PROBLEMS

Computer Simulation Problems 9.5 A particular small-geometry BJT has fT of 10 GHz and
Cμ = 0.1 pF when operated at IC = 1.0 mA. What is Cπ in
Problems identified by this icon are intended to
this situation? Also, find gm . For β = 120, find rπ and fβ .
demonstrate the value of using SPICE simulation to verify
hand analysis and design, and to investigate important issues 9.6 Starting from the expression of fT for a MOSFET,
such as gain–bandwidth trade-off. Instructions to assist in gm
setting up simulations for all the indicated problems can be fT =
2π(Cgs + Cgd )
found in the corresponding files on the website. Note that if
a particular parameter value is not specified in the problem and making the approximation that Cgs  Cgd and that the
statement, you are to make a reasonable assumption. overlap component of Cgs is negligibly small, show that

1.5 μn ID
fT 
π L 2Cox WL
Section 9.1: High-Frequency Transistor Models
Thus note that to obtain a high fT from a given device, it must
9.1 Refer to the MOSFET high-frequency model in
be operated at a high current. Also note that faster operation
Fig. 9.4(a). Evaluate the model parameters for an NMOS
is obtained from smaller devices.
transistor operating at ID = 200 µA, VSB = 0.35 V, and
VDS = 0.7 V. The MOSFET has W = 12 µm, L = 0.3 µm, 9.7 Starting from the expression for the MOSFET
2 1/2
tox = 4 nm, μn = 450 cm /V·s, γ = 0.5 V , 2φ f = 0.85 V, unity-gain frequency,
−1
λ = 0.1 V , V0 = 0.9 V, Csb0 = Cdb0 = 5 fF, and gm
Lov = 0.03 µm. [Recall that gmb = χ gm , where χ = fT =
   −11
2π(Cgs + Cgd )
γ / 2 2φf + VSB , and that ox = 3.45 × 10 F/m.]
and making the approximation that Cgs  Cgd and that the
9.2 Find fT for a MOSFET operating at ID = 200 µA and overlap component of Cgs is negligibly small, show that for
VOV = 0.3 V. The MOSFET has Cgs = 25 fF and Cgd = 5 fF. an n-channel device
9.3 A particular BJT operating at IC = 0.5 mA has Cμ = fT 
3μn VOV
1 pF, Cπ = 8 pF, and β = 100. What are fT and fβ for this 4π L2
situation? Observe that for a given channel length, fT can be increased
by operating the MOSFET at a higher overdrive voltage.
9.4 Measurement of β of an npn transistor at 50 MHz
Evaluate fT for devices with L = 0.5 µm operated at over-
shows that |β| = 10 at IC = 0.2 mA and 12 at IC = 1.0 mA. 2
drive voltages of 0.2 V and 0.4 V. Use μn = 450 cm /V·s.
Furthermore, Cμ was measured and found to be 0.1 pF. Find
fT at each of the two collector currents used. What must τF 9.8 Find the intrinsic gain A0 and the unity-gain frequency
and Cje be? fT of an n-channel transistor fabricated in a 0.13-µm

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 741

CHAPTER 9
Transistor IE (mA) re () gm (mA/V) rπ (k) β0 fT (MHz) Cμ (pF) Cπ (pF) fβ (MHz)

(a) 2 100 500 2

(b) 25 2 10.7 4
(c) 2.5 100 500 10.7
(d) 10 100 500 2
(e) 0.1 100 150 2

PROBLEMS
(f) 1 10 500 2
(g) 800 1 9 80

2 D 9.15 In the circuit of Fig. P9.15, the voltage amplifier is

CMOS process for which Lov = 0.1 L, μn = 400 cm /V·s,
 ideal (i.e., it has an infinite input resistance and a zero output
and VA = 5 V/µm. The device is operated at VOV =
resistance).
0.2 V. Find A0 and fT for devices with L = Lmin ,
2Lmin , 3Lmin , 4Lmin , and 5Lmin . Present your results in a table. (a) Use the Miller approach to find an expression for the
3μn VOV input capacitance Cin in terms of A and C.
(Hint: For fT , use the approximate expression fT  .)
4π L2 (b) Use the expression for Cin to obtain the transfer function
9.9 For the transistor described in Problem 9.3, Cπ includes Vo (s)/Vsig (s).
a relatively constant depletion-layer capacitance of 2 pF. If (c) If Rsig = 1 k, and the gain Vo /Vsig is to have a dc value of
the device is operated at IC = 0.25 mA, what does its fT 40 dB and a 3-dB frequency of 100 kHz, find the values
become? required for A and C.
(d) Sketch a Bode plot for the gain and use it to deter-
9.10 An npn transistor is operated at IC = 1 mA and
mine the frequency at which its magnitude reduces to
VCB = 2 V. It has β 0 = 100, VA = 50 V, τF = 30 ps,
unity.
Cje0 = 20 fF, Cμ0 = 30 f F, V0c = 0.75 V, and mCBJ = 0.5.
Sketch the complete hybrid-π model, and specify the values
of all its components. Also, find fT . C

9.11 For a BJT whose unity-gain bandwidth is 5 GHz

Rsig
and β 0 = 200, at what frequency does the magnitude of β

become 50? What is fβ ? 
Vi A
  
*9.12 Complete the table entries at the top of this page for Vsig  
transistors (a) through (g), under the conditions indicated. Vo

Section 9.2: High-Frequency Response of Cin
CS and CE Amplifiers
Figure P9.15
9.13 In a multistage amplifier, the output resistance of stage
1 is found to be 10 k. The succeeding stage, stage 2, has an 9.16 Reconsider Example 9.1 for the situation in which the
input impedance that is mostly capacitive with a value of 10 transistor is replaced by one whose width W is half that of the
pF. Find the frequency of the pole that arises as a result of original transistor while the bias current remains unchanged.
the interconnection between these two amplifier stages. Find modified values for all the device parameters along with
AM , fH , and the gain–bandwidth product, GB. Contrast this
9.14 A common-source amplifier is fed with a signal source
with the original design by calculating the ratios of new value
having a resistance Rsig = 200 k and feeds a load resistance
to old for W, VOV , gm , Cgs , Cgd , Cin , AM , fH , and GB.
RL = 20 k. The MOSFET is operating at gm = 4 mA/V and
has ro = 20 k. The device capacitances are Cgs = 25 fF and 9.17 An IC CS amplifier is fed from a signal source
Cgd = 5 fF. Find the midband gain AM , the 3-dB frequency fH , with a negligibly small resistance and has a total effective

and the frequency of the transmission zero. load resistance RL = 20 k. The MOSFET is operating at
 742 Chapter 9 Frequency Response

gm = 2 mA/V and has a Cgd = 10 fF. The total capacitance 9.20 Consider an ideal voltage amplifier with a gain of
PROBLEMS

