Solved: Determine the driving point impedance at the input

Determine the driving point impedance at the input terminals of the network shown in Fig. P12.1 as a function of s. o(t) + i (t) + R C L Figure P12.1

Determine the driving point impedance at the input terminals of the network shown in Fig. P12.2 as a function of s. + R L C1 C2 o(t) + i (t) Figure P12.2

Determine the voltage transfer function Vo(s)/Vi (s) as a function of s for the network shown in Fig. P12.3. R2 R1 C L o(t) + i (t) + Figure P12.3

Find the transfer impedance Vo(s)/Is(s) for the network shown in Fig. P12.4. 2 4 1 F 2 H o(t) + iS(t) Figure P12.4

Determine the driving-point impedance at the input terminals of the network shown in Fig. P12.5 as a function of s. L C R + i (t) + o(t) Figure P12.5

Compute the voltage transfer function as a function of s for the network in Problem 12.5.

Find the driving point impedance at the input terminals of the circuit in Fig. P12.7 as a function of s. 1 H 1 F Zi 3 3 3 3 Figure P12.7

Determine the driving point impedance at the input terminals 12 for the network shown in Fig. P12.8 as a function of s if (a) terminals 34 are open and (b) terminals 34 are shorted. 1 2 3 1 F 2 H 4 1 2 Z(s) Figure P12.8

Sketch the magnitude and phase characteristics as a function of the frequency of the network functions defined by each transfer function. (a) _______ 1 j + (b) j + _______ j + , > (c) _______ j j +

Given the network functions defined by each transfer function, sketch their magnitude and phase characteristics as a function of frequency. (a) _______ j j + (b) _______ j + j + , >

Draw the Bode plot for the network function H( j) = j4 + 1 ________ j20 + 1

Draw the Bode plot for the network function H( j) = _______________ 1

Draw the Bode plot for the network function H( j) = 10j + 1 _____________ j(0.01j + 1)

Draw the Bode plot for the network function H( j) = j + 40 _______________ ( j + 1)( j + 2)

Draw the Bode plot for the network function H( j) = ( j + 8)( j + 2) _______________

Sketch the magnitude characteristic of the Bode plot for the transfer function G( j) = 400( j + 2)( j + 50) ___________________ 2 ( j + 100)2

Sketch the magnitude characteristic of the Bode plot for the transfer function G( j) = 2 104 _________________________ ( j + 1)( j + 10)( j + 100)

Sketch the magnitude characteristic of the Bode plot for the transfer function G( j) = ( j + 4)2 ___________________ 2 (j 10 + 1 ) (j 20 + 1 )

Draw the Bode plot for the network function H( j) = _________________ j ( j + 1)(0.1j + 1)

Sketch the magnitude characteristic of the Bode plot for the transfer function H( j) = 100( j) ________________________ ( j + 1)( j + 10)( j + 50)

Sketch the magnitude characteristic of the Bode plot for the transfer function H( j) = 20(0.1j + 1) ____________________ j( j + 1)(0.01j + 1)

Draw the Bode plot for the network function H( j) = _____________ 100 ( j) 2 ( j2 + 1)

Sketch the magnitude characteristic of the Bode plot for the transfer function G( j) = 2 ________ ( j + 1)

Sketch the magnitude characteristic of the Bode plot for the transfer function G( j) = 10( j + 2)( j + 100) j(2 + 4j + 100)

Sketch the magnitude characteristic of the Bode plot for the transfer function G( j) = _________________ 10j ( j + 1)( j + 10)2

Sketch the magnitude characteristic of the Bode plot for the transfer function G( j) = 2 104 __________________________ ( j + 1)2 ( j + 10)( j + 100)

Sketch the magnitude characteristic of the Bode plot for the transfer function H( j) = +6.4 ______________________ ( j + 1)(2 + 8j + 16)

Sketch the magnitude characteristic of the Bode plot for the transfer function H( j) = 0.5(10j + 1)( j + 1) _______________________ j(0.1j + 1)(0.01j + 1)2

Sketch the magnitude characteristic of the Bode plot for the transfer function H( j) = +81( j + 0.1) ____________________ ( j)(2 + 3.6j + 81)

