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Essentials of Electrical and Computer Engineering

David V. Kerns, Jr., J. David Irwin

Chapter 12

Small-Signal Transisfor Amplifiers - all with Video Answers

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Chapter Questions

Problem 1

What is a small-signal transistor model?

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Problem 2

Define the midband frequency region. In this region what can be said about an amplifier's voltage gain?

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05:15

Problem 3

A $p-n$ junction diode has a forward bias applied of $0.68 \mathrm{~V}$ and is conducting $2 \mathrm{~mA}$. (a) Determine $I_o$. (b) Determine the static forward resistance. (c) Determine the ac small-signal resistance of the diode at room temperature.

Keshav Singh
Keshav Singh
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05:15

Problem 4

Determine the ac resistance of a silicon diode at room temperature that is conducting $4 \mu \mathrm{A}$.

Keshav Singh
Keshav Singh
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01:16

Problem 5

Two silicon diodes are connected in series and are conducting a dc current of $2 \mathrm{~mA}$; what is the ac resistance of the combination?

DW
David Walther
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01:30

Problem 6

The dc current through a silicon diode is doubled. What is the effect of this on the ac resistance of the diode?

Ajay Singhal
Ajay Singhal
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05:15

Problem 7

At room temperature, what is the ac resistance of a diode conducting $0.5 \mathrm{~A}$ ?

Keshav Singh
Keshav Singh
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Problem 8

A two-port network as illustrated in Figure 12.2 has the following parameters: $y_{11}=0$; $y_{12}=0 ; \quad y_{21}=3.5 \times 10^{-3} \mathrm{~S} ; y_{22}=1 \times 10^{-4} \mathrm{~S}$. If an external load resistance of $12 \mathrm{k} \Omega$ is connected to the output, what is the voltage gain of this network?

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02:33

Problem 9

A set of $h$ parameters are provided as follows:, $h_{11}=20 \mathrm{k} \Omega ; h_{12}=0 ; h_{21}=100 ;$ and $h_{22}=1 \times 10^{-5}$. If the output is connected to an external load resistance of $50 \mathrm{k} \Omega$, determine: (a) the network's input resistance, (b) the network's current gain, (c) the network's voltage gain, (d) the network's output resistance.

Prachita Kush
Prachita Kush
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Problem 10

A MOSFET in the common source configuration is modeled as a two-port network as illustrated in Figure 12.4. If $R_L=6 \mathrm{k} \Omega$, and $y_{11}=0 ; y_{12}=0 ; y_{21}=2 \times 10^{-3} \mathrm{~S}$; and $y_{22}=0$, determine the small-signal voltage gain of the amplifier.

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Problem 11

(a) Assume the simplified small-signal model for transistors shown in Figure 12.5 has $r_i=\infty, g_m=1.8 \times 10^{-3} \mathrm{~S}$, and $r_o=100 \mathrm{k} \Omega$. This device is placed in the circuit as shown in Figure P12.11. Calculate the small-signal voltage gain.
(b) In the amplifier circuit shown in Figure P12.11, calculate the small-signal voltage gain assuming $r_1=200 \mathrm{k} \Omega, g_m=$ $2.5 \times 10^{-3} \mathrm{~S}$, and $r_o=120 \mathrm{k} \Omega$.
Figure P12.11 can't copy

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Problem 12

For the $n$-channel enhancement-mode MOSFET with output curves of Figure P12.12, determine an approximate value for $g_m$ at (1) $Q$-point $Q_{P 1}$, and (2) $Q$-point $Q_{P 2}$.
Figure P12.12 can't copy

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Problem 13

For the MOSFET with output curves in Figure P12.12 (a) Determine the approximate value
Figure P12.12 can't copy
of $g_o$ for each $Q$-point. (b) Redraw the output curves of Figure P12.12 for a device with approximately the same $g_m$ values, but $g_o=1 \times 10^{-4} \mathrm{~S}$.

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Problem 14

Consider the common source circuit shown in Figure 12.11(a) with a transistor that has output curves in Figure P12.12, and (a) determine a new value for $R_2$ that will place the $Q$-point on the $V_{G S}=2.5 \mathrm{~V}$ curve. (b) Plot the dc load line to locate the $Q$-point. (c) Compute an approximate value for $g_m$ at this $Q$-point. (d) Draw a small-signal equivalent circuit for this amplifier. (e) Using the equivalent circuit, calculate the small-signal voltage gain.