CL at the output node is 100 fF. Find the midband gain 0.9 V/V, and a resistance R = 100 k connected in the feed-
AM , the 3-dB frequency fH , the unity-gain frequency ft , back path—that is, between the output and input terminals.
the frequency of the transmission zero fz , and the gain at Use Miller’s theorem to find the input resistance of this
very-high frequencies. Sketch and clearly label the Bode plot circuit.
for the gain magnitude.
9.21 The amplifiers listed below are characterized by the
9.18 A common-emitter amplifier is measured at midband descriptor (A, C), where A is the voltage gain from input
CHAPTER 9

and found to have a gain of −50 V/V between base and to output and C is a capacitor connected between input and
collector. If Cπ = 10 pF, Cμ = 1 pF, and the effective source output. For each, find the equivalent capacitances at the input

resistance Rsig = 5 k [refer to Fig. 9.13(c)], find Cin and the and at the output as provided by the use of Miller’s theorem:
3-dB frequency fH .
(a) –1000 V/V, 1 pF
9.19 The discrete-circuit common-emitter amplifier in Fig. (b) –10 V/V, 10 pF
P9.19 has Rsig = 10 k, RB1 = 68 k, RB2 = 27 k, RE = (c) –1 V/V, 10 pF
2.2 k, RC = 4.7 k, and RL = 10 k. The transistor is (d) +1 V/V, 10 pF
operating at a dc collector current of 0.8 mA and has β = 160, (e) +10 V/V, 10 pF
fT = 1 GHz, and Cμ = 0.5 pF. Give the high-frequency
Note that the input capacitance found in case (e) can be used
small-signal equivalent-circuit model of the amplifier assum-
to cancel the effect of other capacitance connected from input
ing the coupling and bypass capacitors behave as short
to ground. In (e), what capacitance can be canceled?
circuits, and neglecting ro . Find AM and fH .

VCC

RB1 RC CC2
Vo
Rsig CC1

RL
Vsig  RB2
 RE
CE

Figure P9.19

A Rin Vi Vo Vo /Vsig

10 V/V
100 V/V
1000 V/V
10,000 V/V

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 743

CHAPTER 9
9.22 A signal source modeled by its Norton’s equivalent
circuit has Rsig = 1 M. It feeds an amplifier whose input
impedance consists of a 1-M resistance in parallel with a Q3 Q2
0.1-pF capacitance. Find the frequency of the pole that arises
as a result of this connection.

9.23 In a particular common-source amplifier for which the IBIAS


midband voltage gain between gate and drain (i.e., −gm RL ) Vo

PROBLEMS
is −39 V/V, the NMOS transistor has Cgs = 1.0 pF and
Cgd = 0.1 pF. What input capacitance would you expect?
For what range of signal-source resistances can you expect Rsig
the 3-dB frequency to exceed 1 MHz? Neglect the effect Q1
of RG .
Vsig
9.24 An ideal voltage amplifier having a voltage gain of
–1000 V/V has a 0.2-pF capacitance connected between its
output and input terminals. What is the input capacitance
of the amplifier? If the amplifier is fed from a voltage Figure P9.27
source Vsig having a resistance Rsig = 1 k, find the transfer
function Vo /Vsig as a function of the complex-frequency 9.28 An IC CS amplifier fed with a signal source of a neg-
variable s and hence the 3-dB frequency fH and the unity-gain ligibly small resistance Rsig is found to have a low-frequency
frequency ft . gain of −50 V/V. The gain falls off with frequency at −20
dB/decade and reaches zero dB at 1 GHz. The gain levels off
D 9.25 Design a CS amplifier for which the MOSFET is at higher frequencies at −20 dB. If the MOSFET is operating
operated at gm = 5 mA/V and has Cgs = 5 pF and Cgd = 1 pF. with gm = 2 mA/V, estimate the values of Cgd and CL . Also
The amplifier is fed with a signal source having Rsig = 1 k. give the value of the 3-dB frequency fH .

What is the largest value of RL for which the upper 3-dB
frequency is at least 6 MHz? What is the corresponding D 9.29 A common-source amplifier fed with a low-
value of midband gain and gain–bandwidth product? If the resistance signal source and operating with gm = 2 mA/V
specification on the upper 3-dB frequency can be relaxed has a unity-gain frequency of 2 GHz. What additional
by a factor of 3, that is, to 2 MHz, what can AM and GB capacitance must be connected to the drain node to reduce
become? ft to 1 GHz?
9.30 It is required to analyze the high-frequency response
D *9.26 In a CS amplifier, such as that in Fig. 9.37(a),
of the CMOS amplifier shown in Fig. P9.27 for the
the resistance of the source Rsig = 100 k, amplifier
case Rsig = 0. The dc bias current is 100 µA. For Q1 ,
input resistance (which is due to the biasing network) 2
μn Cox = 90 µA/V , VA = 12.8 V, W/L = 100 µm/1.6 µm,
Rin = 100 k, Cgs = 1 pF, Cgd = 0.2 pF, gm = 3 mA/V,
Cgs = 0.2 pF, Cgd = 0.015 pF, and   Cdb = 20 fF. For Q2 ,
ro = 50 k, RD = 8 k, and RL = 10 k. Determine the
Cgd = 0.015 pF, Cdb = 36 fF, and VA  = 19.2 V. For simplic-
expected 3-dB cutoff frequency fH and the midband gain.
ity, assume that the signal voltage at the gate of Q2 is zero.
In evaluating ways to double fH , a designer considers the
Find the low-frequency gain, the frequency of the pole, and
alternatives of changing either RL or Rin . To raise fH as
the frequency of the zero. (Hint: The total capacitance at the
described, what separate change in each would be required?
output mode = Cdb1 + Cdb2 + Cgd2 ).
What midband voltage gain results in each case?
9.31 For a CE amplifier represented by the equivalent
9.27 Consider the integrated-circuit CS amplifier in
circuit in Fig. 9.13(b), let Rsig = 10 k, Cπ = 10 pF, Cμ =
Fig. P9.27 for the case IBIAS = 100 µA, Q2 and Q3 are
2 0.5 pF, gm = 40 mA/V, ro = 100 k, RL = 10 k, and β =
matched, and Rsig = 20 k. For Q1 : μn Cox = 400 µA/V ,
100. Find the midband gain and the 3-dB frequency fH .
VA = 5 V, W/L = 5 µm/0.4 µm, Cgs = 30 fF, and Cgd = 5 fF.
For Q2 : |VA | = 5 V. Neglecting the effect of the capacitance *9.32 We want to investigate the high-frequency response
inevitably present at the output node, find the low-frequency of the CE amplifier when it is fed with a relatively large
gain, the 3-dB frequency fH , and the frequency of the zero fZ . source resistance Rsig . Refer to the amplifier in Fig. 9.13(a)
 744 Chapter 9 Frequency Response

