingsweep time.

For many measurements, the tech-niques described in this section aremore than adequate. If the distortionproduct is measurable, then themeasurement procedure is adequate.If only noise is discernible whenmeasuring the distortion product,then techniques in Parts II, III, IVand V must be considered to increasethe dynamic range of the analyzer.

Harmonic Distortion

Harmonic distortion measurementson a CW tone are the most straight-forward of the distortion measure-ments. The method outlined hereallows measurement of harmonics as low as -85 dBc for fundamentalfrequencies below 1.6 GHz and as lowas -110 dBc for fundamental frequen-cies above 1.6 GHz.

The mixer level (mixer level is definedas the power at the RF input portminus the nominal input attenuationvalue) of the analyzer is set such that internally generated harmonic distortion products are at least 18 dB below the harmonic distortionof the DUT. This guarantees that thedistortion measurement uncertaintydue to internal distortion combiningwith DUT distortion is less than 1 dB.

Part I: Distortion Measurement Examples

Notation used in this section

underlined commands = hardkeys

non-underlined commands = softkeys

: (colon) = separator between key sequences

< numeric value > = user entered numeric value

⇑ , ⇓ = the up and down arrow hardkeys

Figure 1–1 Harmonic Distortion Measurement Setup

DUTfi fo PSA

fi < fc < 2fi

fi fo= fi

amplifier

mixer

fi fo

signalsource

fo

DUT:

ampl

itude

freq

. . .

fo 2fo 3fo

23

5

Measurement Setup:The test setup for making harmonic measurements is shown in Figure 1–1.

The DUT is represented as a two-portdevice, which most commonly is anamplifier. For a three-port mixer, the local oscillator (LO) source isincluded in the model of the DUT. In this case the output frequency, fo,is a frequency-translated version ofthe input frequency, fi. One can alsouse this procedure to measure theharmonics of the signal source itself.For two- or three-port devices it maybe necessary to include a filterbetween the signal source and theDUT in order ensure the measuredharmonics are due to the DUT andnot the signal source.

First, tune the signal source to thedesired fundamental frequency, fo. If the DUT is a mixer, then tune thesource to an input frequency of fiand tune the LO source to a frequen-cy appropriate to output a funda-mental frequency of fo from the DUT. For best results, the frequencyreferences of all the sources and thePSA series analyzer should be lockedtogether where applicable.

Setup PSA Series Analyzer:

Auto Couple Couples RBW filter, VBW filter, Span and Sweep time.Couples Reference Level and Input Attenuator.

AMPLITUDE: More: More: Max Mxr Lvl: < Mixer Level Value > : dBmMixer Level Value = / -60 dBm for fo <1.6 GHz

\ -30 dBm for fo ≥1.6 GHz

BW / Avg: VBW/RBW: < .1 >Couples the VBW filter and the RBW filter with a bandwidth ratio of 1:10.

Tune to the Fundamental Tone:

FREQUENCY: Center Freq: < fo >: GHz, MHz, kHz or Hz.fo is the fundamental frequency at the output of the DUT.

SPAN: < 1 > : MHz

AMPLITUDE: Ref Level: < Reference Level Value > :dBmSets Reference Level Value to be higher than the DUT’s fundamental tone output power.

Peak Search Positions marker at the peak of the fundamental tone.

At this point, the source amplitude can be adjusted in order to set the desired DUT output power level.

Marker →: Mkr → Ref LvlBrings displayed fundamental amplitude to the top line of the display graticule to optimize display range.

Marker →: Mkr → CF StepCenter Frequency step size is set to fundamental frequency.

Marker: Delta Activates the Delta Marker.

Tune to the 2nd Harmonic:

FREQUENCY: ⇑ Tune to the 2nd harmonic frequency

SPAN: ⇓ : ⇓ :⇓ , etc. Reducing the frequency span automatically reduces the RBW value, which in turn reduces the displayed noise.

Span down until the distortion product is at least 5 dB above the noise floor. If the noise floor falls below the bottom of the display then follow this procedure:

AMPLITUDE: Attenuation: Attenuation‘Man’ should be underlined. This de-couples the input attenuator from the reference level.

AMPLITUDE: Ref Level: ⇓ :⇓ , etc.Maximum power at the mixer is not altered by changingthe Reference Level setting.

For distortion products close to the noise floor, the variance of the signal amplitude can be reduced by lowering the VBW value.

Bw / Avg: Video BW: ⇓ :⇓ , etc.

Peak Search Positions delta marker at peak of the distortion product

The marker delta amplitude value is the 2nd harmonic power relative to the fundamental tone power.

Compute Output SHI (Second Harmonic Intercept) Power Level:

SHI [dBm]= DUT Output Power [dBm] + ∆2

DUT Output Power is the reference level value read from the display minus any loss between the DUT and the input of the PSA series analyzer. ∆2 is the negative of the marker delta amplitude value; ∆2 is a positive value.

For 3rd, 4th, etc. Harmonic, press FREQUENCY: ⇑ to tune to each harmonic frequency and record the marker delta amplitude value.

Intercept points are computed using:Intercept Point [dBm] = DUT Output Power + ∆i / (i -1); where i is the order of the harmonic.

6

Intermodulation Distortion

Anytime multiple tones are present at the input of any nonlineardevice, these tones will mix together,creating distortion products. Thisphenomenon is known as intermodu-lation. Amplifiers, mixers and spectrum analyzer front ends areexamples of nonlinear devices proneto intermodulation distortion (IMD).Figure 1–2 depicts some of the inter-modulation products generated whentwo tones at frequencies f1 and f2are presented to the input of a non-linear device.

The IMD products falling closest tothe fundamental tones, at frequen-cies 2f1-f2 and 2f2-f1, present themost trouble due to the impracticali-ty of removing these with filtering.These two closest distortion productsfollow a third order characteristic—their power levels increase by a factor of three when measured on alogarithmic display scale in relation-ship to the increase in the two funda-mental tone power levels. The thirdorder IMD traditionally has been thebenchmark distortion figure of meritfor mixers and amplifiers. The thirdorder IMD is also a key predictor forspectral regrowth associated withdigital modulation formats.

This procedure focuses on the measurement of third order IMD fortwo CW tones present at the input of a DUT. In a similar vein to the harmonic distortion measurementprocedure, the suggested configura-tion ensures that IMD products gen-erated by the analyzer are at least 18 dB below the IMD products of theDUT. Again, this guarantees that thedistortion measurement error due tointernal distortion added to DUT distortion is less than 1 dB.

Measurement Setup:Figure 1–3 shows the test setup for making a two-tone, third orderIMD measurement.

As with the harmonic distortionmeasurement, the DUT can be a two- or three-port device. If the DUTis a mixer, then it is assumed thatthe LO source is included in the DUTblock and that the output frequencieswill be frequency-translated versionsof the input frequencies. This proce-dure can also be used to measure the

Figure 1–2Two-Tone Intermodulation Distortion

ampl

itude

freq

. . .

f2-f1 3f1-2f2 2f1-f2 f1 f2 2f2-f1 3f2-2f1 2f1 f1+f2 2f2

Figure 1–3Two-Tone Intermodulation Distortion Measurement Setup

f1

f2

DUT PSAΣ

7

intermodulation of the two sourcesthemselves. The measurementrequires two sources using a meansof power combination with adequateisolation such that the sources do notcreate their own IMD. Do not treatthis part of the measurement lightly;see Part V for a detailed descriptionon source power combination tech-niques. Filtering may be requiredbetween the power combiner and theDUT to remove unwanted harmonics.For the same reason, additional fil-tering may be required between theDUT and the analyzer. Again, seePart V for more information. Source1 is tuned to one of the fundamentalfrequencies, f1, and Source 2 is tunedto the other fundamental tone fre-quency, f2. The frequency separation,∆f, of the two input tones is some-times referred to as the tone spacing.The upper third order IMD compo-nent falls at a frequency of 2 x f2 - f1(or f1 + 2 x ∆f) and the lower thirdorder IMD component falls at a frequency of 2 x f1 - f2 (or f1 - ∆f). For best results, if applicable, the frequency references of all thesources and the analyzer should be locked together.

Setup PSA Series Analyzer:

Auto Couple Couples RBW filter, VBW filter, Span and Sweep time.Couples Reference Level and Input Attenuator.

AMPLITUDE: More: More: Max Mxr Lvl: < -50 > : dBmLimits power at input mixer to less than -50 dBm.

SPAN: < frequency span > GHz, MHz, kHz or HzSets frequency span to be less than the separation frequency, ∆f, to ensure that only one tone is displayed at a time.

FREQUENCY: CF Step : < ∆f >: GHz, MHz, kHz or HzBw / Avg: < .1 > Couples the VBW filter and the RBW filter with a

bandwidth ratio of 1:10.

Tune to the lower fundamental tone frequency:

FREQUENCY: Center Freq: < f1 >: GHz, MHz, kHz or Hz.If the DUT is a mixer, then tune to the translatedfrequency corresponding to f1.

AMPLITUDE: Ref Level: < Reference Level Value > :dBmSet Reference Level Value to be higher than the DUT’s fundamental tone output power.

Peak Search Marker will position itself at the peak of the fundamental at frequency f1.

Fine tune the DUT’s output power while monitoring the PSA’s marker amplitude value.

Marker →: Mkr → Ref LvlBrings displayed fundamental amplitude to the top line of the display graticule to optimize display range.

Marker: Delta Activates the Delta Marker where the reference is the fundamental tone at frequency f1.

Tune to the upper fundamental tone frequency:

FREQUENCY: Center Freq: ⇑If the DUT is a mixer, the frequency translation may reverse the frequency orientation of the tones, in which case substitute a down arrow hardkey, ⇓ , for the up arrow key in the rest of this procedure.

In most cases, the fundamental tones are adjusted to have the same power levels. If so, then adjust the Source 2 power level for a displayed delta marker amplitude of 0 dB. Otherwise, adjust the Source 2 power level to the desired difference from the Source 1 power level.

8

Tune to the upper IMD product:

FREQUENCY: Center Freq: ⇑SPAN: ⇓ : ⇓ :⇓ , etc. Spanning down in frequency will automatically reduce the

RBW value, which in turn reduces the displayed noise.

Span down until the distortion product is at least 5 dB above the noise floor. If the noise floor falls below the bottom of the display then follow this procedure:

AMPLITUDE: Attenuation: Attenuation‘Man’ should be underlined. This de-couples the input attenuator from the reference level.

AMPLITUDE: Ref Level: ⇓ :⇓ , etc.Maximum power at the mixer is not altered by changingthe Reference Level setting

For distortion products close to the noise floor, the variance of the signal amplitude can be reduced by lowering the VBW value.

Bw / Avg: Video BW: ⇓ :⇓ , etc.

The marker delta amplitude value is the upper IMD product power relative to the fundamental tone power.

Tune to the lower IMD product:

FREQUENCY: Center Freq: ⇓, ⇓, ⇓The marker delta amplitude value is the lower IMD product power relative to the fundamental tone power.

To compute output TOI (Third Order Intercept) power level:

TOI [dBm]= DUT Output Power of each tone [dBm] + ∆/2

DUT Output Power is the reference level value read off the display minus any loss between the DUT and the input of the PSA series analyzer. Note that the power is the power of each tone and not the combined power of the two tones. ∆ is the negative of the marker delta amplitude value; ∆ is a positive value. In most cases TOI is computed using the higher amplitude of the upper or lower distortion products yielding the more conservative TOI result.

