Posted: March 12th, 2023

Discussion: Frequency Response

Small-signal amplification and power amplification are dependent on the application where they are going to be applied. In most cases, the frequency range of the signal is critical to its ability to carry the information that is being transferred.

In this activity, we will explore the effects of the internal and external capacitances on the frequency response of the system. We will also discuss the advantages and disadvantages of using the amplifier’s response to eliminate unwanted noise from the system.

Before you begin, be sure you review the following resources:

In your original post, answer the following:

In your own words, explain the difference between low pass filters and high pass filters. A Common-Emitter BJT amplifier acts as what type of filter?
In your own words, explain how internal capacitance and external capacitance affects the overall filter characteristics
How does having two cut off frequencies that are the same effect the overall cut off frequency?
When you have a multi-stage amplifier, how do you determine the bandwidth of the overall frequency response of the amplifier?

Electronic Devices

10th ed.

Chapter 10

Amplifier Frequency Response

Electronic Devices
10th ed.
◆ Explain how circuit capacitances affect the frequency
response of an amplifier
◆ Use the decibel (dB) to express amplifier gain
◆ Analyze the low-frequency response of an amplifier
◆ Analyze the high-frequency response of an amplifier
◆ Analyze an amplifier for total frequency response
◆ Analyze multistage amplifiers for frequency response
◆ Explain how to measure the frequency response of an amplifier
Objectives:

Electronic Devices
Effect of Coupling Capacitors
Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier.

The equivalent circuit for C1 is a high-pass filter:

Electronic Devices
Effect of Coupling Capacitors
Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier.

The equivalent circuit for C1 is a high-pass filter:

Electronic Devices
Effect of Coupling Capacitors
Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier.

The equivalent circuit for C1 is a high-pass filter:

C3 and (RC + RL) form another high-pass filter.

Electronic Devices
Effect of Coupling Capacitors
With FETs, the input coupling capacitor is almost always smaller because of the high input resistance. The output capacitor may be smaller or larger depending on the drain and load resistor size.

For the circuit shown, the equivalent low-pass filter for the input is simply C1 in series with RG because the gate input resistance is so high and can be ignored.

Electronic Devices
Effect of Bypass Capacitors
A bypass capacitor causes reduced gain at low-frequencies and has a high-pass filter response. The resistors “seen” by the bypass capacitor include RE, re’, and the bias resistors.

The equivalent high-pass filter for C2 is:

Question:
How would an emitter swamping resistor affect the response?

The equivalent high-pass filter for C2 is:

Question:
How would an emitter swamping resistor affect the response?
fc would be lower due to increased R.

Electronic Devices
Internal Capacitances
The high-frequency response of an amplifier is determined by internal junction capacitances. These capacitances form low-pass filters with the external resistors.

Sometimes a designer will add an external parallel capacitor to deliberately reduce the high frequency response.

Electronic Devices
Miller’s Theorem

Miller’s theorem states that, for inverting amplifiers, the capacitance between the input and output is equivalent to separate input and output capacitances to ground.

Electronic Devices
Miller’s Theorem

Miller’s theorem states that, for inverting amplifiers, the capacitance between the input and output is equivalent to separate input and output capacitances to ground.
Av is the absolute value of the gain. For the input capacitance, the gain has a large effect on the equivalent capacitance, which is an important consideration when using inverting amplifiers.

Electronic Devices
Miller’s Theorem
Notice that the effect of Miller’s theorem is an equivalent capacitance to ground, which shunts high frequencies to ground and reduces the gain as frequency is increased.

Example:
What is the input capacitance for a 2N3904 inverting amplifier with a gain of 25? Assume the values of Cbc = 4 pF and Cbe = 6 pF.

Solution:
Example:
What is the input capacitance for a 2N3904 inverting amplifier with a gain of 25? Assume the values of Cbc = 4 pF and Cbe = 6 pF.
Cin = Cbc(Av + 1) + Cbe
Cin = 4 pF(25 + 1) + 6 pF =

Electronic Devices
The Decibel
Recall that the decibel was defined in Chapter 6 as a logarithmic measure the ratio of one power to another or one voltage to another. The decibel is used in electronics work in gain or attenuation measurements. Decibels can be expressed as a voltage ratio when the voltages are measured in the same impedance.