and to its high-frequency, equivalent-circuit model and the which the gain reduces to unity. Sketch a Bode plot for the
PROBLEMS

 
analysis shown. Let Rsig  rπ , gm RL  1, and gm RL Cμ  Cπ . gain magnitude.
Under these conditions, show that:
*9.35 Figure P9.35 shows an ideal voltage amplifier with

(a) the midband gain AM  − βRL /Rsig a gain of +2 V/V (usually implemented with an op amp

(b) the upper 3-dB frequency fH  1/2π Cμ βRL connected in the noninverting configuration) and a resistance
(c) the gain–bandwidth product | AM | fH  1/2π Cμ Rsig R connected between output and input.
CHAPTER 9

Evaluate this approximate value of the gain–bandwidth (a) Using Miller’s theorem, show that the input resistance
product if Rsig = 25 k and Cμ = 1 pF. Now, if the transistor Rin = −R.
has β = 100, find the midband gain and fH for the two cases (b) Use Norton’s theorem to replace Vsig , Rsig , and Rin
 
RL = 25 k and RL = 2.5 k. On the same coordinates, with a signal current source and an equivalent parallel
sketch Bode plots for the gain magnitude versus frequency resistance. Show that by selecting Rsig = R, the equivalent
for the two cases. What fH is obtained when the gain is unity? parallel resistance becomes infinite and the current IL

What value of RL corresponds? into the load impedance ZL becomes Vsig /R. The circuit
then functions as an ideal voltage-controlled current
*9.33 Figure P9.33 shows a diode-connected transistor with
source with an output current IL .
the bias circuit omitted. Utilizing the BJT high-frequency,
(c) If ZL is a capacitor C, find the transfer function Vo /Vsig
hybrid-π model with ro = ∞, derive an expression for Zi (s)
and show it is that of an ideal noninverting integrator.
as a function of re and Cπ . Find the frequency at which the
impedance has a phase angle of 45° for the case in which the
BJT has fT = 400 MHz and the bias current is relatively high, Rsig
so that Cπ  Cμ . What is the frequency when the bias current 2 Vo
IL
is reduced so that Cπ  Cμ ? Assume α = 1.
Vsig  ZL

R

Rin

Figure P9.35

9.36 Use Miller’s theorem to investigate the performance of

the inverting op-amp circuit shown in Fig. P9.36. Assume the
op amp to be ideal except for having a finite differential gain,
Figure P9.33 A. Without using any knowledge of op-amp circuit analysis,
find Rin , Vi , Vo , and Vo /Vsig , for each of the following values
9.34 Consider an active-loaded common-emitter amplifier. of A: 10 V/V, 100 V/V, 1000 V/V, and 10,000 V/V. Assume
Let the amplifier be fed with an ideal voltage source Vsig = 1 V. Present your results in the table on page 742.
Vi . Assume that the load current source has a very high
resistance and that there is a capacitance CL present between
10 k
the output node and ground. This capacitance represents the
sum of the input capacitance of the subsequent stage and
1 k
the inevitable parasitic capacitance between collector and 
ground. Show that the voltage gain is given by 
Vi
   
Vo 1 − s Cμ /gm Vsig  
= −gm ro   
Vi 1 + s CL + Cμ ro Vo

If the transistor is biased at IC = 200 µA and VA = 100 V, Rin
Cμ = 0.2 pF, and CL = 1 pF, find the dc gain, the 3-dB
frequency, the frequency of the zero, and the frequency at Figure P9.36

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 745

D 9.41 For a CS amplifier with gm = 5 mA/V, Cgs = 5 pF,

CHAPTER 9
*9.37 The amplifier shown in Fig. P9.37 has

Rsig = RL = 1 k, RC = 1 k, RB = 47 k, β = 100, Cgd = 1 pF, CL = 5 pF, Rsig = 10 k, and RL = 10 k, find
Cμ = 0.8 pF, and fT = 600 MHz. Assume the coupling τH and fH . What is the percentage of τH that is caused by the
capacitors to be very large. interaction of Rsig with the input capacitance? To what value
must Rsig be lowered in order to double fH ?
1.5 V
9.42 A common-emitter amplifier has Cπ = 10 pF, Cμ =

0.3 pF, CL = 3 pF, gm = 40 mA/V, β = 100, RL = 5 k, and

PROBLEMS
Rsig = 1 k. Find the midband gain AM and an estimate of
RC the 3-dB frequency fH using the Miller effect. Also, obtain
CC1 CC2
Rsig RB another estimate of fH using the method of open-circuit time
Vo constants. Which of the two estimates would you consider to
be more realistic, and why?
Vsig 
 RL
9.43 An amplifier with a dc gain of 60 dB has a single-pole,
high-frequency response with a 3-dB frequency of 100 kHz.
Rin
(a) Give an expression for the gain function A(s).
Figure P9.37 (b) Sketch Bode diagrams for the gain magnitude and phase.
(c) What is the gain–bandwidth product?
(a) Find the dc collector current of the transistor. (d) What is the unity-gain frequency?
(b) Find gm and rπ . (e) If a change in the amplifier circuit causes its transfer
(c) Neglecting ro , find the midband voltage gain from base function to acquire another pole at 1 MHz, sketch the
to collector (neglect the effect of RB ). resulting gain magnitude and specify the unity-gain
(d) Use the gain obtained in (c) to find the component of Rin frequency. Note that this is an example of an amplifier
that arises as a result of RB . Hence find Rin . with a unity-gain bandwidth that is different from its
(e) Find the overall gain at midband. gain–bandwidth product.
(f) Find Cin . 9.44 A discrete-circuit CS amplifier is modeled by the
(g) Find fH . circuit of Fig. 9.16 augmented with a bias-resistance RG
between gate and ground. If gm = 5 mA/V, Rsig = 100 k,