9

Small Signal Desensitization

Small signal desensitization measure-ment is a form of a gain compressiontest on components intended for use in receiver architectures.Another term for this measurementis two-tone gain compression. Thismeasurement predicts the amount ofgain change of a relatively low powersignal in the presence of other highpower signals.

Network analyzers commonly areused to measure the gain compres-sion level of a nonlinear device.However, the spectrum analyzer is quite capable of measuring gaincompression as well. Whereas thenetwork analyzer approach sweepsthe power of a single tone at a fixedfrequency to characterize and displaythe power-out vs. power-in response,the spectrum analyzer approach uses two tones in a test setup similarto the two-tone intermodulation distortion measurement procedure.One tone at a lower power level is

monitored by the spectrum analyzerwhile the other tone at a much high-er power level drives the DUT intogain compression. When in gain compression, the amplitude of thelower power tone decreases by thegain compression value (that is, for a 1 dB gain compression measurement,the amplitude of the lower powertone is 1 dB lower than when thehigher power tone is turned off).When the desired gain compressionis reached, the amplitude of the higher power tone is measured bythe spectrum analyzer.

The two-tone method is not recom-mended for high power amplifiers inwhich a large CW signal could causelocalized heating, thereby affectingthe measured results. In these casesthe network analyzer is more appro-priate. For more information refer tothe techniques in reference [3].

Figure 1–4Two-Tone Gain Compression Measurement Setup

f1

f2

DUT PSAΣ

HighPowerSource

Low PowerSource

10

Measurement Setup:The measurement setup for the two-tone gain compression test isshown in Figure 1–4.

The isolation requirements for thesignal combiner described for theIMD measurement do not apply tothe gain compression test. The sepa-ration frequency of the two sourcesmust be within the bandwidth of theDUT. The high power source needsenough power to drive the DUT intogain compression. The power level ofthe low power source is set at least40 dB below the power level of thehigh power source.

Setup PSA Series Analyzer:

Auto Couple Couples RBW filter, VBW filter, Span and Sweep time.Couples Reference Level and Input Attenuator.

AMPLITUDE: More: More: Max Mxr Lvl: < -10 > : dBmDefault setting.

AMPLITUDE: Ref Level: < Reference Level Value >: dBmReference Level must be greater than the anticipated DUT output power at gain compression.

AMPLITUDE: Attenuation: AttenuationThe ‘Man’ should be underlined. The PSA series’ Input Attenuator is now de-coupled at a setting where the analyzer will not be driven into compression.

Tune to the Low Power Source Frequency:

FREQUENCY: Center Freq: < f2 > : GHz, MHz, kHz or Hz.If the DUT is a mixer, then tune to the translated frequency corresponding to f2.

Set the Source 2 power level such that the displayed DUT output amplitude at frequency f2 is at least 40 dB below the estimated DUT output power at gain compression.

SPAN: ⇓, ⇓ , etc. Span down until the displayed amplitude at f2 is at least 20 dB above the noise floor.

Bw / Avg: Video BW: ⇓, ⇓ , etcReduce video bandwidth to reduce amplitude variance due to noise.

Drive DUT into Compression:

First, reduce Source 1 power such that the DUT is not gain compressed. Or better yet, turn off the Source 1 power.

Marker: Delta Activate the delta marker.

Increase Source 1 power until Delta Marker amplitude decreases by the desired gain compression amount. For example, if DUT output power at 1 dB gain compression is desired, then increase Source 1 power until the Delta Marker amplitude decreases by 1 dB.

Measure DUT Output Power:

FREQUENCY: Center Freq: < f1 >: GHz, MHz, kHz or HzTune to Source 1 frequency.

Marker: Normal Turn off the delta marker mode.

Marker amplitude is the DUT output power at the specified gain compression level. The digital IF in thePSA series allows valid measurement of signals whose amplitudes fall above or below the display graticule. As long as the ‘Final IF Overload’ message is not present, the marker amplitude is valid.

11

Spectral Regrowth of a Digitally Modulated Signal

Digital modulation employing bothamplitude and phase shifts generatesdistortion known as spectralregrowth. As depicted in Figure 1–5,spectral regrowth falls outside themain channel into the lower andupper adjacent channels.

Like other distortion measurements,the spectrum analyzer creates itsown internally generated distortionwhich, in the case of digitally modulated signals, is called spectralregrowth. In most cases, the spectralregrowth distortion generated withinthe spectrum analyzer is third order,meaning that for every 1 dB increasein main channel power, the spectralregrowth power increases by 3 dB. Inaddition to spectral regrowth, phasenoise and broadband noise of thespectrum analyzer also limit thedynamic range of this type of distortion measurement.

Adjacent Channel Power Ratio(ACPR) is the measure of the ratio ofthe main channel power to the powerin either of the adjacent channels.Some modulation formats require a spot measurement where powermeasurements are made at specificfrequency offsets in the main andadjacent channels. Other formatsrequire an integrated power meas-urement where the spectrum analyz-er individually computes the total

power across the entire main channel and each of the adjacentchannels. In either case the usermust set the proper mixer level ofthe spectrum analyzer to minimizethe internally generated spectralregrowth. However, minimizing inter-nally generated spectral regrowthcomes at the price of increasingbroadband noise, therefore a balance

must be reached between the two.Another complicating matter withdigitally modulated signals is that themixer level cannot be set based onaverage power at the mixer alone.The peak-to-average ratio of the modulated signal affects the amountof internally-generated spectralregrowth and must be factored into the setting of the mixer level.

Figure 1–5Spectral Regrowth of a Digitally Modulated Signal

SpectralRegrowth

MainChannelSignal

MainChannel

UpperAdjacentChannel

LowerAdjacentChannel

Setup PSA Series Analyzer:

Auto Couple Couples RBW filter, VBW filter, Span and Sweep time.Couples Reference Level and Input Attenuator.

Bw/Avg: Resolution BW: < RBW Value >Set RBW Value to the specified setting according to the modulation format guidelines. RBW setting must be much less than the modulation bandwidth.

Frequency: Center Freq: < Main Channel Frequency > GHz, MHz, kHz or Hz

Span: < Span > Set span in order to view the main channel and the adjacent channels.

Det/Demod: Detector: AverageActivates the Averaging detector, which reports the average signal amplitude between trace display points.

Sweep: < Sweep Time > With the average detector on, longer sweep times reducethe displayed variance of a noise-like signal.

Amplitude: Ref Level: < Reference Level Value >Set Reference Level Value in order to place the mainchannel amplitude near the top of the display.

Amplitude: Attenuation < Attenuation Value > dBStart from a low attenuation setting. Increase attenuation until spectral regrowth amplitude in the adjacent channel no longer changes. Then increase attenuation by 10 dB.

Marker: Span Pair: Center: < Main Channel Center Frequency >

Marker: Span Pair: Span: < Channel Bandwidth >Record marker amplitude value. This is the main channel power in dBm.

Marker: Span Pair: Center: < Adjacent Channel center frequency >Record marker amplitude value. This is the adjacent channel power.

ACPR = Main channel power - Adjacent channel power [dB].

12

The distortion measurementsdetailed in Part I have the spectrumanalyzer configured such that itsinternally generated distortion products fall below the distortionbeing measured. While guaranteed to make accurate measurements byensuring that the spectrum analyzergenerated distortion does not maskthe DUT generated distortion, thesetechniques do not allow full use ofthe available dynamic range of thespectrum analyzer. In order to makedistortion measurements on highlylinear devices whose distortion isalready very low, the user must over-ride the auto-couple features of thespectrum analyzer. Removing theauto-coupling allows more flexibilityin optimizing the dynamic range ofthe spectrum analyzer. Beginningwith this part, techniques pertainingto optimizing the PSA series settingsfor maximum distortion measure-ment capability are explained. This discussion begins with setting the mixer level.

Controlling the amount of powerpresent at the first mixer of the spectrum analyzer is the first step in making distortion measurements.Optimizing this power, known as themixer level, maximizes the dynamicrange of the spectrum analyzer.Where a mixer level is set too low,the spectrum analyzer noise floorlimits the distortion measurement.Where a mixer level is set too high,the distortion products generatedwithin the spectrum analyzer limitthe distortion measurement. The

dynamic range charts found in manyspectrum analyzer data sheets showthe dynamic range plotted againstthe mixer level. This is an extremely useful tool in understanding how tobest set the mixer level for secondharmonic distortion and third orderintermodulation distortion measure-ments. Normally the dynamic rangecharts in data sheets use specifiedspectrum analyzer performance andnot the better typical performance.Learning how to construct thesecharts not only assists in under-standing how to use them, but it also allows flexibility so that the usercan customize the chart for actualspectrum analyzer performance.

Signal-to-noise ratio, signal-to-distortion ratio and phase noise contribute to the construction of thedynamic range chart. All of theseindividual terms will be discussedstarting with signal-to-noise versusmixer level.

Signal-to-Noise versus Mixer Level

The spectrum analyzer can bethought of as a two-port device characterized by a power-out versuspower-in transfer function, as shownin Figure 2–1.

Power-in (Pin) is the power presentat the RF input port and power-out(Pout) is the signal as it appears onthe display of the spectrum analyzer.Both axes of the graph indicate RMSpower of a CW signal. The apparentgain of the spectrum analyzer is 0 dB, meaning that the displayedamplitude is the value of the powerat the RF input port. The noise floorof the spectrum analyzer places alimitation on the smallest amplitudethat can be measured. DisplayedAverage Noise Level (DANL) is thenoise floor as it appears on the dis-play. For the PSA series, specifiedDANL is given in units of dBm/Hz(the noise is normalized to a 1 HzResolution Bandwidth setting, meas-ured in a 0 dB Input Attenuation setting). Additionally, specified DANLin the PSA series is measured usingthe Log-Power (Video) averagingscale. (More on this subject later).

Figure 2–1 demonstrates that forevery 1 dB drop in input power, theoutput signal-to-noise ratio (S/N)drops by 1 dB. Input power can be reduced in one of two ways: either the power level is decreasedexternally or the spectrum analyzerInput Attenuation is increased.

Part II: Mixer Level Optimization

Figure 2–1Spectrum Analyzer Pout vs. Pin Characteristic

Pin(dBm)

Pout(dBm)

S/N

SA Noise Floor

1Displayed Signal

13

Another way of presenting the information in Figure 2–1 is to plotS/N versus power at the input mixer.Figure 2–2 shows this plot. Thestraight line data representing DANLrelative to mixer level (or invertedS/N) has a slope of -1 signifying thatfor every 1 dB decrease in power atthe input mixer, the S/N decreases 1 dB. The spectrum analyzer’s DANLvalue locates the anchor point for the straight line. At the y-axis 0 dBcpoint, the x-axis mixer level is theDANL for 1 Hz RBW and 0 dB InputAttenuation. For example, in Figure2–2, the spectrum analyzer DANL is -155 dBm in a 1 Hz RBW, measuredwith 0 dB Input Attenuation.

The noise floor of the spectrum analyzer can be affected in two ways. One is with the RBW setting.The noise floor rises over the 1 Hznormalized DANL value according to the equation: 10 Log(RBW); whereRBW is the Resolution Bandwidthsetting in Hz. Increasing the RBW by a factor of 10 increases the noisefloor by 10 dB. Figure 2–3 shows the noise floor with 1 Hz, 10 Hz and1 kHz settings, demonstrating thatthe noise floor increases by 10 and30 dB respectively relative to the 1 Hz RBW setting.