Electronic Devices
The Decibel
To express power gain in decibels, the formula is
Ap(dB) = 10 log Ap
Recall that the decibel was defined in Chapter 6 as a logarithmic measure the ratio of one power to another or one voltage to another. The decibel is used in electronics work in gain or attenuation measurements. Decibels can be expressed as a voltage ratio when the voltages are measured in the same impedance.

Electronic Devices
The Decibel
To express power gain in decibels, the formula is
Ap(dB) = 10 log Ap
To express voltage gain in decibels, the formula is
Av(dB) = 20 log Av
Recall that the decibel was defined in Chapter 6 as a logarithmic measure the ratio of one power to another or one voltage to another. The decibel is used in electronics work in gain or attenuation measurements. Decibels can be expressed as a voltage ratio when the voltages are measured in the same impedance.

Electronic Devices
The Decibel
Sometimes, 0 dB is assigned as a convenient reference level for comparison. Then, other power or voltage levels are shown with respect to 0 dB.

Electronic Devices
The Decibel
Sometimes, 0 dB is assigned as a convenient reference level for comparison. Then, other power or voltage levels are shown with respect to 0 dB.
Some useful decibel ratios to remember are:

Ratio
Power gain, Ap
Voltage gain, Av

0.1
-10 dB
-20 dB

0.5
-3 dB
-6 dB

1
0 dB
0 dB

2
3 dB
6 dB

10
10 dB
20 dB

Ratio
Power gain, Ap
Voltage gain, Av

0.1
-10 dB
-20 dB

0.5
-3 dB
-6 dB

1
0 dB
0 dB

2
3 dB
6 dB

10
10 dB
20 dB

The -3 dB power gain corresponds to a power reduction of one-half. The frequency at which this occurs is referred to as the critical frequency.

Electronic Devices
Low-Frequency Response
In capacitively coupled amplifiers, the coupling and bypass capacitors affect the low frequency cutoff. These capacitors form a high-pass filter with circuit resistances. A typical BJT amplifier has three high-pass filters.

For example, the input coupling capacitor forms a high-pass filter with the input resistance of the amplifier:

Electronic Devices
Low-Frequency Response
The output RC circuit is composed of the series combination of the collector and load resistors with the output capacitor. The cutoff frequency due to the output circuit is

Electronic Devices
Low-Frequency Response
What is the lower cutoff frequency due to C1?

Example:
Assume re’ = 3.5 W and b = 200.

Electronic Devices
Low-Frequency Response
What is the lower cutoff frequency due to C1?

Solution:
Example:
Assume re’ = 3.5 W and b = 200.
RE1 is not bypassed, so it is added to re’. Then:

= 2.77 kW

Electronic Devices
Low-Frequency Response
What is the lower cutoff frequency due to C1?

Solution:
Example:
Assume re’ = 3.5 W and b = 200.
RE1 is not bypassed, so it is added to re’. Then:

= 2.77 kW

Electronic Devices
Low-Frequency Response
The bypass RC circuit response can be found by observing the charge/discharge paths.
For this circuit, there is one path through RE2 as shown in blue.

A second path goes through RE1, re’, and the parallel combination of bias and source resistances as shown in red (source resistance not shown).

Electronic Devices
Low-Frequency Response
The bypass RC circuit response can be found by observing the charge/discharge paths.
For this circuit, there is one path through RE2 as shown in blue.

A second path goes through RE1, re’, and the parallel combination of bias and source resistances as shown in red (source resistance not shown).
The total resistance of the paths can be found by:

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
Solution:
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).
= 79.7 W

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
Solution:
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).
= 79.7 W

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
Solution:
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).
= 79.7 W

42.5 Hz

Electronic Devices
Low-Frequency Response
The input RC circuit for a FET is a basic high-pass filter consisting of the bias resistor (or resistors) and the input coupling capacitor. The FET gate circuit has such high resistance, it can be ignored.

Example:
What is the critical frequency due to the input RC circuit?

Example:
What is the critical frequency due to the input RC circuit?
Solution:

1.6 Hz

Electronic Devices
The Bode Plot
The Bode plot is a plot of decibel voltage gain verses frequency. The frequency axis is logarithmic; the decibel gain is plotted on a linear scale. The -3dB point is the critical frequency.