Section 9.3: The Method of Open-Circuit Time RG = 500 k, RL = 10 k, Cgs = 1 pF, Cgd = 0.2 pF, and
Constants CL = 20 pF, find the midband gain and estimate fH using the
method of open-circuit time constants.
9.38 A direct-coupled amplifier has a low-frequency gain of
40 dB, poles at 2 MHz and 20 MHz, a zero on the negative 9.45 Consider the high-frequency response of an amplifier
real axis at 200 MHz, and another zero at infinite frequency. consisting of two identical transconductance amplifier stages
Express the amplifier gain function in the form of Eqs. (9.56) in cascade, each with an input resistance of 10 k and an
and (9.57), and sketch a Bode plot for the gain magnitude. output resistance of 2 k. The two-stage amplifier is driven
What do you estimate the 3-dB frequency fH to be? from a 10-k source and drives a 1-k load. Associated with
each stage is a parasitic input capacitance (to ground) of 10
9.39 An IC CS amplifier has gm = 2 mA/V, Cgs = 30 fF, pF and a parasitic output capacitance (to ground) of 2 pF.
 
Cgd = 5 fF, CL = 30 fF, Rsig = 10 k, and RL = 20 k. Parasitic capacitances of 10 pF and 7 pF also are associated
Use the method of open-circuit time constants to obtain an with the signal-source and load connections, respectively.
estimate for fH . Also, find the frequency of the transmission For this circuit, find the three poles and estimate the 3-dB
zero, fZ . frequency fH .
9.40 A CS amplifier that can be represented by the equiva-
D 9.46 For the CS amplifier in Example 9.5, find the value
lent circuit of Fig. 9.16 has Cgs = 2 pF, Cgd = 0.1 pF, CL =
 of the additional capacitance to be connected at the output
2 pF, gm = 4 mA/V, and Rsig = RL = 20 k. Find the midband
node in order to lower fH to 40 MHz.
gain AM , the input capacitance Cin using the Miller effect,
and hence an estimate of the 3-dB frequency fH . Also, obtain 9.47 Use the method of open-circuit time constants to find
another estimate of fH using open-circuit time constants. fH for a CS amplifier for which gm = 1.5 mA/V, Cgs = Cgd =
Which of the two estimates is more appropriate and why? 0.2 pF, ro = 20 k, RL = 12 k, and Rsig = 100 k for the
 746 Chapter 9 Frequency Response

2
following cases: (a) CL = 0, (b) CL = 10 pF, and (c) CL = 200 µA/V , W/L = 50, Cgd = 0.1 pF, and CL = 1 pF.
PROBLEMS

50 pF. Compare with the value of fH obtained using the Miller Assuming that RL = Ro , determine the overdrive voltage and
effect. the drain current at which the MOSFETs should be operated.
Find the unity-gain frequency and the 3-dB frequency. If the
9.48 Consider a CS amplifier loaded in a current source with
cascode transistor is removed and RL remains unchanged,
an output resistance equal to ro of the amplifying transistor.
what will the dc gain, the 3-dB frequency, and the unity-gain
The amplifier is fed from a signal source with Rsig = ro /2. The
frequency become?
transistor is biased to operate at gm = 2 mA/V and ro = 20 k;
CHAPTER 9

Cgs = Cgd = 0.1 pF. Use the Miller effect to determine an 9.54 Consider a bipolar cascode amplifier biased at a current
estimate of fH . Repeat for the following two cases: (i) the of 1 mA. The transistors used have β = 100, ro = 100 k,
bias current I in the entire system is reduced by a factor of 4, Cπ = 10 pF, Cμ = 2 pF, Ccs = 0, and rx = 50 . The amplifier
and (ii) the bias current I in the entire system is increased by is fed with a signal source having Rsig = 5 k. The load
a factor of 4. Remember that both Rsig and RL will change as resistance RL = 2 k. Find the low-frequency gain AM , and
ro changes. estimate the value of the 3-dB frequency fH .

9.49 Consider the CE amplifier whose equivalent circuit is 9.55 Sketch the high-frequency equivalent circuit of a CB
shown in Fig. 9.13(b) but with a capacitance CL connected amplifier fed from a signal generator characterized by Vsig
across the output terminals. Let Rsig = 5 k, gm = 20 mA/V, and Rsig and feeding a load resistance RL in parallel with a

β = 100, Cπ = 10 pF, Cμ = 1 pF, RL = 5 k, and CL = 10 capacitance CL . Neglect ro .
pF. Find AM and fH .
(a) Show that the circuit can be separated into two parts: an
input part that produces a pole at
Section 9.4: High-Frequency Response of
Common-Gate and Cascode Amplifiers 1
fP1 =  
2π Cπ Rsig  re
9.50 A CG amplifier is specified to have Cgs = 4 pF, Cgd =
0.2 pF, CL = 2 pF, gm = 5 mA/V, Rsig = 1 k, and RL = and an output part that forms a pole at
10 k. Neglecting the effects of ro , find the low-frequency
gain Vo /Vsig , the frequencies of the poles fP1 and fP2 , and hence 1
fP2 =
an estimate of the 3-dB frequency fH . 2π(Cμ + CL )RL

9.51 An IC CG amplifier is fed from a signal source with Note that these are the bipolar counterparts of the MOS
Rsig = ro /2, where ro is the MOSFET output resistance. It expressions in Eqs. (9.76) and (9.77).
has a current-source load with an output resistance equal (b) Evaluate fP1 and fP2 and hence obtain an estimate for
to ro . The MOSFET is operated at ID = 100 µA and has fH for the case Cπ = 10 pF, Cμ = 1 pF, CL = 1 pF,
gm = 1.5 mA/V, VA = 10 V, Cgs = 0.2 pF, Cgd = 0.015 pF, IC = 1 mA, Rsig = 1 k, and RL = 10 k. Also, find fT
and Cdb = 20 fF. As well, the current-source load provides of the transistor.
an additional 30 fF capacitance at the output node. Find fH .
9.56 Consider a CG amplifier loaded in a resistance RL =
9.52 Find the dc gain and the 3-dB frequency of a MOS ro and fed with a signal source having a resistance Rsig =
cascode amplifier operated at gm = 2 mA/V and ro = 20 k. ro /2. Also let CL = Cgs . Use the method of open-circuit
The MOSFETs have Cgs = 20 fF, Cgd = 5 fF, and Cdb = 5 fF. time constants to show that for gm ro  1, the upper 3-dB
The amplifier is fed from a signal source with Rsig = 100 k frequency is related to the MOSFET fT by the approximate
and is connected to a load resistance of 1 M. There is also expression
 
a load capacitance CL of 20 fF. fH = fT gm ro
D 9.53 Design a cascode amplifier to provide a dc gain 9.57 For the CG amplifier in Example 9.9, how much
of 74 dB when driven with a low-resistance generator and additional capacitance should be connected between the
utilizing NMOS transistors for which VA = 10 V, μn Cox = output node and ground to reduce fH to 200 MHz?

