Ch10

Chapter 10Chapter 10Amplifier Frequency Amplifier Frequency

ResponseResponse

ObjectivesObjectives

Discuss frequency response of an amplifier

Express the gain of an amplifier in decibels (dB) Analyze the frequency response of a BJT amplifier Analyze the frequency response of an FET amplifier Analyze the frequency response of a multistage amplifier

IntroductionIntroduction

Most amplifiers have a finite range of frequencies in which they will operate. We will discuss what determines the frequency response of an amplifier circuit and how it is measured.

Basic Concepts Basic Concepts

In previous analysis of amplifier circuits we disregarded the reactance of the capacitors. You should already be familiar with the characteristics of a capacitor. We will discuss how the capacitor limits the passage of certain frequencies. This is called the frequency response of an amplifier.

Basic ConceptsBasic Concepts

Coupling capacitors C1 and C3 limit the passage of very low frequencies. Emitter bypass C2 capacitor will have high reactance to low frequencies as well, limiting the gain. Also the capacitance causes a phase shift of the signal.

Figure 10–2 Nonzero reactance of the bypass capacitor in parallel with RE Figure 10–2 Nonzero reactance of the bypass capacitor in parallel with RE creates an emitter impedance, (creates an emitter impedance, (ZZee), which reduces the voltage gain.), which reduces the voltage gain.


Internal capacitance of BJTs and FETs comes into play at high frequencies limiting the gain. Remember reactance is low at high frequencies.

Figure 10–4 AC equivalent circuit for a BJT amplifier showing effects of the internal Figure 10–4 AC equivalent circuit for a BJT amplifier showing effects of the internal capacitances capacitances CCbebe and and CCbcbc. .

Thomas L. Floyd Thomas L. Floyd Electronic Devices, 7eElectronic Devices, 7e

Copyright ©2005 by Pearson Education, Inc.Copyright ©2005 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458Upper Saddle River, New Jersey 07458

All rights reserved.All rights reserved.

Figure 10–5 General case of Miller input and output Figure 10–5 General case of Miller input and output capacitances. C represents capacitances. C represents CbcCbc or or CgdCgd. .





Miller’s theorem allows us to view the internal capacitances as external capacitors for better understanding of the effect they have on the frequency response.

The DecibelThe Decibel

The decibel is a common unit of measurement of voltage gain and frequency response. It is a logarithmic measurement of the ratio of one power to another or one voltage to another. The formulas below are used for calculation of decibels for power gain and voltage gain.

Ap(db) = 10 log Ap

Av(db) = 20 log Av

Figure 10–7 Normalized voltage gain versus frequency curve.Figure 10–7 Normalized voltage gain versus frequency curve.




Voltage gain vs Frequency curve

This typical voltage gain vs frequency curve illustrates the relationship of gain measurement in decibels. Note that every 6 dB represents a doubling or halving of gain.

The critical frequency

The critical frequency, also known as the cutoff frequency, is the frequency at which the output power drops by 3 dB, which represents one-half of its midrange value. An output voltage drop of 3 dB represents about a 70.7% drop from the midrange value.Power is often measured in units of dBm. This is decibels with reference to 1 mW of power. This means that 0 dBm = 1 mW.

Low-Frequency Amplifier ResponseLow-Frequency Amplifier Response


In looking at the low frequency ac equivalent circuit of a capacitor coupled amplifier, we can see there are three RC circuits that will limit low frequency response. The input at the base, the output at the collector, and the emitter.

Low-Frequency Amplifier ResponseLow-Frequency Amplifier Response The input RC circuit

The input circuit’s effects on the signal at a given frequency can be more easily understood by looking at this simplified input circuit. The frequency at which the gain is down by 3 dB is called the lower critical frequency (fc). This frequency can be determined by the formula below.

fc = 1/2RinC1


The decrease in voltage gain with frequency is called the roll-off. A ten times change in frequency is called a decade. The attenuation measured in dB at each decade is is the dB/decade. This typical dB Av vs frequency illustrates the relationship. Sometimes roll-off is expressed in dB/octave, which is a doubling or halving of the frequency.

Figure 10–12Figure 10–12 Phase angle versus frequency Phase angle versus frequency for the input RC circuit. for the input RC circuit.





Phase shifting occurs at the lower frequencies as the capacitive reactance increases. This occurs in all of the capacitive parts of the circuits at low frequencies.

Figure 10–13 The input RC circuit causes the base Figure 10–13 The input RC circuit causes the base voltage to lead the input voltage below midrange by an voltage to lead the input voltage below midrange by an amount equal to the circuit phase angle, amount equal to the circuit phase angle, ..




Low-Frequency Amplifier ResponseLow-Frequency Amplifier Response The output RC circuit

The output RC circuit affects the response similarly to the input RC circuit. The formula below is used to determine the cutoff frequency of the output circuit.

fc = 1/2(RC + RL)C3

Figure 10–14 Development of the equivalent low-Figure 10–14 Development of the equivalent low-frequency output RC circuit.frequency output RC circuit.