Electronic Devices
The Bode Plot

Multisim has a fictitious instrument called the Bode plotter. This is the previous BJT amplifier.

Electronic Devices
The Bode Plot

Multisim has a fictitious instrument called the Bode plotter. This is the previous BJT amplifier.

Connect the IN of the plotter to a constant level to the left of the Thevenin source.

Electronic Devices
The Bode Plot

Multisim has a fictitious instrument called the Bode plotter. This is the previous BJT amplifier.

The Bode plotter allows you to see the Bode plot directly. By selecting the proper scales, you can magnify the response. Move the cursor to the point where the total response is – 3dB from midband and read fc as shown here.

Set the cursor 3dB below the midband gain and read fc.

Electronic Devices
High-Frequency Response
The high frequency response of inverting amplifiers is primarily determined by the transistor’s internal capacitance and the Miller effect. The equivalent high-frequency ac circuit is shown for a voltage-divider biased CE amplifier with a fully bypassed emitter resistor.

Electronic Devices
High-Frequency Response
If there is an unbypassed emitter resistor, such as RE1 in the earlier example, it is shown in the emitter circuit and acts to increase re’ and thus reduce fc.

Electronic Devices
High-Frequency Response
For the fully bypassed case, such as the one shown in the text in Example 10-11, the ac emitter resistance (re’) is multiplied by bac to obtain the equivalent input resistance at the transistor’s base.

Electronic Devices
High-Frequency Response
Combining the capacitors in parallel and Thevenizing forms an equivalent basic RC low-pass filter:

Electronic Devices
High-Frequency Response
If there is an unbypassed emitter resistor (RE1 in this case), the Thevenin resistance is modified to

Electronic Devices
High-Frequency Response
The high frequency analysis of FETs is similar to that of BJTs. Like the CE amplifier, the CS amplifier inverts the signal, so the Miller effect must be taken into account. You may see special circuits such as cascode connections in very high frequency applications to minimize the Miller effect.
A high frequency ac model of a CS amplifier is:

Electronic Devices
Total Amplifier-Frequency Response
In general, the overall frequency response is the combination of three lower critical frequencies due to coupling and bypass capacitors and two upper critical frequencies due to internal capacitances.
The ideal Bode plot for a typical amplifier is:

The bandwidth is measured between the dominant critical frequencies.
BW

Electronic Devices
Total Amplifier-Frequency Response
The overall response can be viewed on the Bode plotter by choosing the appropriate scales. The overall response for the BJT example given previously is shown.

Electronic Devices
Total Amplifier-Frequency Response
For multistage amplifiers, the individual stages have an effect on the overall response.
In general, with different cutoff frequencies, the dominant lower cutoff frequency is equal to the highest fcl; the dominant upper critical frequency is equal to lowest fcu.

and the upper critical frequency is given by

When the critical frequencies for multistage amplifiers are equal, the lower critical frequency is higher than any one as given by

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Roll-off

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Roll-off
The gain that occurs for the range of frequencies between the lower and upper critical frequencies.

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Roll-off
The gain that occurs for the range of frequencies between the lower and upper critical frequencies.
The frequency at which the response of an amplifier or filter is 3 dB less than at midrange.
The rate of decrease in the gain of an amplifier above or below the critical frequencies.

Electronic Devices
Key Terms-2

Decade

Bode Plot

Bandwidth

Electronic Devices
Key Terms-2

Decade

Bode Plot

Bandwidth
A ten times increase or decrease in the value of a quantity such as frequency.

Electronic Devices
Key Terms-2

Decade

Bode Plot

Bandwidth
A ten times increase or decrease in the value of a quantity such as frequency.
An idealized graph of the gain in dB verses frequency used to graphically illustrate the response of an amplifier or filter.

Electronic Devices
Key Terms-2

Decade

Bode Plot

Bandwidth
The characteristic of certain types of electronic circuits that specifies the usable range of frequencies that pass from input to output.
A ten times increase or decrease in the value of a quantity such as frequency.
An idealized graph of the gain in dB verses frequency used to graphically illustrate the response of an amplifier or filter.