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 747

CHAPTER 9
9.58 Consider a CG amplifier driven by a current-source *9.62 In this problem we consider the frequency response
signal Isig having a predominantly capacitive source of the bipolar cascode amplifier in the case that ro can be
impedance; that is, the signal source can be represented neglected.
by a current source Isig in parallel with a capacitance Csig .
(a) Refer to the circuit in Fig. 9.22, and note that the total
Neglecting ro of the MOSFET, find an expression for the
resistance between the collector of Q1 and ground will be
transfer function Vo / Isig obtained when the load consists of
equal to re2 , which is usually very small. It follows that
a resistance RL in parallel with a capacitance CL . Hence find
the pole introduced at this node will typically be at a very

PROBLEMS
expressions for the frequencies of the two poles.
high frequency and thus will have negligible effect on fH .
9.59 (a) Consider a CS amplifier having Cgd = 0.3 pF, It also follows that at the frequencies of interest the gain
Rsig = RL = 20 k, gm = 4 mA/V, Cgs = 2 pF, CL (including from the base to the collector of Q1 will be −gm1 re2  −1.
Cdb ) = 1 pF, Cdb = 0.2 pF, and ro = 20 k. Find the Use this to find the capacitance at the input of Q1 and
low-frequency gain AM , and estimate fH using open-circuit hence show that the pole introduced at the input node
time constants. Hence determine the gain–bandwidth will have a frequency
product.
1
(b) If a CG stage utilizing an identical MOSFET is cascaded fP1   
2π Rsig Cπ 1 + 2Cμ1
with the CS transistor in (a) to create a cascode amplifier,
determine the new values of AM , fH , and gain–bandwidth Then show that the pole introduced at the output node
product. Assume RL remains unchanged. will have a frequency
9.60 (a) Show that introducing a cascode transistor to an IC 1
CS amplifier whose bandwidth is limited by the interaction fP2   
2π RL CL + Ccs2 + Cμ2
of Rsig and the input capacitance, and whose load resistance
is equal to ro , increases the dc gain by approximately a factor (b) Evaluate fP1 and fP2 , and use the sum-of-the-squares
of 2 and fH by the factor N, formula to estimate fH for the amplifier with I = 1 mA,
Cπ = 10 pF, Cμ = 2 pF, Ccs = CL = 0, β = 100, RL = 2
1 k, and rx = 0 in the following two cases:
Cgs + (gm ro )Cgd
N= 2 (i) Rsig = 1 k
Cgs + 3 Cgd (ii) Rsig = 10 k

Assume that the bandwidth of the cascode amplifier is 9.63 A BJT cascode amplifier uses transistors for which β =
primarily determined by the input circuit. 100, VA = 100 V, fT = 1 GHz, and Cμ = 0.1 pF. It operates
(b) If Cgd = 0.1 Cgs and the dc gain of the CS amplifier is 50, at a bias current of 0.1 mA between a source with Rsig = rπ
what is the value of N? and a load RL = βro . Let CL = Ccs = 0. Find the overall
2
(c) If VA = 10 V, μn Cox = 400 µA/V , and W/L = 10, voltage gain at dc. By evaluating the various components
find VOV and ID at which the transistors must be of τH show that the pole introduced at the output node is
operating. dominant. Find its frequency and hence an estimate of fH and
the gain–bandwidth product.
9.61 (a) For an integrated-circuit MOS cascode amplifier
fed with a source having a very small resistance and loaded Section 9.5: High-Frequency Response of
in a resistance equal to its Ro , use the expression for the Source and Emitter Followers
unity-gain bandwidth in Fig. 9.21 to show that
9.64 A source follower has gm = 5 mA/V, gmb = 0, ro =

2μn Cox (W/L)  20 k, Rsig = 20 k, RL = 2 k, Cgs = 2 pF, Cgd = 0.1 pF,
ft = ID and CL = 1 pF. Find AM , Ro , fZ , the frequencies of the two
2π(CL + Cgd )
poles, and an estimate of fH .
2
(b) For μn Cox = 400 µA/V , W/L = 20, CL = 20 fF, Cgd = 9.65 Refer to Fig. 9.23(c). In situations in which Rsig is
5 fF, and VA = 10 V, provide in table form ft (GHz), VOV (V), large, the high-frequency response of the source follower is
gm (mA/V), ro (k), Ro (M), AM (V/V), and fH (MHz) for determined by the low-pass circuit formed by Rsig and the
ID = 100 µA, 200 µA, and 500 µA. input capacitance. An estimate of Cin can be obtained by
 748 Chapter 9 Frequency Response

using the Miller approximation to replace Cgs with an input (d) If, in a different situation, the amplifier is fed symmetri-
PROBLEMS

capacitance Ceq = Cgs (1 − K) where K is the gain from gate cally with a signal source of 40 k resistance (i.e., 20 k

to source. Using the low-frequency value of K = gm RL /(1 + in series with each gate terminal), use the open-circuit

gm RL ) find Ceq and hence Cin and an estimate of fH . time-constants method to estimate fH .