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Problem 15

In the common source amplifier circuit in Figure P12.15, (a) draw a small signal equivalent circuit, (b) calculate the voltage gain. Assume that for this transistor, $g_m=3.0 \times 10^{-3} \mathrm{~S}$ and $g_o=1.66 \times 10^{-5} \mathrm{~S}$.
Figure P12.15 can't copy

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Problem 16

In the circuit in Figure P12.15, what value of $g_m$ would be required for the circuit to have a voltage gain of magnitude 10 ?

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Problem 17

The common gate $n$-channel enhancement mode MOSFET circuit shown in Figure 12.12(a) has new component values as follows: $R_S=1 \mathrm{k} \Omega, R_D=3 \mathrm{k} \Omega$, and $g_m$ for the transistor is determined to be $2 \times 10^{-3} \mathrm{~S}$; assume $r_o$ is infinite. (a) Draw a small-signal equivalent circuit. (b) Compute the small-signal voltage gain. (c) Determine the amplifier input resistance, $R_i$.

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00:50

Problem 18

If the value of $R_D$ is doubled in problem 12.17 , what is the new value of the small signal voltage gain?

Khoobchandra Agrawal
Khoobchandra Agrawal
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Problem 19

The common drain amplifier circuit shown in Figure P12.19 utilizes a transistor with $g_m=3.8 \mathrm{mS}$ and $R_S=4 \mathrm{k} \Omega$. (a) Compute the small-signal voltage gain. (b) If a different transistor is used with $g_m=10 \mathrm{mS}$, what is the new value of the voltage gain?
Figure P12.19 can't copy

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01:01

Problem 20

As shown in Figure 12.20, an amplifier has a voltage gain of 10 , and is driven by an input voltage source with an internal resistance of $20 \mathrm{k} \Omega$. Calculate the voltage gain of the entire circuit if the input resistance to the amplifier is
(a) $50 \mathrm{k} \Omega$,
(b) $100 \mathrm{k} \Omega$, (c) $1 \mathrm{M} \Omega$.
Figure P12.20 can't copy

Narayan Hari
Narayan Hari
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Problem 21

In order to maximize the voltage gain of an amplifier circuit, state whether each of these should be made high or low in value:
(a) Source resistance
(b) Amplifier input resistance

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02:00

Problem 22

If the internal resistance of a voltage source is $50 \Omega$, what is the required input resistance of the amplifier in order to only lose $10 \%$ of the signal amplitude at the input?

Narayan Hari
Narayan Hari
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Problem 23

An amplifier using a BJT common emitter configuration is shown in Figure P12.23. If the following parameters apply, calculate
(a) the input resistance of the amplifier and
(b) the small-signal voltage gain.
$$
r_{i b}=10 \mathrm{k} \Omega, \beta=120, r_o=200 \mathrm{k} \Omega .
$$
Figure P12.23 can't copy

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01:39

Problem 24

A BJT in a common emitter amplifier circuit is biased in the active region. The measured dc currents are $I_C=3 \mathrm{~mA}, I_B=15 \mu \mathrm{A}$; when $V_{C E}$ is increased $5 \mathrm{~V}, I_C$ increases $0.2 \mathrm{~mA}$. (a) Determine the small-signal model parameters for this transistor. (b) Construct a small-signal equivalent circuit for the amplifier assuming $R_{\text {Leq }}=8 \mathrm{k} \Omega$. (c) Calculate the small-signal voltage gain. (d) Calculate the amplifier's input resistance.

Chai Santi
Chai Santi
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01:21

Problem 25

Repeat problem 12.23 if $R_{\text {Leq }}=100 \mathrm{k} \Omega$.

Kajal Gautam
Kajal Gautam
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01:21

Problem 26

Repeat problem 12.24 if $I_B=10 \mu \mathrm{A}$.

Kajal Gautam
Kajal Gautam
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01:10

Problem 27

If the common emitter current gain of a BJT, $\beta$, is 150 , calculate the value of the common base current gain, $\alpha$.

Varsha Aggarwal
Varsha Aggarwal
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01:10

Problem 28

If the common base current gain, $\alpha$, of a BJT is 0.97 , calculate the value of common emitter current gain, $\beta$.

Varsha Aggarwal
Varsha Aggarwal
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Problem 29

Consider the circuit in Figure P12.29, assuming $\beta=80$ and $V_{B E}=0.7 \mathrm{~V}$. (a) Determine the dc bias currents, $I_C$ and $I_B$. (b) Construct a midband ac equivalent circuit. (c) Determine the small-signal voltage gain.
Figure P12.29 can't copy

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Problem 30

Repeat problem 12.29 with $\beta=180$ and $\mathrm{R}_{\mathrm{C}}=4 \mathrm{k} \Omega$.

