Problem2_EEL7300

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EEL7300
Chapter 2 - Problems
1 Group A
Consider the switched-capacitor network of Fig. 1 with C1 = C2 = 1 pF and Tc = 10 µs.
1. Plot vOUT as a function of time if vIN is a 1−V step function.
2. Repeat part 1 for the case C1 = 1 pF and C2 = 3 pF.
3. What general class of filter is simulated by this circuit?
Figure 1
Now, using switched-capacitor elements only, modify the circuit so that its output is amplified by a factor
of 10.
1
2 Grupo B
The circuit of Fig. 2 functions as a bandpass filter in which R1, and C1 set the high-frequency endpoint of
the passband, and R2 and C2 set the low-frequency endpoint.
1. Derive an expression for the transfer function of the filter in the sinusoidal steady state.
2. Choose values for the resistors and capacitors such that the passband endpoints are set to 100 Hz and
10 kHz, with a passband gain of 40 dB.
3. What is the input resistance of the filter in the passband region?
Figure 2
2
3 Grupo C
1. By cascading a first-order op amp-RC low-pass ciccuit with a first-order op amp-RC high-pass circuit
one can design a wideband bandpass filter. Provide such a design for the case in which the midband
gain is 12 dB and the 3-dB bandwidth extends from 100 Hz to 10 kHz. Select appropriate component
values under the constraint that no resistors higher than 100 kΩ are to be used, and that the input
resistance is to be as high as possible.
2. A third-order low-pass filter has transmission zeros at ω = 2 rad/s and ω =∞. Its natural modes are
at s = −1 and s = −0.5± j0.8. The dc gain is unity. Find T(s).
3
4 Grupo D
Consider a fifth-order filter whose poles are all at a radial distance from the origin of 103 rad/s. One pair
of complex conjugate poles is at 18◦ angles from the jω axis, and the other pair is at 54◦ angles. Give the
transfer function in each of the following cases:
1. The transmission zeros are all at s =∞ and the dc gain is unity.
2. The transmission zeros are all at s = 0 and the high frequency gain is unity.
What type of filter results in each case?
4
5 Grupo E
For the Wien-bridge oscillator circuit in Fig. 3, show that the transfer function of the feedback network
[Va(s)/Vo(s)] is that of a bandpass filter. Find ω and Q of the poles, and find the center-frequency gain.
Figure 3
5
6 Grupo F
1. Show that the circuit of Fig. 4 functions as a single-pole high-pass filter of first order. Find an
expression for the cutoff frequency and gain in the passband region. Evaluate these expressions for
R1 = R2 = 2.7 kΩ, R3 = 18 kΩ, and C = 0.33 uF.
Figure 4
2. Design a first-order active filter that has a gain magnitude of 20 between 0 Hz and 5 kHz and a gain
magnitude of 1 at higher frequencies. These design objectives can be achieved using a single capacitor
only. What is the width of the transition region for your filter?
6
7 Grupo G
The positive-feedback network of the Wienbridge oscillator circuit of Fig. 5 has the form of a band-pass
filter. Find the transfer function that relates V+ to Vout. Identify ω0, and Q of this band-pass filter function.
Figure 5
7
8 Grupo H
For the Wien-bridge oscillator circuit in Fig. 6, show that the transfer function of the feedback network
[Va(s)/Vo(s)] is that of a bandpass filter. Find ω and Q of the poles, and find the center-frequency gain.
Figure 6
8
9 Grupo I
Consider the switched-capacitor network of Fig. 7 with C1 = C2 = 1 pF and Tc = 10 µs.
1. Plot vOUT as a function of time if vIN is a 1−V step function.
2. Repeat part 1 for the case C1 = 1 pF and C2 = 3 pF.
3. What general class of filter is simulated by this circuit?
Figure 7
9
10 Grupo J
For the Wien-bridge oscillator of Fig. 8, let the closed-loop amplifier (formed by the op amp and the resistors
R1 and R2) exhibit a phase shift of −0.1 rad in the neighborhood of ω = 1/CR. Find the frequency at which
oscillations can occur in this case, in terms of CR.
Figure 8
10
11 Grupo K
1. Find the transfer function of the circuit of Fig. 9 in the sinusoidal steady state if R1 = R2 = R3 =
R4 = R. This circuit functions as a non-inverting integrator.
Figure 9
2. Consider the Wien-bridge oscillator of Fig. 10 in which the two resistors RF have unequal values RA,
and RB , and the two capacitors C have unequal values CA and CB , where RA and CA, form the
parallel-connected input devices and RB and CB the series-connected feedback devices.
(a) What is the criterion for oscillation in this case?
(b) Derive an expression for the frequency of oscillation.
Figure 10
11
12 Grupo L
1. For the circuit in Fig. 11 find H(s), H(jω), the frequency for zero loop phase, and R2/R1 for oscillation.
Figure 11
2. Design a first-order active filter that has a gain magnitude of 2 at frequencies well below about 1 kHz
and a gain magnitude of 10 at frequencies well above 1 kHz. What is the width of the transition region
for your filter? You can achieve these design goals using a single capacitor only.
12
13 Grupo M
1. The transfer function of a first-order low-pass filter (such as that realized by an RC circuit) can be
expressed as T (s) = ω0/(s + ω0), where ω0 is the 3-dB frequency of the filter. Give in table form the
values of |T |, φ, G, and A at ω0 = 0, 0.5ω0, ω0, 2ω0, 5ω0, 100ω0, and 1000ω0.
2. For the circuit in Fig. 12 find H(s), H(jω), the frequency for zero loop phase, and R2/R1 for oscillation.
Figure 12
13
14 Grupo N
For the circuit in Fig. 13, break the loop at node X and find the loop gain (working backward for simplicity
to find Vx in terms of Vo). For R = 10 kΩ, find C and Rf to obtain sinusoidal oscillations at 10 kHz.
Figure 13
14
15 Grupo O
For each of the op-amp circuits of Fig. 14, find an expression for the closed-loop gain as a function of
frequency.
Figure 14
15
16 Grupo P
The block diagram of a positive-feedback oscillator is shown in Fig. 15, where P = 1 6 45◦ for all ω. Find
the minimum gain A necessary to sustain oscillation and find the frequency of oscillation.
Figure 15
16
	Group A
	Grupo B
	Grupo C
	Grupo D
	Grupo E
	Grupo F
	Grupo G
	Grupo H
	Grupo I
	Grupo J
	Grupo K
	Grupo L
	Grupo M
	Grupo N
	Grupo O
	Grupo P