Electronic Devices
Quiz Q1

1. For a CE amplifier, the emitter bypass capacitor affects the
a. low-frequency response
b. high-frequency response
c. both of the above
d. none of the above

Electronic Devices
Quiz Q2

2. For a CS amplifier, the gate-drain capacitance affects the
a. low-frequency response
b. high-frequency response
c. both of the above
d. none of the above

Electronic Devices
Quiz Q3

3. For an inverting amplifier, the Miller effect causes the equivalent capacitance to ground to appear
a. smaller for both Cin and Cout
b. smaller for Cin and larger for Cout
c. larger for Cin and smaller for Cout
d. larger for both Cin and Cout

Electronic Devices
Quiz Q4

4. For the CE amplifier shown, the output low-frequency response is determined by
a. (RC||RL) C3
b. (RC||RL) + C3
c. (RC+RL) C3
d. (RC+RL) + C3

Electronic Devices
Quiz Q5

5. For the CE amplifier shown, the resistor that is not part of the RC charge and discharge path for (C2) is
a. R1
<p</p[removed]

Electronic Devices

10th ed.

Chapter 10

Amplifier Frequency Response

Electronic Devices
Effect of Coupling Capacitors
Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier.

The equivalent circuit for C1 is a high-pass filter:

Electronic Devices
Effect of Coupling Capacitors
Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier.

The equivalent circuit for C1 is a high-pass filter:

Electronic Devices
Effect of Coupling Capacitors
Coupling capacitors are in series with the signal and are part of a high-pass filter network. They affect the low-frequency response of the amplifier.

The equivalent circuit for C1 is a high-pass filter:

C3 and (RC + RL) form another high-pass filter.

For the circuit shown, the equivalent low-pass filter for the input is simply C1 in series with RG because the gate input resistance is so high and can be ignored.

The equivalent high-pass filter for C2 is:

Question:
How would an emitter swamping resistor affect the response?

The equivalent high-pass filter for C2 is:

Question:
How would an emitter swamping resistor affect the response?
fc would be lower due to increased R.

Sometimes a designer will add an external parallel capacitor to deliberately reduce the high frequency response.

Electronic Devices
Miller’s Theorem

Miller’s theorem states that, for inverting amplifiers, the capacitance between the input and output is equivalent to separate input and output capacitances to ground.

Electronic Devices
Miller’s Theorem

Example:
What is the input capacitance for a 2N3904 inverting amplifier with a gain of 25? Assume the values of Cbc = 4 pF and Cbe = 6 pF.

Electronic Devices
The Decibel
Sometimes, 0 dB is assigned as a convenient reference level for comparison. Then, other power or voltage levels are shown with respect to 0 dB.

Ratio
Power gain, Ap
Voltage gain, Av

0.1
-10 dB
-20 dB

0.5
-3 dB
-6 dB

1
0 dB
0 dB

2
3 dB
6 dB

10
10 dB
20 dB

Ratio
Power gain, Ap
Voltage gain, Av

0.1
-10 dB
-20 dB

0.5
-3 dB
-6 dB

1
0 dB
0 dB

2
3 dB
6 dB

10
10 dB
20 dB

The -3 dB power gain corresponds to a power reduction of one-half. The frequency at which this occurs is referred to as the critical frequency.

For example, the input coupling capacitor forms a high-pass filter with the input resistance of the amplifier:

Electronic Devices
Low-Frequency Response
What is the lower cutoff frequency due to C1?

Example:
Assume re’ = 3.5 W and b = 200.

Electronic Devices
Low-Frequency Response
What is the lower cutoff frequency due to C1?

Solution:
Example:
Assume re’ = 3.5 W and b = 200.
RE1 is not bypassed, so it is added to re’. Then:

= 2.77 kW

Electronic Devices
Low-Frequency Response
What is the lower cutoff frequency due to C1?

Solution:
Example:
Assume re’ = 3.5 W and b = 200.
RE1 is not bypassed, so it is added to re’. Then:

= 2.77 kW

Electronic Devices
Low-Frequency Response
The bypass RC circuit response can be found by observing the charge/discharge paths.
For this circuit, there is one path through RE2 as shown in blue.

A second path goes through RE1, re’, and the parallel combination of bias and source resistances as shown in red (source resistance not shown).