The other mechanism that affects thedisplayed noise floor is the averagingscale. Averaging scale selection isfound under the Mode Setup hardkey,Avg/VBW type softkey. The PSAseries has two averaging scales forpower measurements: Log-Power(Video) and Power (RMS). We discussthe distinction between these twoaveraging scales at this point becauseof their affect on displayed noise.Later we will discuss which averag-ing scale is most appropriate for thetype of distortion measurement being made.

Figure 2–2Signal to Noise vs. Power at the Input Mixer

-120

-100

-80

-60

-40

-20

0

-180 -160 -140 -120 -100 -80 -60 -40

DA

NL

rela

tive

toM

ixer

Lev

el (d

Bc)

Mixer Level (dBm)

1

SA DANL Value (dBm)

Figure 2–3Noise Floor with Different RBW Settings

DA

NL

rela

tive

toM

ixer

Lev

el (d

Bc)

Mixer Level (dBm)-100 -90 -80 -70 -60 -50

-30-40-50-60-70-80-90

-100

1 kHz RBW

10 Hz RBW

1 Hz RBW

10 dB

30 dB

Figure 2–4Averaging Scale Effect on Displayed Noise

2.51 dB

Noise Level using Log-Power (Video) Averaging Scale

Noise Level using Power (RMS) Averaging Scale

Noise Level in an Ideal Rectangular RBW Filter

.25 dB

2.26 dB

14

Figure 2–4 shows the relationshipbetween noise, displayed noise usingthe Log-Power (Video) scale, and displayed noise using the Power(RMS) scale.

Ideally, noise is measured using arectangular filter that has a flat passband response and infiniteattenuation in the stopband.However, the PSA series measure all signals, including noise, using RBWfilters that approximate a Gaussianresponse. These filters offer muchbetter time domain performancethan the theoretical rectangular RBW filter. The consequence of usingnon-rectangular RBW filters is that,when subjected to noise with a flatpower spectral density, the noise thatfalls outside of the specified -3 dBbandwidth will be measured alongwith the noise that falls inside thepassband of the filter. So, if the rectangular RBW filter has the samebandwidth as the near-Gaussian RBWfilter, the measured noise power willbe greater when using the RBW filter.Noise-power bandwidth (or equiva-lent noise bandwidth) describes thebandwidth of an ideal rectangular filter (this is different than the ideal rectangular RBW filter!) whosepower response is the same as thepower response of the actual filterused for the noise measurement. For

PSA series, the noise-power bandwidth (NBW) of any RBW filteris approximately 6 percent widerthan its -3 dB bandwidth. The ratioof the NBW to the -3 dB bandwidthof a RBW filter is the power gainwhen measuring noise or noise-likesignals. For the PSA series this powergain is 10 x Log(1.06) or +0.25 dB.

The displayed noise power of thePSA series when using the Power(RMS) averaging scale is 0.25 dBhigher than when using the ideal rectangular RBW filter, indicatingthat it reports the NBW filter powerresponse. As the name implies, thePower averaging scale reports thepower of the signal, whether this signal be Gaussian noise, CW, or asignal with modulation. This powermeasurement is equivalent to theroot-mean-square of the signal voltage.

When using the Log-Power (Video)averaging scale, Gaussian noise isdisplayed 2.51 dB lower in powerthan when using the Power (RMS)averaging scale. References [1] and [4] explain the reasons for the under-response of noise whenusing the Log-Power averaging scale.To compute the noise in an ideal rectangular RBW filter from thenoise measured using the Log-Poweraveraging scale, add 2.51 dB to correct for logarithmic averagingscale conversion and subtract 0.25dB to account for the ratio of NBW to the -3 dB bandwidth of the RBWfilter. The total correction for thePSA series is +2.26 dB.

One important point is that themeasured amplitude of CW signalsdoes not change with averaging scale.Log-Power (Video) averaging scale ispreferred for measuring CW signalsbecause it gives 2.51 dB of added S/Nover the Power (RMS) display scale.The Power (RMS) display scale is the proper averaging scale whenmeasuring digitally modulated sig-nals that have noise-like behavior. As explained in reference [4], if thestatistics of the modulated signal arenot exactly known, the 2.51 dB cor-rection factor that strictly applies to white Gaussian noise cannot beassumed. The hard to quantify offsets associated with the Log-Power(Video) scale do not exist in thePower (RMS) scale when measuringmodulated signals with unknownpower statistics.

15

Signal-to-Noise with Excess Noise

The S/N vs. mixer level graph alsoworks when the noise at the input isgreater than the noise floor of thespectrum analyzer, something not all that uncommon, especially whenpreamplifiers are used as part of themeasurement system. This excessnoise can stem from devices with relatively low signal-to-noise ratios as compared with the spectrum analyzer. Some examples of thesedevices are signal sources and elements in receiver architectures. In this discussion, we are concernedwith excess broadband noise, notclose-in phase noise.

Figure 2–5 depicts the situationwhere the external noise from theDUT is greater than the noise floor of the spectrum analyzer (SA). At higher signal power levels theexternal signal-to-noise ratio staysconstant. As the input signal powerdecreases, the external noise fallsbelow the noise floor of the spectrumanalyzer, in which case the S/Ndecreases in the familiar 1 dB per 1 dB of signal power reduction.

Figure 2–6 shows how external noiseappears on the S/N versus mixerlevel graph. At higher powers, theDANL relative to the power at themixer stays constant and at lowermixer levels the S/N curve shows the familiar slope of -1. The SA Noise and the external noise add asuncorrelated powers such that at theintersection of the SA noise and the

external noise curves, the combinednoise is 3 dB higher than the twoindividual contributors alone. Theexternal noise as displayed on thespectrum analyzer follows the samedependency on RBW setting as theSA noise, such that for every decadeincrease in RBW value, both the SANoise and the external noise curvesshift up by 10 dB on the dynamicrange chart.

Figure 2–5SA Pout vs. Pin with External Noise

Pin(dBm)

Pout(dBm)

SA Noise Floor

S/Nexternal

Delayed Signal

ExternalNoise

Figure 2–6Signal-to-Noise vs. Mixer Level with External Noise Greater than SA Noise

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External Noise Combined Noise

SA Noise

Signal-to-Distortion versus Mixer Level

Distortion products can also beviewed on the Power-out vs. Power-ingraph. Figure 2–7 shows that Nthorder distortion product amplitudesincrease N dB for every dB of funda-mental tone power increase. The signal-to-distortion ratio (S/D)decreases N-1 dB for every 1 dB of increase in fundamental tonepower. Above a certain power level,however, the spectrum analyzer gaincompresses, at which point the out-put power no longer increases in alinear relationship when plotted on alog power scale. By extrapolating the

16

below gain compression Pout vs. Pincurves for both the fundamental toneand the distortion products, the twolines cross at a fictional outputpower level above gain compression.The output power where these twolines meet is termed Third OrderIntercept (TOI) for third order inter-modulation distortion and SecondHarmonic Intercept (SHI) for secondharmonic distortion.

For the spectrum analyzer, TOI andSHI are specified with respect to the power at the input mixer.Another way of thinking about thesespecifications is that TOI and SHI are measured assuming 0 dB InputAttenuation. Referring to Figure 2–8,SHI is calculated as: SHI = P + ∆;where P is the input power minus theInput Attenuation value and ∆ is thedB difference between the secondorder distortion product power leveland the fundamental tone powerlevel (∆ is a positive value). TOI ismeasured assuming two equal powertones at the input and is calculatedas: TOI = P + ∆/2. In this case P is thepower at the input mixer of eachtone; P is not the combined tonepower, which would be 3 dB higher.Again ∆ is the power differencebetween each fundamental tone and the intermodulation distortionproduct and is a positive value. If thetwo intermodulation products haveunequal amplitudes, the productwith the higher amplitude is used,giving a worst-case TOI result.

Having demonstrated the conversionof S/N from the Power-out versusPower-in graph to the S/N versusmixer level graph, we can also plotS/D versus mixer level. Figure 2–9shows distortion relative to mixerlevel (or inverted signal-to-distor-tion) in dBc units versus the inputpower at the mixer for second andthird order distortion.

For second order distortion the slopeof the S/D versus mixer level curve is+1, signifying that for every 1 dBincrease in power at the mixer, theS/D decreases 1 dB. For third orderthe slope of this curve is +2; forevery 1 dB increase in the two fundamental tone power levels, the S/D decreases by 2 dB. For thesecond harmonic curve the 0 dBc

intersection point on the y-axis corresponds to the SHI value in dBmon the x-axis. In the example shownin Figure 2–9, the SHI performanceof the spectrum analyzer is +45 dBm.For the third order curve the 0 dBcintersection point on the y-axis corresponds to the TOI value in dBm. In this example, the TOI of thespectrum analyzer is +20 dBm.

Figure 2–7Pout vs. Pin Curves for Distortion

Pin(dBm)

Pout(dBm)

S/D

1N

Output InterceptPoint (dBm)

Fundamental Tone

DistortionProduct

Figure 2–8Second and Third Order Distortion Spectrum

Second Order Third Order

P P

f0 2f0 2f1-f2 f1 f2 2f2-f1

Figure 2–9Signal to Distortion versus Power at the Input Mixer

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0

Mixer Level (dBm)

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2

Second Order

17

The Dynamic Range Chart

Combining the signal-to-noise andthe signal-to-distortion versus mixerlevel curves into the same graphyields the dynamic range chart asshown in Figure 2–10.

The dynamic range chart allows avisual means of determining themaximum dynamic range and theoptimum power at the first mixerwhere the maximum dynamic rangeoccurs. Using simple geometry on thecurves that make up the dynamicrange chart yields closed form equations for maximum dynamicrange and optimum mixer level.

Second Harmonic Distortion:

Maximum Dynamic Range = 1/2 SHI - DANL] dB (2–1)

Optimum Mixer Level = 1/2 [SHI + DANL ] dBm (2–2)

Third Order Intermodulation Distortion:

Maximum Dynamic Range = 2/3 [TOI - DANL] dB (2–3)

Optimum Mixer Level = 1/3 [2 x TOI + DANL] dBm (2–4)

For example, the values in Figure 2–10 are:

DANL = -145 dBm in 10 Hz RBW

TOI = +20 dBm

SHI = +45 dBm

Second Order Distortion in 10 Hz RBW:

Maximum Dynamic Range = 1/2 [45 - (-145)] = 95 dB

Optimum Mixer Level = 1/2 [45 - 145] = -50 dBm

Third Order Intermodulation Distortion in 10 Hz RBW:

Maximum Dynamic Range = 2/3 [20 - (-145)] = 110 dB

Optimum Mixer Level = 1/3 [2 x 20 - 145 ] = -35 dBm

Figure 2–10Dynamic Range Chart

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Second OrderDistortion

Third OrderDistortion

DANL10 Hz RBW

DANL1 Hz RBW

18

Adding Phase Noise to the Dynamic Range Chart

Phase noise, due to either the DUT or the spectrum analyzer, can hidedistortion products, as demonstratedin Figure 2–11a. In this case, thethird order intermodulation productsfall under the phase noise skirt, pre-venting them from being measured.

Like broadband noise, the displayedphase noise floor also changes levelwith RBW setting, as shown in Figure2–11b. The spectrum analyzer phasenoise at a particular frequency offsetis specified in dB relative to carrierin a 1 Hz noise bandwidth. This 1 Hznoise bandwidth assumes a phasenoise measurement on a power scalewith the over-response due to theratio of the equivalent noise band-width to the -3 dB bandwidth of theRBW filter removed. The relationshipof displayed broadband noise versusaveraging scale depicted in Figure 2–4 also applies to phase noise.Therefore, if phase noise measure-ments are to be made using the Log-Power (Video) scale, which is the preferred display mode for CWsignals, the phase noise value needsto be offset by -2.26 dBc from itsspecified level. When using the Power (RMS) averaging scale, thephase noise is offset by +0.25 dBcfrom its specified value.