Low-Frequency Amplifier ResponseLow-Frequency Amplifier Response The bypass RC circuit

The bypass RC circuit is no different in its effect on the gain at low frequencies. Thevenin analysis can be applied to the bypass circuit along with the formula below. Detailed discussion of the use of Thevenin’s theorem and formulas are within the text.

Figure 10–16 Development of the equivalent bypass RC circuit.Figure 10–16 Development of the equivalent bypass RC circuit.




EX. 10-6EX. 10-6

Low-Frequency Amplifier ResponseLow-Frequency Amplifier ResponseFET AmplifiersFET Amplifiers

The input and output capacitors limit the low frequency response of the FET just as they do with the BJT. Calculations are similar as well.

Figure 10–19 Input RC circuit for the FET amplifier in Figure 10–18.Figure 10–19 Input RC circuit for the FET amplifier in Figure 10–18.




Figure 10–21 Development of the equivalent low-frequency output RC Figure 10–21 Development of the equivalent low-frequency output RC

circuit.circuit.




EX. 10-8EX. 10-8

The Bode PlotThe Bode PlotFigure 10–23 An RC circuit and its low-frequency response. Figure 10–23 An RC circuit and its low-frequency response.

(Blue is ideal; red is actual.)(Blue is ideal; red is actual.)




Total Low-Frequency Amplifier ResponseTotal Low-Frequency Amplifier Response

The combined effect of each capacitor is shown in this Bode plot of the frequency response.

Figure 10–25 Composite Bode plot of an amplifier response where all RC Figure 10–25 Composite Bode plot of an amplifier response where all RC circuits have the same circuits have the same ffcc. (Blue is ideal; red is actual.) . (Blue is ideal; red is actual.)




EX. 10-9EX. 10-9

Figure 10–27 Ideal Bode plot for the total low-frequency response of the Figure 10–27 Ideal Bode plot for the total low-frequency response of the amplifier in Figure 10–26. amplifier in Figure 10–26.




High-Frequency Amplifier ResponseHigh-Frequency Amplifier Response

High-frequency response is limited by internal capacitances of the transistors. These act like shunts around the transistor. Note these are undesirable. Detailed analysis using Miller’s theorem is discussed further within the text.

Figure 10–29 High-frequency equivalent circuit after applying Miller’s Figure 10–29 High-frequency equivalent circuit after applying Miller’s

theorem.theorem.




Figure 10–30 Development of the equivalent high-frequency input RC Figure 10–30 Development of the equivalent high-frequency input RC

circuit.circuit.




EX. 10-10EX. 10-10

Figure 10–32 High-frequency equivalent input RC Figure 10–32 High-frequency equivalent input RC circuit for the amplifier in Figure 10–31.circuit for the amplifier in Figure 10–31.




Figure 10–33 Development of the equivalent high-frequency output RC circuit.Figure 10–33 Development of the equivalent high-frequency output RC circuit.




Figure 10–35 Example of a JFET amplifier and its high-frequency equivalent Figure 10–35 Example of a JFET amplifier and its high-frequency equivalent

circuit.circuit.




Figure 10–36 High-frequency equivalent circuit after applying Miller’s Figure 10–36 High-frequency equivalent circuit after applying Miller’s

theorem.theorem.




Figure 10–37 Input RC circuit.Figure 10–37 Input RC circuit.




Figure 10–39 Output RC circuit.Figure 10–39 Output RC circuit.




Total High-Frequency Amplifier ResponseTotal High-Frequency Amplifier Response

The Bode plot of the high frequency response shown shows the combined effects of each internal capacitance.

Figure 10–41 A BJT amplifier and its generalized ideal response curve Figure 10–41 A BJT amplifier and its generalized ideal response curve

(Bode plot).(Bode plot).




Total Frequency ResponseTotal Frequency Response

This plot shows the total combined effects of both the coupling capacitors and the internal capacitances.

Figure 10–43 Simplified response curve where Figure 10–43 Simplified response curve where fclfcl is is negligible (assumed to be zero) compared to negligible (assumed to be zero) compared to fcufcu..




Total Frequency ResponseTotal Frequency Response

In determining the total frequency response of a multistage amplifier, each stage’s frequency response must be considered.

When the critical frequency of each stage is different, the lowest and highest cutoff frequencies determine the bandwidth.

When the critical frequencies of each stage are the same, it increases the low frequency cutoff and decreases the high frequency cutoff.

Frequency Response MeasurementFrequency Response Measurement

Frequency response measurement can be made with a function generator and an oscilloscope by checking the output voltage across the frequency spectrum.

The step-response measurement can be used by applying a step voltage, first observing the rise time for the upper cutoff frequency and the fall time for lower cutoff frequency.

SummarySummary

Capacitances both internal and external limit frequency response.

Critical frequency or cutoff is when the output voltage is at 70.7% of the mid-range value.

The bandwidth of an amplifier is the difference between the upper and lower critical frequencies.

High and low cutoff are determined by the dominant critical frequencies.

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