Electronic Devices
Low-Frequency Response
The bypass RC circuit response can be found by observing the charge/discharge paths.
For this circuit, there is one path through RE2 as shown in blue.

A second path goes through RE1, re’, and the parallel combination of bias and source resistances as shown in red (source resistance not shown).
The total resistance of the paths can be found by:

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
Solution:
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).
= 79.7 W

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
Solution:
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).
= 79.7 W

Electronic Devices
Low-Frequency Response

Example:
What is the critical frequency due to the bypass RC circuit?
Solution:
(Assume Rs = 600 W and b = 200 and re’ = 2.6 W).
= 79.7 W

42.5 Hz

Example:
What is the critical frequency due to the input RC circuit?

Example:
What is the critical frequency due to the input RC circuit?
Solution:

1.6 Hz

Electronic Devices
The Bode Plot

Multisim has a fictitious instrument called the Bode plotter. This is the previous BJT amplifier.

Electronic Devices
The Bode Plot

Multisim has a fictitious instrument called the Bode plotter. This is the previous BJT amplifier.

Connect the IN of the plotter to a constant level to the left of the Thevenin source.

Electronic Devices
The Bode Plot

Multisim has a fictitious instrument called the Bode plotter. This is the previous BJT amplifier.

Set the cursor 3dB below the midband gain and read fc.

Electronic Devices
High-Frequency Response
Combining the capacitors in parallel and Thevenizing forms an equivalent basic RC low-pass filter:

Electronic Devices
High-Frequency Response
If there is an unbypassed emitter resistor (RE1 in this case), the Thevenin resistance is modified to

The bandwidth is measured between the dominant critical frequencies.
BW

and the upper critical frequency is given by

When the critical frequencies for multistage amplifiers are equal, the lower critical frequency is higher than any one as given by

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Roll-off

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Roll-off
The gain that occurs for the range of frequencies between the lower and upper critical frequencies.

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Electronic Devices
Key Terms-1

Midrange gain

Critical frequency

Electronic Devices
Key Terms-2

Decade

Bode Plot

Bandwidth

Electronic Devices
Key Terms-2

Decade

Bode Plot

Bandwidth
A ten times increase or decrease in the value of a quantity such as frequency.

Electronic Devices
Key Terms-2

Decade

Bode Plot

Electronic Devices
Key Terms-2

Decade

Bode Plot

Electronic Devices
Quiz Q1

1. For a CE amplifier, the emitter bypass capacitor affects the
a. low-frequency response
b. high-frequency response
c. both of the above
d. none of the above

Electronic Devices
Quiz Q2

2. For a CS amplifier, the gate-drain capacitance affects the
a. low-frequency response
b. high-frequency response
c. both of the above
d. none of the above

Electronic Devices
Quiz Q3

Electronic Devices
Quiz Q4

4. For the CE amplifier shown, the output low-frequency response is determined by
a. (RC||RL) C3
b. (RC||RL) + C3
c. (RC+RL) C3
d. (RC+RL) + C3

Electronic Devices
Quiz Q5

5. For the CE amplifier shown, the resistor that is not part of the RC charge and discharge path for (C2) is
a. R1
b. R2
c. RC
d. RE

Electronic Devices
Quiz Q6

6. The decibel is a ratio of two powers; for this reason the measurement unit is
a. the volt
b. the watt
c. the volt-amp
d. dimensionless

Electronic Devices
Quiz Q7

7. At the cutoff frequency for an amplifier, the power output compared to the midband power output is
a. -2 dB
b. -3 dB
c. +2 dB
d. +3 dB

Electronic Devices
Quiz Q8

8. The effect of an unbypassed emitter resistor on the upper cutoff frequency in a CE amplifier is
a. to increase fcu
b. to decrease fcu
c. no effect

Electronic Devices
Quiz Q9

9. The y-axis of a Bode Plot is used for the
a. frequency scale
b. power scale
c. voltage scale
d. decibel scale

Electronic Devices
Quiz Q10

10. The term bandwidth refers to those frequencies
a. between the lower and upper critical frequencies
b. above the upper critical frequency
c. below the lower critical frequency
d. none of the above

Electronic Devices
Answers
Answers:
1. a
2. b
3. d
4. c
5. c
6. d
7. b
8. b
9. d
10. a

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