Figure 2–12 demonstrates how phase noise appears on the dynamicrange chart. Note that phase at oneoffset frequency is presented. Forthis case the specified phase noise at the particular offset frequency ofinterest is -110 dBc/Hz. Using theLog-Power (Video) averaging scale,the phase noise appears to be -110 minus 2.26 dB or -112.26 dBcnormalized to the 1 Hz RBW. Whenusing the Power display scale, thephase noise appears to be 2.51 dBhigher than with the Log-Power display scale, or -109.75 dBc normalized to the 1 Hz RBW.

Referring to Figure 2–6 where external noise is shown adding to the broadband noise of the spectrumanalyzer, when two uncorrelatednoise signals combine, the resultingtotal power is computed as shown inequation 2–5.

The phase noise and the broadbandnoise, being uncorrelated, also followequation 2–5 when they combine. So,at the intersection of the phase noiseand the DANL curves, assuming bothare shown on the same display scalesetting, the resulting total noisepower is 3 dB higher than the twoindividual contributors.

Figure 2–11aPhase Noise Limitations on Dynamic Range

RBW2

RBW1

Phase Noisemasks thedistortionproducts

f1 f2

PhaseNoise

f0 foffset

Figure 2–11bPhase Noise as a function of RBW

Figure 2–12Phase Noise Represented on the Dynamic Range Chart

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DANL1 Hz RBW

Third OrderDistortion

Phase Noise(Power Scale)

Phase Noise(Log Power Scale)

Total Power = 10 x Log (10^(P1/10) + 10^(P2/10)) [dBm] (2-5)

where P1 and P2 are the individual power terms in dBm

19

Noise Adding to the Distortion Product

This section concerns the measure-ment of CW-type distortion productsmeasured near the noise floor whenusing the Log-Power averaging scale.An overview is given here, and references [4] and [6] explain thissubject in greater detail.

When a CW tone amplitude is closeto the noise floor, the signal andnoise add together as shown in Figure 2–13.

The apparent signal is the signal andnoise added together that the userwould see displayed on the spectrumanalyzer. Reference [4] gives this thename S+N for signal-plus-noise. Thedisplayed signal-to-noise ratio is theapparent signal peak to the broad-band noise (noise level with the CW tone removed). The term, actualsignal-to-noise ratio, means the ratioof the true CW tone peak amplitudeto the broadband noise level. Theactual signal-to-noise ratio is some-what lower than the displayed signal-to-noise ratio. Figure 2–14 showsgraphically the signal-to-noise ratioerror versus the displayed signal-to-noise ratio. The difference betweenthe displayed S/N and the actual S/N is the signal-to-noise ratio error.This graph pertains to CW distortionmeasurements using the Log-Power(Video) averaging scale, not thePower (RMS) averaging scale

To use the graph shown in Figure 2–14, locate the displayed signal-to-noise ratio on the x-axis, then readoff the error on the y-axis. Subtractthis error value from the displayedsignal amplitude to compute the trueCW signal amplitude. For example,suppose the displayed S/N is 3 dB for a displayed signal measuring -100 dBm. The corresponding error is 1.1 dB, which means that the true signal amplitude is -100 dBmminus the 1.1 dB error term, or

-101.1 dBm. One key observation is that when the CW tone amplitudeis equal to the broadband noise level, that is, 0 dB actual S/N, thedisplayed S/N is approximately 2.1 dB. For an error in the displayedS/N to be less than 1 dB, the dis-played S/N should be at least 3.3 dB.

When making distortion measure-ments on CW-type signals, the information in Figure 2–14 can betransferred to the dynamic rangechart. Figures 2–15 and 2–16 showhow the second and third orderdynamic range curves change as a result of noise adding to the distortion products.

Figure 2–13CW Tone Plus Noise

Actual S/N

DisplayedS/N

CW Signal

Apparent Signal

Figure 2–14S/N error versus displayed Actual S/N for CW Signals using a Log-Power Display

0.001.002.003.004.005.006.007.008.009.00

10.00

Displayed S/N (dB)0 1 2 3 4 5 6

S/N

Err

or (d

B)

20

Below the solid, heavy lines repre-senting distortion-plus-noise, the CW distortion products are not dis-cernable. This translates to a reduc-tion in the spectrum analyzer’smaximum dynamic range. Both thesecond and third order maximumdynamic ranges reduce by approxi-mately 2.1 dB when the effect ofnoise is added to the CW distortionproducts displayed on the Log-Powerscale. The corresponding optimummixer level is offset by +0.5 dB forsecond harmonic distortion and by -0.36 dB for third order intermodula-tion distortion. All of these values are relative to the ideal maximumdynamic ranges and optimum mixerlevels given by equations 2–1 through 2–4.

Figures 2–15 and 2–16 show thereduced dynamic range assuming no steps are taken to remove thenear-noise measurement errors. TheS/N Error versus Displayed S/Ngraph (Figure 2–14) indicates thatwhite Gaussian noise adding to a CW signals results in a predictableamount of error, which is differentthan an uncertainty. To regain thelost 2.1 dB of dynamic range, onecould measure the displayed S/N ofthe near-noise distortion productand, using the information in Figure2–14, remove the corresponding error value.

Figure 2–15Dynamic Range Chart with Noise Added to the CW Second Order Distortion Products

Figure 2–16Dynamic Range Chart with Noise Added to the CW Third Order Distortion Products

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DANL

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21

SA Distortion Adding to DUT Distortion

When the amplitudes of the distor-tion products of the DUT fall close to the amplitudes of the internallygenerated distortion products of thespectrum analyzer, an uncertainty inthe displayed distortion amplituderesults. The DUT distortion productsfall at the same frequencies as the SA generated distortion productssuch that they add as voltages withunknown phases. The error uncer-tainty due to the addition of twocoherent CW tones is bounded by the values shown in equation 2–6.

Uncertainty = 20 x Log (1 ±10d/20) dB (2–6)

where ‘d’ is the relative amplitudes of the two tones in dB (a negative number).

+ is the case where the DUT and SA distortion products add in-phase.

- is the case where the DUT and SA distortionproducts add 180 degrees out of phase.

Equation 2–6 is shown graphically inFigure 2–17. The amplitude errorcould vary anywhere between thetwo curves.

For the situation when the internallygenerated distortion product is equalin amplitude to the external distor-tion product, and they are in-phase,the resulting displayed amplitudecould be 6 dB higher than the ampli-tudes of the individual contributors.For individual contributors of equalamplitude that are 180 degrees out ofphase, these signals would complete-ly cancel, resulting in no displayeddistortion product.

Equation 2–6 and Figure 2–17 applywithout qualification to harmonicdistortion measurements. For two-tone intermodulation distortionmeasurements there is an exception.For most distortion measurements,the input power at the spectrum analyzer’s first mixer is far below itsgain compression level, making thespectrum analyzer a weakly-nonlin-ear device. Reference [5] makes thecase that for cascaded stages thatexhibit a weak nonlinearity, theintermodulation distortion compo-nents add in-phase only. Tests performed on the PSA series confirmthis conclusion if the tone spacing isno greater than 1 MHz. Thus for twotone intermodulation measurementswith tone spacing ≤1MHz, the dis-played amplitude error due to twodistortion products adding is givenby equation 2–7.

Amplitude error = 20 x Log (1 + 10d/20) dB (2–7)

where ‘d’ is the relative amplitudes in dB between the internally generated distortion and the external DUT generated distortion amplitudes (a negative number).

To ensure that measurement errordue to the combination of DUT andSA distortion products falls below agiven threshold, the optimum mixerrequires readjustment. Unfortunately,this readjustment has an adverseeffect on the maximum dynamicrange available from the spectrumanalyzer. The following procedurehelps compute the readjusted dynam-ic range and the resulting optimummixer level needed to ensure that thedistortion measurement uncertaintyfalls below a desired error level.

Start with a desired amount of maximum measurement error and,using the chart in Figure 2–17, readoff the relative amplitudes corre-sponding to the desired threshold.For harmonic measurements or two-tone intermodulation measurementswhose tone separations are >1 MHz,use the lower curve as it gives themost conservative result. For IMDmeasurements with tone separations≤1 MHz, use the upper curve inFigure 2–16. Or instead, equations2–6 and 2–7 could be solved for ‘d’,which is the relative amplitude valuebetween external and internal distortion product amplitudes. Therelative amplitude value is then usedto determine how to offset the distor-tion curves in the dynamic rangechart. Either offset the distortion

Figure 2–17Amplitude Uncertainty due to Two Coherent CW Tone Adding Together

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Am

plitu

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22

curves up by -d dB or offset the inter-cept point by d/(Intercept order -1).For example, for second order distor-tion, the effective SHI is offset by ‘d’and for third order intermodulationthe effective TOI is offset by 1/2 d. Byoffsetting the intercept points,instead of offsetting the curves onthe dynamic range chart, equations2–1 through 2–4 can be used to cal-culate the optimum mixer levels andthe maximum dynamic ranges.

Here is an example of how to use the information presented on nearnoise and near distortion measure-ments. Consider the situation whereRBW = 10 Hz, DANL = -155 dBm/Hzand SA TOI = +20 dBm. The objectiveis to compute the modified maximumthird order intermodulation dynamicrange and the optimum mixer level.Using equations 2–3 and 2–4, we ear-lier computed the ideal case maxi-mum dynamic range as being 110 dBand the corresponding optimummixer level as being -35 dBm.Suppose the error uncertainty due toDUT and SA distortion addition is tobe less than 1 dB. Solve equation 2–7for d:

d = 20 x Log(10 dB Error/20 - 1 ) dB

d = 20 x Log(10 1/20 - 1) dB

d = -18.3 dB

The SA’s effective TOI is computed as SA TOI - d/2 or +20 - 18.3/2 =+10.85 dBm. Figure 2–18 shows thatthe distortion curve has been shiftedup by 18.3 dB, corresponding to aneffective loss of 9.2 dB in SA TOI. An intermediate maximum dynamicrange and optimum mixer level canbe computed using the new effectiveTOI value:

Thus in order to drive down measurement error, the loss indynamic range is 6.1 dB and the optimum mixer level is shifted downin power by 6.1 dB.

But we are not done yet. Noise addsto the distortion product, contribut-ing to a dynamic range loss of 2.1 dBand an optimum mixer level offset of -0.36 dB. If no steps are taken toremove this noise error, a final valuefor maximum dynamic range equals101.8 dB with a corresponding opti-mum mixer level of -41.5 dBm. Thevalid measurement region is the areaof the dynamic range chart wheredistortion interference error is belowthe desired error value and the distortion product is discernableabove the noise floor. The valid meas-urement region for this example isshown in Figure 2–17. Keep in mindthat the error due to near noise addi-tion is still present. This error can beremoved with the aid of the graph inFigure 2–14, resulting in an improve-ment of 2.1 dB in dynamic range.