9.66 For an emitter follower biased at IC = 1 mA, having 9.71 A MOS differential amplifier is biased with a current
Rsig = RL = 1 k, and using a transistor specified to have source having an output resistance RSS = 100 k and an
fT = 2 GHz, Cμ = 0.1 pF, CL = 0, β = 100, and VA = 20 V, output capacitance CSS = 1 pF. If the differential gain is
CHAPTER 9

evaluate the low-frequency gain AM , the frequency of the found to have a dominant pole at 20 MHz, what is the 3-dB
transmission zero, the pole frequencies, and an estimate of frequency of the CMRR?
the 3-dB frequency fH .
9.72 A current-mirror-loaded MOS differential amplifier
9.67 Using the expression for the source follower fH in is biased with a current source I = 0.2 mA. The two
Eq. (9.107) show that for situations in which CL = 0, Rsig is NMOS transistors of the differential pair are operating
large, and RL is small, at VOV = 0.2 V, and the PMOS devices of the mirror  are
1
fH    operating at |VOV | = 0.2 V. The Early voltage VAn = VAp  =
Cgs
2π Rsig Cgd + 10 V. The total capacitance at the input node of the mirror is
1 + gm RL 0.1 pF and that at the output node of the amplifier is 0.2 pF.
Find fH for the case Rsig = 100 k, RL = 2 k, ro = 20 k, Find the dc value and the frequencies of the poles and zero
gm = 5 mA/V, Cgs = 12 pF, and Cgd = 0.1 pF. of the differential voltage gain.

9.68 A source follower has a maximally flat gain response 9.73 The differential gain of a MOS amplifier is 100 V/V
with a dc gain of 0.8 and a 3-dB frequency of 1 MHz. Give with a dominant pole at 10 MHz. The common-mode gain
its transfer function. is 0.1 V/V at low frequencies and has a transmission zero at
1 MHz. Sketch a Bode plot for the CMRR.
9.69 A discrete-circuit source follower driven with Rsig =
100 k has Cgs = 10 pF, Cgd = 1 pF, CL = 10 pF, gmb = 0, and 9.74 A differential amplifier is biased by a current source
ro very large. The transfer function of the source follower is having an output resistance of 1 M and an output capaci-
measured as RL is varied. At what value of RL will the transfer tance of 1 pF. The differential gain exhibits a dominant pole
function be maximally flat? At this value of RL the dc gain at 2 MHz. What are the poles of the CMRR?
is found to be 0.9 V/V. What is the 3-dB frequency? What is
the value of gm at which the source follower is operating? 9.75 In a particular MOS differential amplifier design, the
bias current I = 100 µA is provided by a single transistor
operating at VOV = 0.4 V with VA = 40 V and output
Section 9.5: High-Frequency Response capacitance CSS of 100 fF. What is the frequency of the
of Differential Amplifiers  
common-mode gain zero fZ at which Acm begins to rise
9.70 A MOSFET differential amplifier such as that shown above its low-frequency value? To meet a requirement for
in Fig. 9.26(a) is biased with a current source I = 400 µA. reduced power supply, you consider reducing VOV to 0.2 V
 2
The transistors have W/L = 16, kn = 400 µA/V , VA = 20 V, while keeping I unchanged. Assuming the current-source
Cgs = 40 fF, Cgd = 5 fF, and Cdb = 5 fF. The drain resistors capacitance to be directly proportional to the device width,
are 10 k each. Also, there is a 100-fF capacitive load what is the impact on fZ of this proposed change?
between each drain and ground.
9.76 A BJT differential amplifier operating with a 0.5-mA
(a) Find VOV and gm for each transistor. current source uses transistors for which β = 100, fT = 500
(b) Find the differential gain Ad . MHz, Cμ = 0.5 pF, and rx = 100 . Each of the collector
(c) If the input signal source has a small resistance Rsig and resistances is 10 k, and ro is very large. The amplifier is fed
thus the frequency response is determined primarily by in a symmetrical fashion with a source resistance of 10 k in
the output pole, estimate the 3-dB frequency fH . series with each of the two input terminals.

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 749

CHAPTER 9
(a) Sketch the differential half-circuit and its high-frequency (a) Find the low-frequency gain AM , and use open-circuit
equivalent circuit. time constants to estimate the 3-dB frequency fH . Hence
(b) Determine the low-frequency value of the overall differ- determine the gain–bandwidth product.
ential gain. (b) If a 400- resistance is connected
 in the source lead,
(c) Use the Miller approximation to determine the input find the new values of AM , fH , and the gain–bandwidth
capacitance and hence estimate the 3-dB frequency fH product.
and the gain–bandwidth product.

PROBLEMS
D 9.80 (a) Use the approximate expression in Eq. (9.138)
*9.77 Consider the current-mirror-loaded CMOS differen- to determine the gain–bandwidth product of a CS amplifier
tial amplifier of Fig. 9.29(a)
  for the case of all transistors
  with a source-degeneration resistance. Assume Cgd = 0.2 pF
operated at the same VOV  and having the same VA . Also and Rsig = 100 k.
 
let the total capacitance at the output node CL be four times (b) If a low-frequency gain of 20 V/V is required, what fH
the total capacitance at the input node of the current mirror corresponds?
Cm . Give expressions for Ad , fP1 , fP2 , and fZ . Hence show that (c) For gm = 5 mA/V, A0 = 100 V/V, and RL = 20 k, find
fP2 /fP1 = 4Ad and ft = gm /2π CL . For VA = 20 V, VOV = 0.2 V, the required value of Rs .
I = 0.2 mA, CL = 100 fF, and Cm = 25 fF, find the dc value
*9.81 In this problem we investigate the bandwidth exten-
of Ad , and
 the
 value of fP1 , ft , fP2 , and fZ and sketch a Bode sion obtained by placing a source follower between the signal
plot for Ad .
source and the input of the CS amplifier.
*9.78 For the current mirror in Fig. P9.78, derive an expres-
(a) First consider the CS amplifier of Fig. P9.81(a). Show
sion for the current transfer function Io (s)/Ii (s) taking into
that
account the BJT internal capacitances and neglecting ro .
Assume the BJTs to be identical. Observe that a signal
ground appears at the collector of Q2 . If the mirror is AM = −gm ro
  
biased at 1 mA and the BJTs at this operating point are τH = Cgs Rsig + Cgd Rsig 1 + gm ro + ro + CL ro
characterized by fT = 500 MHz, Cμ = 2 pF, and β0 = 100,
find the frequencies of the pole and zero of the transfer
where CL is the total capacitance between the output
function.
node and ground. Calculate the value of AM , fH , and
the gain–bandwidth product for the case gm = 1 mA/V,
ro = 20 k, Rsig = 20 k, Cgs = 20 fF, Cgd = 5 fF, and
CL = 10 fF.