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01:21

Problem 31

Repeat problem 12.29 with $R_2=4 \mathrm{k} \Omega$.

Kajal Gautam
Kajal Gautam
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Problem 32

In the circuit in Figure P12.32, the external load resistance is considered infinite. For the case where $\beta=50$, (a) Calculate the dc bias currents, $I_C$ and $I_B$. (b) Calculate the value of $V_{C E}$. (c) Construct a midband ac equivalent circuit. (d) Determine the small-signal voltage gain. (Assume $V_{B E}=0.7 \mathrm{~V}$.)
Figure P12.32 can't copy

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Problem 33

Repeat problem 12.32 if $V_{C C}=10 \mathrm{~V}$.

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01:28

Problem 34

A common emitter amplifier circuit has a transistor with $\beta=100$ and $r_{i b}=2 \mathrm{k} \Omega$. If the circuit provides $R_{\text {Leq }}=6 \mathrm{k} \Omega$, what is the small-signal voltage gain?

Prachita Kush
Prachita Kush
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01:11

Problem 35

A transistor with $\beta=50$ is placed in a common base amplifier circuit with $I_E=1 \mathrm{~mA}$ and $R_{\text {Leq }}=5 \mathrm{k} \Omega$. (a) What is the small-signal voltage gain? (b) Does this circuit invert the signal?

Brian Francisco
Brian Francisco
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Problem 36

Sketch the small-signal common base BJT model, assuming the output resistance is high enough to be ignored. If $r_{i e}=45 \Omega$ and $\alpha=0.98$, (a) determine the dc emitter current, $I_E$, in the bias circuit. (b) Find the dc base current, $I_B$. (c) Construct a small-signal equivalent circuit for an amplifier using this model and with $v_s$ as the voltage input source, $R_s=50 \Omega, R_{\text {Leq }}=2 \mathrm{k} \Omega, \quad$ and assume $R_i=r_{i e}$. (d) Determine the small-signal voltage gain, including any loss in the input circuit; that is, find $v_o / v_s$.

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Problem 37

The circuit in Figure $\mathrm{P} 12.37$ uses a transistor with $\beta=120$ and $V_{B E}=-0.6 \mathrm{~V}$. Find the small-signal voltage gain.
Figure P12.37 can't copy

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Problem 38

A transistor is placed in a common collector circuit with $I_E=2 \mathrm{~mA}$ and $R_{\text {Leq }}=500 \Omega$. Find the small-signal voltage gain.

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Problem 39

A transistor with a measured $\beta=60$ is placed in the circuit in Figure P12.39; assume $V_{B E}=0.7 \mathrm{~V}$. (a) Construct an ac equivalent circuit. (b) Determine the small-signal voltage gain.
Figure P12.39 can't copy

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Problem 40

A common base amplifier uses a transistor with $\alpha=0.97$. If $I_E$ is measured to be $1.3 \mathrm{~mA}$, and the total effective load resistance $R_{\text {Leq }}=2.5 \mathrm{k} \Omega$, what is the small-signal voltage gain?

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02:10

Problem 41

Determine the composite voltage gain of three voltage amplifiers cascaded together as shown in Figure 12.21 and with gains as follows: $A_{v 1}=40, A_{v 2}=50$, and $A_{v 3}=-20$.

Kajal Gautam
Kajal Gautam
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02:10

Problem 42

Repeat problem 12.41 if the voltage gains are: $A_{v 1}=30, A_{v 2}=80$, and $A_{v 3}=0.9$.

Kajal Gautam
Kajal Gautam
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Problem 43

Determine the current gain of the multi-stage current amplifier comprised of two stages, $A_{i 1}=30, A_{i 2}=-15$.

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02:10

Problem 44

(a) Express the voltage gains of each of the stages in problem 12.41 in decibels. (b) Compute the gain for the multi-stage amplifier in $\mathrm{db}$.

Kajal Gautam
Kajal Gautam
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02:10

Problem 45

The voltage gain of a multi-stage amplifier is measured to be $100 \mathrm{db}$. The gain of the first stage was calculated as $A_{v 1}=8$. Determine the total gain of the remaining stages.

Kajal Gautam
Kajal Gautam
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