One final note, we mentioned thatwhen measuring TOI with tone spacing ≤1MHz, the DUT distortionproducts add in-phase with the distortion products generated by the PSA series analyzers, resulting in what looks like an error term. This situation seems very similar tothe near-noise case, in which theerror term can be subtracted fromthe displayed amplitude of the CWsignal. Theoretically, the TOI productaddition is an error term, and theoretically, this error could be subtracted out to regain lost dynamicrange. The difficulty with TOI is withthe inability to accurately measurethe TOI of the spectrum analyzer.Spectrum analyzer TOI fluctuateswith tune frequency due to constant-ly changing match, as seen by thefirst mixer. To accurately measure SATOI in the hopes of removing theerror term, the same input matchwould be required for both the SATOI measurement as well as the finalDUT measurement. Removing theTOI related error term is not impos-sible, but for practical reasons it isbest to consider the error term as anuncertainty that cannot be accuratelyremoved from the measurement.

Figure 2–18Dynamic Range Chart Showing Valid Measurement Region for <1 dB Measurement Uncertainty for Third Order IMD

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-95-90-85-80-75-70

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Valid MeasurementRange

9.2 dB

18.3 dB

Third Order Distortion in 10 Hz RBW:

Maximum Dynamic Range = 2/3 [10.85 - (-145)] = 103.9 dB

Optimum Mixer Level = 1/3 [2 x 10.85 - 145 ] = -41.1 dBm

23

In Part II we concentrated on the distortion measurements of CW sig-nals containing no modulation. InPart III, we turn our attention to out-of-channel leakage measure-ments, such as adjacent channelpower (ACP) and alternate channelpower on digitally modulated signals.Optimizing the mixer level of thespectrum analyzer is equally asimportant for these types of distor-tion measurements as it is for distor-tion measurements on CW signals.However, setting the mixer level fordigitally modulated signals requiresdifferent considerations than whatwe will discuss here in Part III.

Reference [4] states that under conditions where the measurementbandwidth is much narrower thanthe modulation bandwidth (BWm) of a digitally modulated signal, thesignal exhibits noise-like statistics inits amplitude distribution. In mostpractical cases, the spectrum analyz-er RBW is much narrower than BWmand satisfies the above condition. Forexample, when measuring adjacentchannel power ratio (ACPR) on anIS-95 CDMA signal with a 1.23 MHzBWm, the specified measurementRBW is 30 kHz. Why is the fact thatthe signal exhibits noise-like behaviorimportant? First, unlike with CWtones, greater care must be exercisedin selecting the display mode, boththe display detector and the averag-ing scale, when measuring digitallymodulated signals. Second, both the

displayed main channel power andthe displayed spectral regrowth (thatis, distortion products) are a functionof the RBW setting of the spectrumanalyzer. Finally, the manner inwhich the digitally modulated sig-nal’s noise-like distortion compo-nents and broadband noise addtogether behaves differently thanwhen the distortion is CW. Thesepoints will all be discussed in greater detail in the following.

Choice of Averaging Scale andDisplay Detector

One of the first considerations whenmeasuring digitally modulated sig-nals is the choice of the averagingscale (Log-Power vs. Power scale). In order for the digitally modulatedsignal to behave exactly like noise, itsamplitude versus time characteristicmust possess a Gaussian ProbabilityDensity Function (PDF). If theGaussian PDF is assumed then thedisplayed main channel power spec-tral density (PSD) follows the samerules as white noise, where a 2.51 dBdisplayed amplitude differenceoccurs between measurements on the Log-Power (Video) scale and thePower (RMS) scale. However, if thePDF of the digitally modulated signalis not known exactly, which is usual-ly the case, then the 2.51 dB offsetdoes not necessarily hold true. ThePower (RMS) averaging scale must beused for digitally modulated signalsas this scale avoids the uncertaintiesincurred when computing the amplitudes on the Log-Power (Video) averaging scale.

The Peak detector and the Normaldetector should not be used formeasurements on digitally modulatedsignals. These detectors report thepeak amplitude excursions that occurbetween display measurement cells,thus overemphasizing the amplitudepeaks of noise and noise-like signals.The Sample detector, by contrast,reports the signal amplitude thatoccurs at the display measurementcell (sometimes referred to as display“bucket”), which does not peak biasthe measurement. The PSA seriesanalyzer has another detector, calledthe Average detector, which reportsthe average of the data across eachdisplay bucket. When using theAverage detector, the longer thesweep time, the greater the amountof averaging. Either the Sampledetector or the Average detectorshould be used for measurements ondigitally modulated signals.

The Video Bandwidth (VBW) filterreduces the amplitude fluctuations ofthe displayed signals and, dependingon the spectrum analyzer, is placedeither before or after the linear tologarithmic conversion process in theintermediate frequency (IF) chain.One new feature in the PSA seriesanalyzer not found in previous gener-ation Agilent spectrum analyzers isthat the VBW filter does not affectthe power summation performedwhen using the Power (RMS) scale.When using spectrum analyzers inwhich the VBW filter is placed afterthe linear to logarithmic conversionprocess, the user is cautioned to keepthe VBW ≥3 x RBW for the measure-ment of signals that are random innature. This ensures that averagingoccurs on the Power scale and avoidsthe offsets that occur on the logscale. When using the Power (RMS)averaging scale, the PSA series ana-lyzer allows an arbitrarily narrowVBW setting without the worry thatthe measured amplitude will containlog scale uncertainties. This allowsmore flexibility to use the VBW toreduce the measured amplitude vari-ance of the digitally modulated signal.

Part III: Distortion Measurements on Digitally Modulated Signals

24

Maximizing Spectrum AnalyzerDynamic Range

Three mechanisms inherent to thespectrum analyzer limit its dynamicrange when measuring out of channeldistortion on digitally modulated signals. These mechanisms are: thespectrum analyzer noise floor, thespectrum analyzer phase noise andthe spectrum analyzer intermodula-tion distortion. The noise floor isalways a limit as it is with CW distor-tion measurements. Phase noise andintermodulation, however, are limitsthat depend on such parameters aschannel separation and modulationbandwidth. In other words, in themajority of cases, depending on themodulation format, phase noise orintermodulation will limit thedynamic range of the spectrum analyzer.

Signal-to-Noise of DigitallyModulated Signals

The spectrum analyzer displays themain channel PSD at a level lower by 10 x Log(BWm) than the amplitudeof a CW tone with equal power.Therefore, the displayed S/N of thedigitally modulated signal is reducedby 10 x Log(BWm). Figure 3–1a showsthis effect. Furthermore, the dis-played amplitude and displayedbroadband noise are functions of theRBW setting which, unlike the CWcase, renders the S/N independent of the RBW. See Figure 3–1b.

The displayed main channel PSD is Pch - 10 x Log(BWm/RBW) + 10 x Log(NBW/RBW). Pch is the total signal power and NBW is the noise power bandwidth of theRBW filter used for the measure-ment. For the PSA series analyzer NBW/RBW is 1.06 or 10 x (NBW/RBW) = 0.25 dB. The fol-lowing is an example for computingthe displayed amplitude of a -10 dBm IS-95 CDMA signal measured with a30 kHz RBW filter setting:

Broadband noise on the Power (RMS)averaging scale appears at the speci-fied DANL + 10 x Log(RBW) + 2.51 +the Input Attenuator setting. So for a spectrum analyzer with a DANL of -155 dBm/Hz measured with a 30 kHz RBW filter with 10 dB ofInput Attenuation, the displayednoise level on the Power Scale is: -155 + 10 x Log(30 kHz) + 2.51 + 10 = -97.7 dBm. The signal-to-noise ratiocomputes to 71.8 dB.

For purposes of plotting the S/N onthe dynamic range chart, it is best to

think of the channel power in termsof the power at the input mixer ofthe spectrum analyzer; call thispower MLch. MLch = Pch - Input Attenuation. Thus, S/N as a function of power at the first mixer is given by equation 2–8.

Equation 2–8 makes it evident thatfor digitally modulated signals, theS/N is a function of the modulationbandwidth. Wider bandwidths leadto a lower S/N. Figure 3–2 shows the dynamic range chart with theS/N plotted against the input powerat the first mixer for an IS-95 CDMAmodulated signal. The S/N curve of the modulated signal is offset from the DANL curve by 10 x Log(BWm) - 2.26.

Figure 3–1aDisplayed Amplitude of a CW Tone and a Digitally Modulated Signal with Equal Powers

Figure 3–1bDisplayed Amplitude of Both Digitally Modulated Signal and DANL varies with RBW

PSD in 1 Hz BW

CW Tone

10*Log(BWm)

RBW1

RBW2

S/N1S/N2

Figure 3–2S/N vs. Mixer Level for Digitally Modulated Signals

-120-110-100

-90-80-70-60-50-40-30-20-10

0

-100 -90 -80 -70 -60 -50 -40 -30 -20 -10

Mixer Level (dBm)

DA

NL

Rel

ativ

e to

Mix

er

Leve

l (dB

c) a

nd -S

/N (d

B)

-S/N of aModulatedSignal

DANL in1 Hz RBW

10Log[BWm] + 2.26 dB

Average Displayed Amplitude = Pch - 10 x Log(BWm/RBW) +10 x Log(NBW/RBW)

Average Displayed Amplitude = -10 - 10 x Log(1.2288 MHz/30 kHz) + 10 x Log(1.06)

Average Displayed Amplitude = -25.9 dBm

S/N as a Function of Power at the first mixer

S/N = MLch -10 x Log(BWm) +10 x Log(NBW/RBW) - DANL -2.51 [dB] (2–8)

S/N = MLch - DANL -10 x Log(BWm) - 2.26 [dB]

25

Spectral Regrowth Due to SpectrumAnalyzer Intermodulation Distortion

Third, and in some cases fifth orderintermodulation distortion of thespectrum analyzer create distortionproducts that fall outside of the mainchannel. Unlike power amplifiers,and especially power amplifiers with feed-forward architectures, thespectral regrowth internal to thespectrum analyzer can easily beapproximated with simple algebra.The analysis of spectral regrowthgenerated by spectrum analyzerintermodulation distortion relies on the premise that when the powerat the input mixer is far below gaincompression power level (by at least15 dB), the spectrum analyzerbehaves as a weakly-nonlineardevice. Such a device has a voltage-in to voltage-out transferfunction given by the power series:Vo = a1Vi + a2Vi

2 + a3Vi3 + . . . + anVi

n.For spectrum analyzer front ends,the power series does an excellentjob of predicting the frequencies ofthe intermodulation distortion termsand their relative amplitudes. As the input power approaches the spectrum analyzer gain compressionlevel, the power series approximationno longer hold true, indicating thelimitation of this equation to relatively low power levels.

Spectral regrowth modeling for thespectrum analyzer front end beginsby breaking up the main channel intoa series of equal spaced divisions inthe frequency domain. Each divisionis represented by a CW tone whosepower is the same as the total powerin that particular division. Figure 3–3a depicts this interpretation of

the spectral regrowth model. EachCW tone representing a segment ofthe main channel interacts with all of the other CW tones creating inter-modulation distortion products.Intermodulation products resultingfrom different tones start combiningwith each other, with the most prod-ucts adding at the edges of the mainchannel. It has been determinedempirically that the individual distortion products add as voltagesusing the 20 Log( ) relationship. Inmost cases a log amplitude scale is used that displays the spectral

regrowth falling off on a curve asshown in Figure 3–3b. For third order distortion, the upper and lowerspectral regrowth bandwidths areonly as wide as the modulation bandwidth of the digitally modulatedsignal. The third order distortionextends out in frequency away fromthe main channel by one modulationbandwidth and fifth order extends by two modulation bandwidths.Third order distortion dominates in adjacent channel measurements.For alternate channel measurements,fifth order distortion becomes a concern.