(b) For the CD−CS amplifier in Fig. P9.81(b), show that

ro1  
AM = − gm2 ro2
1/gm1 + ro1
 
Rsig + ro1 1
τH = Cgd1 Rsig + Cgs1 + Cgs2 r
1 + gm1 ro1 gm1 o1
  
1  
+ Cgd2  ro1 1 + gm2 ro2 + ro2
gm1

Figure P9.78 + CL ro2

Calculate the values of AM , fH , and the gain–bandwidth

product for the same parameter values used in (a). Compare
Section 9.6: Other Wideband Amplifier with the results of (a).
Configurations
9.82 Consider the circuit of Fig. P9.82 for the case:
9.79 A CS amplifier is specified to have gm = 5 mA/V, I = 200 µA and VOV = 0.2 V, Rsig = 100 k, RD = 50 k,
ro = 40 k, Cgs = 2 pF, ggd = 0.1 pF, CL = 1 pF, Cgs = 4 pF, and Cgd = 0.5 pF. Find the dc gain, the
Rsig = 20 k, and RL = 40 k. high-frequency poles, and an estimate of fH .
 750 Chapter 9 Frequency Response
PROBLEMS

I
I
Vo
Vo
Rsig Rsig
CHAPTER 9

Q1
Q2
Vsig  Vsig  I

(a) (b)

Figure P9.81

VDD
and  
Cgs Rsig A0
τH  + Cgd Rsig 1 +
RD 1 + (k/2) 2+k
 
  1+k
+ CL + Cgd ro
Vo 2+k
Rsig
Q1 Q2 where k ≡ gm Rs
 
Vsig  D *9.85 Generate a table of AM , fH , and GB versus k ≡

gm Rs for a CS amplifier with a source-degeneration resistance
I Rs . The table should have entries for k = 0, 1, 2, . . ., 15. The
amplifier is specified to have gm = 5 mA/V, ro = 40 k,
RL = 40 k, Rsig = 20 k, Cgs = 2 pF, Cgd = 0.1 pF, and
CL = 1 pF. Use the formulas for AM and τH given in the
Figure P9.82 statement for Problem 9.84. If fH = 2 MHz is required,
find  value needed for Rs and the corresponding value
 the
9.83 In a discrete-circuit CS amplifier a source-
of AM .
degeneration resistance is being used to control the
bandwidth. Assume that ro is very large and CL is negligibly
*9.86 The transistors in the circuit of Fig. P9.86 have
small. Adapt the formulas given in the text for this case and
β 0 = 100, VA = 100 V, and Cμ = 0.2 pF. At a bias current
thus give the expressions for AM and fH . Let Rsig = 100 k,
of 100 µA, fT = 200 MHz. (Note that the bias details are not
gm = 5 mA/V, RL = 5 k, Cgs = 10 pF, and Cgd = 2 pF. Find
shown.)
|AM |, fH , and the gain–bandwidth product for these three
cases: Rs = 0, 100 , and 200 . (a) Find Rin and the midband gain.
(b) Find an estimate of the upper 3-dB frequency fH . Which
9.84 For the CS amplifier with a source-degeneration
capacitor dominates? Which one is the second most
resistance Rs , show for Rsig  Rs , ro  Rs , and RL = ro that
significant?
−A0
AM = (Hint: Use the formulas in Example 9.10.)
2+k

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 751

CHAPTER 9
**9.90 Consider the  BiCMOS  amplifier shown in
100 A
Fig. P9.90. The BJT has VBE  = 0.7 V, β = 200, Cμ = 0.8 pF,
Rsig and fT = 600 MHz. The NMOS transistor has Vt = 1 V,
 2
kn W/L = 2 mA/V , and Cgs = Cgd = 1 pF.
Vsig 5 V

100 A

PROBLEMS
3k
C2
RG 10 M
Figure P9.86 Vo
C1 1 F
100 k Vi
9.87 For the amplifier in Fig. 9.37(a), let I = 1 mA, β = 120, Q1 1k
fT = 500 MHz, and Cμ = 0.5 pF, and neglect ro . Assume that 0.1 F
Q2
a load resistance of 10 k is connected to the output terminal.
Vsig
If the amplifier is fed with a signal Vsig having a source 6.8 k
resistance Rsig = 12 k, find AM and fH .
Rin
9.88 Consider the CD–CG amplifier of Fig. 9.34(c) for
the case gm = 5 mA/V, Cgs = 2 pF, Cgd = 0.1 pF, CL (at the Figure P9.90
output node) = 1 pF, and Rsig = RL = 20 k. Neglecting ro ,
find AM and fH . (Hint: Evaluate fH directly from the transfer (a) Consider the dc bias circuit. Neglect the base current
function.) of Q2 in determining the current in Q1 . Find the dc
bias currents in Q1 and Q2 , and show that they are
*9.89 Figure P9.89 shows an amplifier formed by cascading approximately 100 µA and 1 mA, respectively.
two CS stages. Note that the input bias voltage is not shown. (b) Evaluate the small-signal parameters of Q1 and Q2 at
Each of Q1 and  Q 2 is operated at an overdrive voltage their bias points.
of 0.2 V, and VA  = 10 V. The transistor capacitances (c) Consider the circuit at midband frequencies. First, deter-
are as follows: Cgs = 20 fF, Cgd = 5 fF, and Cdb = 5 fF. mine the small-signal voltage gain Vo /Vi . (Note that RG
The signal-source resistance Rsig = 10 k. Also, the output can be neglected in this process.) Then use Miller’s
resistance of each of the current sources is equal to the theorem on RG to determine the amplifier input resistance
MOSFET ro . Rin . Finally, determine the overall voltage gain Vo /Vsig .
(a) Find the dc voltage gain. Assume ro of both transistors to be very large.
(b) Use the method of open-circuit time constants to deter- (d) Consider the circuit at higher frequencies. Use Miller’s
mine an estimate for the 3-dB frequency fH . theorem to replace RG with a resistance at the input.
(The one at the output will be too large to matter.) Use
open-circuit time constants to estimate fH .
VDD
***9.91 In each of the six circuits in Fig. P9.91, let β =
0.1 mA 100, Cμ = 2 pF, and fT = 400 MHz, and neglect ro . Calculate
the midband gain AM , the 3-dB frequency fH , and the
Q2
gain–bandwidth product. Provide a summary of your results
in a table with the following columns: Case, Configuration
Rsig Vo Name, AM (V/V), fH (MHz), and GB (MHz).
Q1 0.1 mA
Section 9.7: Low-Frequency Response
Vsig
of Discrete-Circuit CS and CE Amplifiers
D 9.92 For the amplifier in Fig. 9.37(a), if RG1 = 2 M,
RG2 = 1M, and Rsig = 200k, find the value of the coupling
capacitor CC1 (specified to one significant digit) that places
Figure P9.89 the associated pole at 10 Hz or lower.
 752 Chapter 9 Frequency Response
PROBLEMS

