01/04/2011 - 1 ATLCE - B6 - © 2010 DDC

Politecnico di Torino - ICT School

Analog and Telecommunication Electronics

B6 - Non-linear circuits

» Nonlinear circuits taxonomy» Log amplifiers: Error sources» Ratiometric, bipolar circuits» Saturating amplifier chain, RSSI» circuit example

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Lesson B6: Nonlinear circuits

• Nonlinear circuits taxonomy

• Logarithmic amplifiers– Parameters of a logarithmic transfer function– Circuits: Error sources, Design procedure– Exponential, ratiometric, bipolar circuits

• Saturating amplifier chain, RSSI circuits

• References » Nonlinear circuits – taxonomy and basic circuits 2.2.1» Log and antilog amplifiers 2.2.3

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Nonlinear circuits

• Errors– offset, gain– “nonlinearity”: deviation from the designed behavior

• Piecewise approximation– Amplifiers with gain and offset related with specific input voltage

Vi ranges » Active diode» Wave shaper» RSSI circuits

• Continuous approximation– Need for a nonlinear element

» Multipliers: squaring, root, polynomial function» Semiconductor junction: log or exponential function

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Logarithmic amplifier: transfer function

• Generic log transfer function

– k2 and k3 represent the same parameter

• Two degrees of freedom – Input offset k4

Vo = k1 log(k2(Vi+k4)) + k3

X X+ +logVi Vo

k4 k2 k1 k3

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Log amplifier: transfer diagram (linear)

• Vo = k1 log(k2(Vi+k4)) + k3

• Representation on linear plot– X axis: Vi;

Y axis: Vo = log Vi– Fixed ratio on Vi fixed shift on Vo

– Vi = 0 ??– Hard to see

effects of Ks

Vo

Vi

54321

1 2 4 8 16

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Log amplif.: transfer diagram (half-log)

• Vo = k1 log(k2(Vi+k4)) + k3

• Representation on semilog plot– X axis: log k2 Vi– Straight line: y = k1 x + k3– Changing k1

modifies the slope (rotation)– Changing k3 (or k2)

causes a shift (translation)– Changing k4 causes

nonlinearity for low Vi

logVi

Vo

k3

k2k1

k4Vo = k1 log(k2(Vi+k4)) + k3

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Effects of input offset k4

• Input additive constant input offset– The same offset (k4) corresponds to different shifts on the log

Vi axis he actual value of – The effect on output depends on the actual value of Vi

logVi

Vo

k4k4k4

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Logarithmic element

• Functional specification: Vu = K log Vi» Wide dynamic» Low errors» Wide band» ….

• Exploit the V(I) relation in a PN junction

– Set the current I

– Read the voltage V

VD =

V

I

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Logarithmic amplifier: circuit

• Use transconductance Op. Amp. circuit

– Set the current» I = I2 = I1 = Vi / R

– Read the voltage» VU = -VD

– Control the parameters» V I conversion at the input: k2 (and k3)

» Output gain: k1 (negative)– Correct temperature-related errors:

» Is: cancel with reference junction, constant current» Vt: correct with temperature-dependent gain element (NTC)

AO 1

Vi-+

VO

DR

Vd

I1

I2

I- VD

VD =

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Basic circuit for logarithmic amplifiers

• Logarithmic junction Reference junction

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Error sources

• Low input values:– Low V across R1 Op. Amp. Offset (Voffset)– Low I in the log junction Ioff and Ibias

• High input values: High currents– Additional voltage drop on junction intrinsic resistance rBB’

logVi

Vo

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[mV]

Total errors

• Overall transfer function (inverting)

Errors causedby Ib, Ioff, Voff

Error causedby rBB’

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Ratiometric logarithmic amplifier

• Log of voltage ratiolog (x) - log(y) = log(x/y)

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Bipolar logarithmic amplifier

• Twin junctions to handle bipolar Vi (bidirectional current)

• Compression transcaracteristic

• If R ↔ diodes expander transcaracteristic

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Applications of log amplifiers

• DC amplifiers:– lin-log conversion (dB, bode diagrams, …)– Analog “computation”– After AM demodulation

» Level measurement (IF chain, RSSI…),» Gain control (AGC)

• AC and bipolar amplifiers:– Dynamic range compression

• AC-DC log converters– Sequence of saturating stages – Wide dynamic range level measurement

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AC-DC log converters

• Piecewise approximation

• Sequence of amplifiers with breakpoint – A/1 amplifiers:

» Gain A for Vi > E; 1 for Vi > E» Direct output from last stage

– A/0 amplifiers: » Gain A for Vi > E; 0 (Vu = S = E*A) for Vi > E» output = sum of single amplifier outputs

• Obtained with saturating amplifiers– Usually differential stages, with summation of currents– As the level increases, the number of saturated stages

increases

Vo

ViE

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Saturating chain

• Eeach stage has Gain = 2, and saturation at Vo = S– Stage 1 with gain for Vi < S/2; saturated for: Vo = 2 Vi, – Stage 2 with gain for Vi < S/4; saturated for: Vo = 4 Vi, – Stage 3 with gain for Vi < S/8; saturated for: Vo = 8 Vi, – Stage 4 with gain for Vi < S/16; saturated for: Vo = 16 Vi,

• Total gain– 0<Vi<S/16 active: 1, 2, 3, 4 G = 24 = 16– 0<Vi<S/8 active: 1, 2, 3 saturated: 4 G = 23 = 8– 0<Vi<S/16 active: 1, 2 sat.: 3, 4 G = 22 = 4– 0<Vi<S/16 active: 1 sat.: 2, 3, 4 G = 21 = 2

• Saturation = gain 0: sum of the outputs

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Chain with saturation

• Low Vi :all stages have gain

• High Vi:only first stages have gain

• Higher gain for lower Vi:16, 8, 4, 2, 1

• Compression

Vo

Vi

1 2 3 4Σ

VoVi

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Saturating logarithmic amplifiers

• Good for AC, wideband band, wide dynamic

• Conversion AC-DC on each stage– Reduced dynamic on the single converter

• Applications: RF power measurement– AGC for LNA and IF amplifiers– Power control for PA

• RSSI (Received Signal Strength Indicator) output– Carrier detection– RF signal level– Squelch control

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Example of saturation log circuit

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Limiting amplifier + RSSI

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Log amplifiers

• Lab exercise:– Design a log amplifier from the assigned specs– Evaluate errors– Verify with simulation– Verify with measurements

• Specs:– Provided each year in the lesson

• Design procedure: Sect 2, 2.P2

• Lab experience: Sect 2, 2.L2

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Design procedure

• Selection of circuit configuration

• Definition of current dynamic range– Evaluation of error at upper range limit

» RBB’, maximum current– Evaluation of errors at lower range limit

» Op. Amp (Ib), minimum current– Selection of Op. Amp.– Current range selected to get balanced error at the dynamic

range extremes

• Positioning input & output constants and parameters– Gain and translation of Vu’ = log Vi

• Temperature compensation (if required)

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Lesson B6 – final test

• Which are the techniques to obtain nonlinear transfer functions?

• How can Op Amp be used to get nonlinear transfer functions?

• How many parameters describe a log transfer function?

• Describe an application for logarithmic amplifiers

• Draw the diagram of a basic log amplifier.

• Which are the main error sources at low end of input range?

• Which are the main error sources at high end of input range?

• Describe how to get nonlinear transfer functions using saturating amplifiers.

• Which is the meaning of the acronym RSSI?

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