Figure 3–3aSpectral Regrowth Generated Within the Spectrum Analyzer can be Modeled by Treating the Digital Signal as a Series of CW Tones

Figure 3–3bSpectral Regrowth as Displayed on the Log Scale 3rd Order

Distortion5th OrderDistortion

BWm BWm BWm BWm BWm

LowerAlternateChannel

LowerAdjacentChannel

MainChannel

UpperAdjacentChannel

UpperAlternateChannel

26

Spectral regrowth due to intermodu-lation distortion is noise-like, imply-ing that the main signal power tospectral regrowth power ratio isindependent of the spectrum analyz-er RBW setting. In other words, thedisplayed main channel PSD and thespectral regrowth PSD both vary bythe 10 x Log(RBW) relation. Anotherimplication is that when the distor-tion approaches the system noisefloor, the distortion and noise add as uncorrelated powers using therelationship:

Calculating the level of third ordergenerated spectral regrowth dependson the frequency offset from themain channel center frequency and the peak-to-average-ratio of thesignal. A further complication iswhether or not the adjacent channelmeasurement is made at fixed offsetfrequencies, as with IS-95 CDMA, orthe measurement, is an integratedpower measurement as with W-CDMA. For measurements at fixed offset frequencies, Figure 3–4can be used to estimate the thirdorder spectral regrowth for the PSAseries analyzer. Note that theseresults cannot be generalized forother spectrum analyzers. Shown isthe TOI offset from the two-tone TOIperformance of the spectrum analyz-er versus the frequency offset fromthe center of the main channel forthree different peak-to-averageratios.

So at an offset of 885 kHz from themain channel center frequency, thethird order spectral regrowth gener-ated within the spectrum analyzerwould be 66 dB below the main channel average PSD.

For measurements that rely on anintegrated power measurementacross the adjacent channel, predicting the level of spectralregrowth due to third order distortion depends on modulationbandwidth and channel spacing.Channel spacing is importantbecause it determines the unusedfrequency band between channels,where the spectral regrowth can beignored. W-CDMA is one importantclass of digitally modulated signalsthat use an integrated measurement.

Figure 3–4Effective TOI of Digitally Modulated Signal versus Frequency Offset from Main Channel

20

15

10

5

0

-50.5 0.75 1 1.25

Foffset / BWm

TOI O

ffse

t (dB

)

Pk/Avg (dB)

5.5

11

16

Total Power = 10 x Log(10 Noise Power / 10 +10 Distortion Power / 10 ) dBm (3–1)

where Noise Power is the system noise in dBm and Distortion Power is the intermod-generated spectral regrowth in dBm.

The best way to show how to useFigure 3–4 is through illustration.Suppose the ACPR is to be calculatedat an offset of 885 kHz for an IS-95CDMA signal whose modulationbandwidth is 1.23 MHz and peak-to-average ratio is 11 dB. TheFoffset/BWm ratio = .885/1.23 = 0.72.From Figure 3–4, the TOI offset atFoffset/BWm of 0.72 is +3 dB.Suppose the spectrum analyzer has atwo tone TOI of +20 dBm, the effec-tive TOI at 885 kHz offset would be20 dBm + 3 dB or +23 dBm. If thepower at the spectrum analyzer’sinput mixer is -10 dBm, the spectralregrowth can be calculated by manip-ulating the equation: TOI = P + ∆/2.In this case, ∆ is the dB difference ofthe main channel PSD to the thirdorder spectral regrowth. For theexample in this discussion, thispower difference is computed as

∆ = 2*(TOI - P)

∆ = 2 x (23 - (-10))

∆ = 66 dB

27

For W-CDMA with 3.84 MHz symbolrate and a 5 MHz channel spacing,the effective TOI offset is given inTable 3–1.

This table shows how to calculate theintegrated adjacent channel powerdue to third order distortion. Forexample, suppose the W-CDMA signalhas a peak-to-average ratio of 11 dBand the spectrum analyzer has a two-tone TOI of +20 dBm. The effec-tive TOI with a W-CDMA modulatedsignal is 20 dBm + 4 dB or +24 dBm.Manipulating the math as in the pre-vious example, the spectral regrowthin the adjacent channel, assuming -10 dBm power at the input mixer, is:

∆ = 2 x (24 - (-10))

∆ = 68 dB

That is, the power integrated acrossthe adjacent channel is 68 dB belowthe power integrated across the mainchannel.

Phase Noise Contribution

Just as internally generated phasenoise can limit the dynamic rangewhen measuring CW tones, phasenoise also places a limitation on thedynamic range when measuring digi-tally modulated signals. The modelused to calculate intermodulationdistortion of a digitally modulatedsignal also proves useful in showinghow the phase noise adds to thespectral regrowth in the adjacentchannel. In Figure 3–5, the mainchannel is divided into segments of equal frequency width with a CW tone representing the power in each segment.

Associated with each CW tone is aphase noise skirt. The phase noisepower contributed by individualtones at any given frequency add in an uncorrelated fashion (that is,the 10 Log( ) relationship). The clos-er the frequency offset is to the mainchannel, the greater the summationof the phase noise power. The endresult is a reduction in the phase

noise dynamic range of roughly 10 x Log(BWm). For example, suppose at 100 kHz offset, the spectrum analyzer’s specified phase noise is -118 dBc/Hz. With amodulation bandwidth of 1.23 MHz,the phase noise power at 100 kHzaway from the edge of the main channel relative to the PSD of the main channel would be -118 + 10 x Log(1.23 x 106) +0.25 = -56.85 dB (the 0.25 dB term is the 10 x Log(NBW/RBW) discussed earli-er). This relative phase noise poweris not exact, because at any given frequency outside of the main chan-nel, the phase noise derives fromcontributors that span the width ofthe main channel. Therefore, use the10 x Log(BWm) as a first order guideand that is probably within a coupledB of the true phase noise. From thedepiction in Figure 3–5, for narrowlyspaced channels, the phase noise canbe a serious limitation for ACPR measurements.

Figure 3–5Phase Noise Contribution of a Digitally Modulated Signal

Individual Phase Noises add as uncorrelatedpowers

Table 3–1. Effective TOI Offset for W-CDMA

Pk/Avg (dB) TOI Offset (dB)

5.5 7.5

11 4

14.5 2

28

Dynamic Range Chart for DigitallyModulated Signals

We now have all the ingredients tocreate the dynamic range chart whenmaking distortion measurements on digitally modulated signals.Remember, the goal is to determinethe optimum input power at themixer, which is a natural outcome of the dynamic range chart.Unfortunately, the dynamic rangechart for digitally modulated signalsis highly format dependent.Parameters such as modulationbandwidth and channel spacing—whether or not the ACPR measure-ment is at fixed offset frequencies or is an integrated power measure-ment—and the peak-to-average ratioof the main channel signal all affectthe formation of the dynamic rangechart. While it is impossible to generalize the dynamic range chart,we can get a feel for the considera-tions involved in constructing a suit-able dynamic range chart by showinga couple of specific examples.

Figure 3–6 shows the dynamic rangechart for IS-95 CDMA with an 11 dBpeak-to-average ratio measured at asingle offset frequency of 885 kHz.The parameters used to constructthis chart are: modulation bandwidth= 1.23 MHz, DANL = -155 dBm/Hz,TOI = 20 dBm + 3 dB offset toaccount for the 11 dB peak-to-aver-age ratio, Fifth Order Intercept = +12 dBm, and phase noise = -132 dBc/Hz at an offset of 270 kHz.

The frequency offset value used toapproximate the phase noise resultsfrom the following computation: thehalf-bandwidth of the measurementchannel is (1.23 MHz / 2), or 615 kHz. At a measurement frequen-cy 885 kHz away from the center ofthe main channel, the frequency difference between the measurementfrequency and the edge of the mainchannel is 885 kHz minus 615 kHz, or270 kHz.

A few observations can be maderegarding Figure 3–6. First, becausethe measurement frequency is only270 kHz away from the edge of themain channel, phase noise is the limiting mechanism for dynamicrange. Fifth order intermodulationdistortion is negligible. Third orderintermodulation distortion andbroadband noise are minor contribu-tors in the region of maximumdynamic range. The optimum mixerlevel is nearly 20 dB higher than the mixer level for the two-tone intermodulation distortion shown in Figure 2–10.

Figure 3–6Dynamic Range Chart for IS-95 CDMA at 885 kHz Offset

-40 -35 -30 -25 -20 -15 -10 -5 0

-50

-55

-60

-65

-70

-75

-80

-85

Mixer Level (dBm)

Spec

tral

Reg

row

th R

elat

ive

to M

ain

Chan

nel P

ower

(dB

)

Noise

PhaseNoise 3rd

Order

5th Order

Figure 3–7Dynamic Range Chart for W-CDMA

-40 -35 -30 -25 -20 -15 -10 -5 0

-55

-60

-65

-70

-75

-80

-85

-90

Mixer Level (dBm)

Spec

tral

Reg

row

th R

elat

ive

to M

ain

Chan

nel P

ower

(dB

)

Noise

PhaseNoise

3rd Order

5th Order

29

Figure 3–7 shows the dynamic range chart for W-CDMA. Again, thepeak-to-average ratio for the signal is11 dB. The measurement uses inte-grated power across both the mainand the adjacent channel as opposedto the single frequency measurementfor IS-95 CDMA. The parametersused to construct this chart are: symbol rate = 3.84 MHz, channel spacing = 5 MHz, DANL = -155 dBm/Hz, TOI = 21 dBm + 4 dBoffset to account for the 11 dB peak-to-average ratio, Fifth OrderIntercept = +12 dBm, and phasenoise = -150 dBc/Hz at an offset of1.17 MHz. The frequency offset usedto estimate the phase noise contribu-tion results from the fact that the frequency difference between theedge of the main channel and theedge of the adjacent channel is 1.17 MHz.

Because of the 1.17 MHz spacingbetween channel edges, the phasenoise is considerably lower than withthe IS-95 CDMA example. In fact,phase noise is not a significant contributor at all. In the region ofmaximum dynamic range, fifth orderintermodulation distortion is alsonot a significant contributor. Thirdorder intermodulation distortion

spectral regrowth and broadbandnoise are the only limitations in theregion of highest dynamic range.Notice that the range of mixer levelswhere the dynamic range is maxi-mized is narrower than for the IS-95CDMA case. Optimum mixer level isabout -13 dBm.

Figure 3–7 can also be used to interpret the optimum mixer level for the alternate channel powermeasurement. In the alternate chan-nel, as depicted in Figure 3–3b, thethird order distortion products donot exist, leaving only the fifth orderdistortion contributing to intermodu-lation generated spectral regrowth.For the PSA series, phase noisepower stays at a near constant valuebetween 1 and 6 MHz offsets. Thusthe phase noise curve in Figure 3–7used for the adjacent channel applieswith little error for the alternatechannel measurement. For this measurement the optimum mixerlevel is about -5 dBm.

30

Measurement Error Due to SASpectral Regrowth Adding to DUTSpectral Regrowth

For CW distortion, we demonstratedthat to reduce the measurementerror, the DUT and spectrum analyz-er distortion product levels must beoffset by an amount dictated by thedesired measurement error. For digitally modulated signals, a similarconsideration must be taken intoaccount. In the case of digitally mod-ulated signals, the level of intermod-ulation generated spectral regrowthof the spectrum analyzer must bebelow the DUT spectral regrowth bya calculated amount.