Vo

Vo Vo
CHAPTER 9

Vsig
Vsig Vsig

(a) (b) (c)

Vo

Vsig
Vo
Vsig

(d) (e)

Vo

Vsig

(f)

Figure P9.91

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem
 Problems 753

VDD
employs RC = 20 k, RB = 200 k, and operates between

CHAPTER 9
a 20-k source and a 10-k load. The transistor β =
100. Select CE first, for a minimum value specified to one
RD
CC2 significant digit and providing up to 80% of fL where fL is
Vo to be 100 Hz. Then choose CC1 and CC2 , each specified to
Rsig CC1
RL
one significant digit, and each contributing about 10% of fL .
What fL results? What total capacitance is needed?

PROBLEMS
CS

Vsig  RG *9.96 The BJT common-emitter amplifier of Fig. P9.96


includes an emitter-degeneration resistance Re .
I
(a) Assuming α  1, neglecting ro , and assuming the cur-
rent source to be ideal, derive an expression for the
–VSS small-signal voltage gain A(s) ≡ Vo /Vsig that applies in
the midband and the low-frequency band. Hence find the
Figure P9.94
midband gain AM and the lower 3-dB frequency fL .
(b) Show that including Re reduces the magnitude of AM by
a certain factor. What is this factor?
9.93 The amplifier in Fig. 9.37(a) is biased to operate at
(c) Show that including Re reduces fL by the same factor
gm = 5 mA/V, and has the following component values:
as in (b) and thus one can use Re to trade off gain for
Rsig = 100 k, RG1 = 47 M, RG2 = 10 M, CC1 = 0.01 µF,
bandwidth.
RS = 2 k, CS = 10 µF, RD = 4.7 k, RL = 10 k, and
CC2 = 1 µF. Find AM , fP1 , fP2 , fZ , fP3 , and fL .  I = 0.25 mA, RC = 10 k, and CE = 10 µF, find
(d) For
AM  and fL with Re = 0. Now find the value of Re that
D 9.94 Figure P9.94 shows a CS amplifier biased by a lowers fL by a factor of 10. What will the gain become?
constant-current source I. Let Rsig = 0.5 M, RG = 2 M, Sketch on the same diagram a Bode plot for the gain
gm = 3 mA/V, RD = 20 k, and RL = 10 k. Find AM . magnitude for both cases.
Also, design the coupling and bypass capacitors to locate the
three low-frequency poles at 100 Hz, 10 Hz, and 1 Hz. Use
a minimum total capacitance, with the capacitors specified
only to a single significant digit. What value of fL results? VCC

D 9.95 Figure P9.95 shows a current-source-biased CE

amplifier operating at 100 µA from ±3-V power supplies. It
RC

VCC Vo

RC
CC2
Vo
Vsig 
Rsig CC1  Re
RL

CE CE
Vsig  RB

I
I

–VEE

Figure P9.95 Figure P9.96

 754 Chapter 9 Frequency Response

9.97 A signal source Vsig with a resistance Rsig = 1 k is (d) Give an approximate value for the 3-dB frequency fL .
PROBLEMS

connected to a load resistance RL = 4 k via a capacitor (e) Sketch a Bode plot for the gain of this amplifier. What
C = 1 µF. Find: does the plot tell you about the gain at dc? Does this
(a) the transfer function Vo /Vsig ; make sense? Why or why not?
(b) the magnitude of transmission at high frequencies for
which the coupling capacitor acts as a short circuit; 9.101 Consider the circuit of Fig. 9.41(a). For Rsig = 5 k,
(c) the frequency at which | Vo /Vsig | is 3 dB below the RB ≡ RB1  RB2 = 10 k, rπ = 1 k, β 0 = 100, and
CHAPTER 9

high-frequency value; and RE = 1.5 k, what is the ratio CE /CC1 that makes their
(d) the transmission at dc. contributions to the determination of fL equal?
D 9.98 For the amplifier in Fig. 9.37(a), if RD = 10 k, RL = D *9.102 For the common-emitter amplifier of Fig. P9.102,
10 k, and ro is very large, find the value of CC2 (specified to neglect ro and assume the current source to be ideal.
one significant digit) that places the associated pole at 10 Hz
(a) Derive an expression for the midband gain.
or lower.
(b) Convince yourself that the two poles caused by CE and
D 9.99 The amplifier in Fig. 9.37(a) is biased to operate CC do not interact. Find expressions for their frequencies,
at gm = 5 mA/V, and RS = 1.8 k. Find the value of CS ωPE and ωPC .
(specified to one significant digit) that places its associated (c) Give an expression for the amplifier voltage gain
pole at 100 Hz or lower. What are the actual frequencies of Vo (s)/Vsig (s) in terms of AM , ωPE , and ωPC .
the pole and zero realized? (d) For Rsig = RC = RL = 10 k, β = 100, and I = 1 mA, find
the value of the midband gain.
D 9.100 The amplifier in Fig. P9.100 is biased to operate at
(e) Select values for CE and CC to place the two pole
gm = 2 mA/V. Neglect ro .
frequencies a decade apart and to obtain a lower
VDD 3-dB frequency of 100 Hz while minimizing the total
capacitance.
(f) Sketch a Bode plot for the gain magnitude, and estimate
RD the frequency at which the gain becomes unity.

Vo
VCC
CS

Vi  RS
 RC
4.5 k

Vo
VSS Rsig CC
RL
Figure P9.100 CE

Vsig 
(a) Determine the value of RD that results in a midband gain 
of −20 V/V. I
(b) Determine the value of CS that results in a pole frequency
of 100 Hz.
(c) What is the frequency of the transmission zero intro-
duced by CS ? Figure P9.103

problems with green numbers are considered essential; * = difficult problem; ** = more difficult; *** = very challenging
= simulation; D = design problem