When the amplitude of the DUT’sspectral regrowth falls near the spec-tral regrowth generated within thespectrum analyzer, the two add in amanner dependent on the character-istics of the modulation format. Forextremely low peak-to-average ratios,the distortion products add, approxi-mately, as uncorrelated powers. Asthe peak-to-average ratio increases,the spectral regrowth levels of theDUT and the SA add in a fashion

consistent with the power addition ofcorrelated signals. The conservativeapproach would be to use equation 2–7 to estimate differences in DUT and SA spectral regrowth levels as afunction of the desired amount ofmeasurement uncertainty. Once thedesired spectral regrowth level differ-ence is calculated, the informationcan be applied to the dynamic rangecharts to estimate the measurementdynamic range and the correspon-ding mixer level. Using the examplein Part II where less than 1 dB of distortion related error was desired,we apply the same +18.3 dB y-axisoffsets to the third and fifth ordercurves in the dynamic range chartsfor digitally modulated signals. Forthe IS-95 example where phase noisemostly limits the ACPR measure-ment, the effect of offsetting thethird order curve is not very signifi-cant to the overall ACPR dynamicrange. But for the W-CDMA example,where S/N and third order distortionlimit the ACPR dynamic range, offsetting the third order curve hasthe same effect on dynamic range aswith the CW example where dynamicrange is reduced by 6.1 dB and theoptimum mixer level is shifted 9.2 dB lower.

31

In Parts II and III we demonstratedthat in order to maximize the dynam-ic range of the spectrum analyzer,the power at the input mixer must beoptimized. Now in Part IV we begindiscussing some block diagram char-acteristics specific to the PSA seriesthat may prove useful in achievingthe optimum mixer level.

Input Attenuator Resolution

Unless the mixer level can be optimally set, the full dynamic rangeperformance of the spectrum analyz-er cannot be achieved. Controllingthe Input Attenuator provides aneasy, and a very accurate, means ofcontrolling the power at the inputmixer. If the step resolution of theInput Attenuator is too coarse, thensetting the optimum mixer level mayprove to be very difficult. Figure 4–1shows the limitation of the achiev-able dynamic range due to the resolution of the Input Attenuator.

If the Input Attenuator is adjustedtoo high in value, broadband spectrum analyzer noise limits theachievable dynamic range and if theInput Attenuator is adjusted too lowin value, internally generated distor-tion limits the dynamic range. Figure4–1 depicts the worst case situationwhere dynamic range is equally limit-ed by noise or distortion as the InputAttenuator toggles between two adja-cent settings. One may get lucky anda particular attenuation setting mayallow an optimal setting for themixer level, but in general this luck cannot be relied upon. Thepotential dynamic range given up isthe difference between the maximumdynamic range and the achievabledynamic range in the worst case scenario. Clearly, a finer resolutionin the input attenuator allows morecontrol of the power at the inputmixer, which in turn minimizes the dynamic range that is given up.

If one takes the simplistic view thatmaximum dynamic range occurs atthe intersection of the noise and thedistortion product curves, then thedynamic range given up can be sub-stantial unless a very fine resolutionof the Input Attenuator step size isused. However, as indicated earlier,when the distortion amplitudeapproaches the noise floor, the noiseand distortion add giving a curvethat is more of a trough where themaximum dynamic range occurs. Inthis case the sensitivity of achievabledynamic range versus attenuatorstep size is not nearly as great as inthe simplistic view.

Table 4–1 summarizes the dynamicrange given up versus attenuatorstep size for three scenarios: the simplistic view where noise and distortion curves meet at a point, CW type distortion on the Log-Power(Video) averaging scale, and noise-like distortion on the Power (RMS)averaging scale where the noise

and distortion add as uncorrelatedpowers. With the simplistic view, oneis led to believe that even finer than1 dB input attenuator resolution iswarranted in order to minimize thelost dynamic range. However, for themore realistic cases where noiseadds to the near-noise distortionproducts, the dynamic range givenup is not nearly as great.

The PSA series offer an InputAttenuator with a 2 dB step size.This allows the user to fine tune themixer level so that in the worst case,only 0.28 dB of potential dynamicrange is given up. One could useexternal fixed attenuators to achievethe same results as the internal stepattenuator. However, convenience is certainly sacrificed and, moreimportantly, so is accuracy. Externalattenuators lack the frequencyresponse calibration that is assuredwhen using the Input Attenuator of the PSA series analyzers.

Part IV: PSA Architectural Effects on Distortion Measurements

Figure 4–1Attenuator Step Size Governs the Ability to Achieve the Optimum Mixer Level

-117

-115

-113

-111

-109

-107

-105

-50 -48 -46 -44 -42 -40 -38 -36 -34

Mixer Level (dBm)

DA

NL

and

Dis

tort

ion

Rel

ativ

e to

Mix

er L

evel

(dB

c)

AttenuatorStep Size

Potential Dynamic Range Given UpWorst Case DR

due to insufficientattenuator step size

Table 4–1. Potential Dynamic Range Given up [dB] versus Attenutor Step Size [dB].

Attenuator Simplistic CW distortion adding to Noise-like distortion adding toStep Size (dB) View noise on the Log-Power scale noise on the Power scale

10 6.7 4.7 4.1

5 3.3 1.6 1.3

2 1.3 .28 .23

1 .67 .08 .06

32

Internal Filtering

Although knowing the internal archi-tecture of the spectrum analyzerseems an unnecessary burden, somesimple concepts such as the internalfilters may help in achieving moredynamic range performance whenmaking distortion measurements.

Figure 4–2 shows a highly simplifiedblock diagram of the PSA series front end.

Two paths exist: lowband for tunedfrequencies less than 3 GHz andhighband for tuned frequencies from3 to 26.5 GHz. Lowband path isbroadband in that all signals that fallbelow 3 GHz are present at the inputof the lowband mixer. Highband path,by contrast, uses a tuning preselectorfilter whose 3 dB bandwidth variesfrom 40 MHz at 3 GHz to more than80 MHz at 26.5 GHz.

When measuring harmonic distor-tion, there is a clear demarcation for fundamental frequencies whoseharmonics fall above and below 3 GHz. For harmonics that fall below 3 GHz, the lowband first mixercontributes its internally generateddistortion to the measurement.However, once the distortion fre-quency falls above 3 GHz, the high-band path’s preselector greatlyattenuates the fundamental tonepower before it can reach the highband mixer. The PSA series specification sheet shows that theSHI performance makes a dramaticimprovement for source frequenciesabove 1.5 GHz.

One should also be aware of thepotential of overloading the front end when the lowband path is select-ed. The PSA series specify a gaincompression level that is the totalpower at the input mixer at whichthe gain of the spectrum analyzerdrops by 1 dB. That is, if the powerat the input mixer is at the gain com-pression level, spectral componentsof the displayed signal could be asmuch as 1 dB lower than when themixer level is less than -10 dBm. This is important when working in a multi-tone environment and thefrequency span of the spectrum analyzer is sufficiently narrow toremove large signals from view. For the highband path, knowledge ofthe preselector bandwidth can helpextend the gain compression per-formance of the spectrum analyzer.The PSA series specification for gaincompression in highband is for thepower at the mixer. As the analyzertunes away from a particularlystrong signal, the preselector filter

will attenuate this signal before itreaches the highband mixer. So in amulti-tone environment, if the spec-trum analyzer is tuned several prese-lector bandwidths away from astrong signal, we can reduce theinput attenuation, thus improvingdynamic range without worryingabout front end compression affect-ing the amplitude accuracy of themeasurement.

One last item regarding internal filtering is the filtering in the final IF of the PSA series. This discussionassumes that the PSA series analyzeris in swept analysis mode as opposedto FFT analysis mode. Swept analysismode is selected by activating theMode Setup hardkey, FFT & Sweepsoftkey, Sweep Type set to Swp. Themaximum mixer level before the finalIF overloads is within 2 dB above -10 dBm. In fact, the user cannot set the reference level such that themixer level is above -10 dBm. Signalsabove this level are displayed abovethe top of the screen and a ‘Final IFOverload’ message appears on thedisplay. However, the specified gaincompression level is more than 10 dB

Figure 4–2PSA Series Front End

3 GHz

DC to 3 GHz

Input Attenuator

RFInput

HighbandMixer

LowbandMixer

3—26.5 GHzHighbandPreselectionFilter

33

above this level, which can yield 10 dB more compression-to-noisedynamic range out of the spectrumanalyzer over what is at first apparent.When measuring a small signal in thepresence of a large signal, first meas-ure the amplitude of the large signalwith sufficient input attenuation todrop the mixer level below -10 dBm.When measuring the small signal,tune the start and stop frequencysuch that the large signal is at least 15 kHz or 15 x RBW setting (whichev-er is greater) outside of the frequen-cy range of the spectrum analyzer.For example, if a large signal is pres-ent at 1 GHz and the user wants tomeasure a small signal above 1 GHzand a 1MHz RBW setting is selected,ensure that the start frequency of the spectrum analyzer is greater than1.015 GHz (1 GHz + 15 x 1 MHz).Once the frequency span is set suchthat the large signal is no longer inview, the Input Attenuator can beadjusted lower to improve the meas-urement sensitivity. However, caremust be observed when lowering the Input Attenuation so that thepower at the mixer is still below the specified compression level.

Internal Preamplifier

The PSA series offer an internal lowband 100 kHz—3GHz preamplifieras an option (Option 1DS). The preamplifier is placed in the blockdiagram after the input attenuator,but before the lowband input mixer.The preamplifier places roughly 28 dB of gain ahead of the lowbandfirst mixer, which lowers the systemDANL by about 15 dB. Normally, the preamplifier is used to measureextremely low amplitude spurioussignals, signals that would normallyfall close to or below the noise floorin the non-preamplifier path.However, it is worth mentioning the behavior of the preamplifier path if this path is selected whenmaking distortion measurements.

As previously mentioned, the pream-plifier lowers the noise floor of thespectrum analyzer by about 15 dB.The preamplifier does not signifi-cantly add distortion to the system,however it does increase the powerat the input mixer by the nominalgain value of 28 dB. This has theeffect of lowering system SHI, TOI,and gain compression level byaround 28 dB. The result is a drop in the second order dynamic range of 6.5 dB, a drop in the third orderdynamic range of 8.5 dB, and a dropin the compression to noise dynamicrange of 13 dB.

Figure 4–3 shows the dynamic rangechart for the internal preamplifierpath selected. For both second order dynamic range and third orderdynamic range, the optimum mixerlevels are considerably lower thanwith the non-preamplifier path. This may be of some benefit for lowlevel applications where there is notenough DUT power to reach the optimum mixer level of the non-preamplifier path.

Figure 4–3Dynamic Range Chart with the Internal Preamp Selected

-120-115-110-105-100

-95-90-85-80-75-70-65-60

-100 -95 -90 -85 -80 -75 -70 -65 -60 -55 -50

Mixer Level (dBm)

DA

NL

and

Dis

tort

ion

Rel

ativ

e to

Mix

er L

evel

(dB

c)

1 Hz DANLSecond OrderDistortion

Third Order Distortion

34

In this final Part, we cover a few miscellaneous items that couldimpact the distortion measurement.

Reducing Source IntermodulationDistortion

Equally as important as ensuringproper configuration of the spectrumanalyzer used to measure intermodu-lation distortion is that the sourcesused to generate the multi-tone stim-ulus be free of IMD. IMD generated inthe sources is normally a result ofinsufficient isolation between thesources. Figure 5–1 shows a highlysimplified block diagram of a signalsource.

The signal source generates the CWtone at frequency f1 . A second CWsource at frequency f2 is connectedto this signal source by some meansof power combination. Signal energyfrom the second source enters theoutput port of the source and, becausethe output coupler does not haveinfinite isolation, a portion of the f2signal leaks into the coupled port ofthe output coupler. Both the signalsat f1 and f2 are detected, which creates a beat note at a frequency of|f2 - f1|. If this beat note is lower infrequency than the loop bandwidthof the automatic leveling control(ALC) circuit, the ALC will respondto this signal causing AM sidebandson the output signal. Unfortunately,the AM sidebands fall right at theintermodulation distortion productfrequencies, resulting in whatappears as IMD out of the source.

The solution to improving sourcegenerated IMD is to prevent the energy of the second source signalfrom entering the output port of thesignal source. The required isolationbetween the two sources is depend-ent on the susceptibility of the signalsource to signals entering the outputport as well as the acceptable AMsideband level needed for the TOImeasurement.

Some of the better power combination techniques are:

Wilkinson Power Combiners—these can achieve greater than 30 dB isolation.

Class A Amplifiers at the output ofthe sources—important to not useamplifiers that have leveling control circuitry of their own.

Fixed Attenuators—these should be used in conjunction with powersplitters and amplifiers.

Isolators—the downside is their relatively narrow bandwidth.

Couplers—high directivity couplersneeded.

Some power combiners that do notwork very well are two- and three-resistor splitters. The temptation touse these are great due to their verywide bandwidth. However the two-resistor splitter only has 12 dBof isolation and the three-resistorsplitter only has 6 dB of isolation. Adevice that should never be used isthe T (BNC T and smb T are exam-ples). These not only have zero isola-tion, but also they present a verypoor match to the DUT, which canhave an adverse effect on the meas-urement accuracy.

Part V: Enhancing Distortion Measurements

Figure 5–1Simplified Output Section of a Signal Generator

LevelAdjust

OutputAmp

PowerDetector

f1

f1

f2

f1

f2

ALC

35

Effects of Harmonics onIntermodulation Distortion

When measuring intermodulationdistortion, an important considera-tion is the harmonic content fromthe sources as well as the deviceunder test. Two-tone IMD will beused in the following example, however this analysis can be extrapolated to multi-tone IMD.

Suppose a nonlinear device, eitherthe DUT or the spectrum analyzerused to make the IMD measurement,

can be modeled using the powerseries up through the third orderterm:

Now subject this nonlinear device tothe following two-tone input signal:

For a two-tone IMD measurement,amplitudes A and B are set to be thesame. The third term represents thesecond harmonic of the first term.Inserting the input voltage into the model of the nonlinear device,performing the trigonometric expan-sions and collecting terms, the lowside IMD product is given by:

Clearly, the second harmonic of the term at 2ω1 contributes to theintermodulation distortion product.In fact, depending on the phase ofthe second harmonic distortion term, the second harmonic can addconstructively or destructively to the IMD term.

For a two-tone measurement setup as shown in Figure 1–3, thesecond harmonic can originate fromeither the sources themselves, thedevice under test, or the spectrumanalyzer used to make the IMD measurement. Evidence of secondharmonic interference is asymmetryin the amplitudes of the low side andhigh side IMD products; this is espe-cially true if one of the sources hasworse harmonic performance thanthe other source. Another clear signis IMD, which varies widely across anarrow frequency range.

The obvious solution to a suspectedharmonic interference problem is toplace filters in the measurementsetup. Filtering in front of the DUTwill reduce harmonic content due tothe sources, and filtering after theDUT will reduce the harmonic inter-ference generated by the DUT itself.

However, caution must be exercisedwhen placing filters in the measure-ment system. Being reflective in thestopband, the filters can contributeto some unexpected results in theIMD measurement. If the DUT is anamplifier, it may be driven into anunstable state if filters are placed ateither the input or the output ports.For DUTs such as mixers, poor matchat image and spurious frequenciescan make the DUT IMD worse than ifno filters were used at all. Placingfixed value attenuators between theDUT and the filters can mitigate theeffects of the poor stopband matches—if the system can tolerate the power loss.

Vo = a1Vi + a2Vi2 + a3Vi

3 (5–1)

Vi = A x Cos(ω1t) + B x Cos(ω2t) + C x Cos(2ω1t) (5–2)

Vo = [(3/4)a3A2B + a2BC] x Cos((2ω2 - ω1)t) (5–3)

36

Noise Subtraction Techniques

Noise subtraction is the process ofmathematically removing the systemnoise of the spectrum analyzer fromdisplayed signals, thus improving theapparent signal-to-noise ratio of themeasurement. This technique is espe-cially powerful for signals that fallwithin a few dB of the displayednoise floor. In reference [4], themathematical justification for noisesubtraction and the measurementrequirements under which noise sub-traction is valid are presented. Herewe will show a couple of distortionmeasurement examples where noisesubtraction can be used.

As stated in reference [4], the signalpower, powers, can be derived from:

powers = powers+n - powern [mW] (5–4)

where powers+n is the displayed signal plusnoise power and

powern is the spectrum analyzer’s noise floormeasured with the signal disconnected from theinput of the spectrum analyzer. All powers are inlinear power units such as mW.

The caveat is that the measurementbe carried out using power detection,that is, the averaging scale on thePSA series analyzer should be set toPower (RMS). This stipulation mustbe observed for CW signals that are normally measured with the Log-Power (Video) averaging scaleselected.

The procedure for performing thenoise subtraction on the PSA seriesanalyzer is as follows:1. Set the Detector Mode to

Average Detector.

Set the Avg/VBW Type to Pwr Avg (RMS)

Set the Input Attenuator, RBW,VBW appropriately for the distortion measurement.

2. Remove the signal from the analyzer input. For even moreaccuracy, the RF input can be terminated in 50 Ohms. Slow thesweep time in order to reduce thevariance of the noise signal. Readin the trace data to an externalcomputer; this is the noise power data.

3. Connect the signal to the analyzerinput. Read in the trace data.Avoid changing the RBW, VBW,Input Attenuator or Sweep speedsettings from the settings in step2. Read in the trace data to anexternal computer; this is the signal plus noise power data.

4. In the external computer, convertthe log measurements to linearvalues, perform the subtraction of equation 5–4 on a point by point basis. Convert the result toconvenient units, such as dBm.

Subtracting the linear power noisedata from the linear power signal-plus-noise data can result in negativepower values, which cause an illegaloperation when mathematically converting the resultant value backto log power. One can set these negative values to an arbitrarilysmall linear value to avoid the mathematical anomaly. However, ifan integrated channel power meas-urement is to be performed it is bestto leave the negative linear powervalues intact, add all the linear tracedata points across the channel, andthen convert the integrated channelpower back to a log power value.Otherwise, the effect of discardingnegative results will increase thecomputed average power.

37

There is a relationship between the amount of noise that can be cancelled and the variance of themeasured data. Lower variance usingaveraging or longer sweep times withthe average detector activated resultsin more noise cancellation. One canexpect about a 10 dB improvement in the amount of noise that can bereliably cancelled.

Figure 5–2 shows the results of noisesubtraction on a CW signal. Theupper trace shows the displayed signal using the Power display scale.It shows a displayed signal to noiseratio of 4 dB. The lower trace showsthe noise subtracted. One observa-tion is that the signal no longer contains the noise error, which inthis case is 2 dB. Also note that thenoise floor drops by at least 10 dB.In this particular example, the sweeptimes for both the noise and the signal plus noise measurements are 45 seconds.

Figure 5–3 shows noise subtractionperformed on a W-CDMA signal. Theupper trace shows that the noisefloor of the PSA series analyzer limits the dynamic range of themeasurement in the adjacent chan-nel. The lower trace shows the resultof noise subtraction. This trace clear-ly shows the third order distortioncomponent of the spectral regrowthin the adjacent channel. Withoutnoise subtraction, the noise floor of the spectrum analyzer limits thedynamic range. However, with noisesubtraction, the third order distor-tion generated within the spectrumanalyzer limits the dynamic range.One could improve the measurementby reducing the signal power in order to drive down the third orderdistortion. The sweep times for thisexample are 120 seconds for both the noise and the signal-plus-noisemeasurements.

Figure 5–2CW Signal with and without Noise Subtraction

Figure 5–3W-CDMA Signal with and without Noise Subtraction

RBWResolution Bandwidth Filter. This IFfilter is placed before the envelopedetector. Reducing its bandwidthimproves the selectivity of closelyspaced signals as well as lowers the displayed noise floor.

RMSRoot Mean Square. Noise measuredon the power scale is reported inRMS notation, which removes the -2.51 dB offset due to log display processing.

SHISecond Harmonic Intercept. A figure of merit for second harmonic distortion.

S/DSignal-to-Distortion Ratio. Units are dB.

S/NSignal-to-Noise Ratio. Units are dB.

TOIThird Order Intercept. A figure ofmerit for third order intermodulationdistortion.

VBWVideo Bandwidth Filter. This filter isplaced after the envelope detector.Reducing its bandwidth reduces thevariability of the displayed signal.

38

One of the primary uses of the spectrum analyzer is for making distortion measurements. This product note has served as both anintroductory tutorial on distortionmeasurements and as a guide tomaking these measurements accu-rately using a PSA series analyzer.Not only has the reader been intro-duced to properly configuring thePSA spectrum analyzer for optimumdynamic range performance, but alsosome of the measurement errors aswell as guidelines on reducing meas-urement error have been presented.

ACPRAdjacent Channel Power Ratio =Adjacent channel power in dBmminus Main channel power in dBm.Units are dB.

CWCarrier Wave or Continuous Wave. A sinusoidal signal without modulation.

DANLDisplayed Average Noise Level. The noise floor as it appears on thedisplay of the spectrum analyzer.

dBcdB relative to the carrier

dBmdB relative to 1 mWatt

IMDIntermodulation Distortion

Log-Power (Video) The default averaging scale for measuring CW type distortion.

Max Mxr LvlMaximum Mixer Level. ReferenceLevel and Input Attenuator are automatically coupled such that,when an input signal amplitude is atthe highest vertical display division,the power at the input mixer is nohigher than the Max Mxr Lvl value.

Mixer LevelPower at the input mixer. Equals theRF Input power minus the nominalInput Attenuator value.

NBWNoise Power Bandwidth. The bandwidth of a fictional rectangularbandpass filter that passes the same amount of white noise power as does the RBW filter. For the PSAseries, NBW/RBW = 1.06

Power (RMS) The averaging scalein which effects of log scale process-ing on displayed noise are removed.

Glossary of TermsConclusions

39

[1] Spectrum Analyzer Basics, AgilentTechnologies Application Note 150,literature number 5952-0292,November, 1989.

[2] Witte, Robert A., Spectrum andNetwork Measurements, Prentice Hall, Inc., 1993.

[3] Using a Network Analyzer toCharacterize High PowerComponents, Agilent TechnologiesApplication Note 1287-6, literature number 5966-3319E, 1998.

[4] Spectrum Analyzer Measurementsand Noise, Agilent TechnologiesApplication Note 1303, literature number 5966-4008E, 1998.

[5] Maas, S. A., Third OrderIntermodulation Distortion inCascaded Stages, IEEE Microwavesand Guided Waves Letters, Vol. 5, No. 6, June 1995, pg. 189-191.

[6] Mouthrup, Andrew A. and Muha,Michael S., Accurate Measurement of Signals Close to the Noise Floorof a Spectrum Analyzer, IEEETransactions on Microwave Theoryand Techniques, Vol. 39, No. 11,November 1991, pg. 1882 - 1885.

References

Product specifications and descriptions in this document subject to change without notice.Copyright © 2000 Agilent Technologies Printed in U.S.A. November 28, 20005980-3079EN

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