Sketch the magnitude characteristic of the Bode plot for the transfer function H( j) = +6.4( j) ______________________ ( j+ 1)(2 + 8j + 64)

Find H( j) for the magnitude characteristic shown in Fig. P12.31. 40 |H| 0 dB 3 5 8 10 (rad/s) +20 dB/dec 20 dB/dec Figure P12.31

Find H( j) for the magnitude characteristic shown in Fig. P12.32. |H| 0 dB 3 54 5.5 7 (rad/s) +40 dB/dec 20 dB/dec 20 dB/dec Figure P12.32

Determine H( j) for the magnitude characteristic shown in Fig. P12.33. |H| 0 dB 1 2 46 (rad/s) +20 dB/dec 40 dB/dec 20 dB/dec Figure P12.33

Given the magnitude characteristic for G(j?) shown in Fig. P.12.34, determine the transfer function G(j?).

The magnitude characteristic of a band-elimination filter is shown in Fig. P12.35. Determine H( j). 20 dB/dec 0 dB +20 dB/dec (rad/s) 10 100 1000 10,000 |H| Figure P12.35

Given the magnitude characteristic in Fig. P12.36, find H( j). +20 dB/dec +20 dB/dec 40 dB/dec 4 10 20 100 600 (rad/s) 0 dB |H| Figure P12.36

Find H( j) if its magnitude characteristic is shown in Fig. P12.37. 0.4 1000 (rad/s) 50 20 dB/dec 40 dB 20 dB/dec 40 dB/dec |H| 400 Figure P12.37

Find H( j) if its amplitude characteristic is shown in Fig. P12.38. 1 812 60 400 (rad/s) 0 dB 20 dB/dec 20 dB/dec 20 dB/dec 40 dB/dec |H| Figure P12.38

Determine H( j) if its magnitude characteristic is shown in Fig. P12.39. 40 dB/dec 40 dB/dec 20 dB/dec 5 50 10 0 dB (rad/s) |H| Figure P12.39

Find G( j) for the magnitude characteristic shown in Fig. P12.40. 20 dB = 0.1 20 900100 (rad/s) 20 dB/dec 40 dB/dec 20 dB/dec 0.8 |G| Figure P12.40

The series RLC circuit in Fig. P12.41 is driven by a variablefrequency source. If the resonant frequency of the network is selected as 0 = 1600 rad/s, find the value of C. In addition, compute the current at resonance and at 0/4 and 40. i(t) 10 mH 2 C 24 cos (t + 30) V + Figure P12.41

Find H( j) if its magnitude characteristic is shown in Fig. P12.42. 1 80 (rad/s) 10 20 dB/dec 120 +20 dB/dec 40 dB 40 dB/dec |H| Figure P12.42

Determine H( j) from the magnitude characteristic of the Bode plot shown in Fig. P12.43. 0.1 51 50 log 20 dB/dec 40 dB/dec 0 dB 20 dB/dec 40 dB/dec |H| Figure P12.43

Given the RLC network in Fig. P12.44, find the value of Q and the output voltage, o(t), at the resonant frequency. o(t) + + 100 F 250 mH 1 12 cos t V Figure P12.44

Given the series RLC circuit in Fig. P12.45, (a) derive the expression for the half-power frequencies, the resonant frequency, the bandwidth, and the quality factor for the transfer characteristic I/Vin in terms of R, L, and C; (b) compute the quantities in part (a) if R = 10 , L = 50 mH, and C = 10 F. + R L C in(t) i(t) Figure P12.45

Given the network in Fig. P12.46, find 0, Q, max, and |Vo|max. 1 2 mH 6 cos t V 10 F o(t) + + Figure P12.46

A series RLC circuit resonates at 1000 rad/s. If C = 20 F, and it is known that the impedance at resonance is 2.4 , compute the value of L, the Q of the circuit, and the bandwidth.

A series resonant circuit has a Q of 120 and a resonant frequency of 10,000 rad/s. Determine the half-power frequencies and the bandwidth of the circuit.

In the network in Fig. P12.49, the inductor value is 10 mH, and the circuit is driven by a variable-frequency source. If the magnitude of the current at resonance is 12 A, 0 = 1000 rad/s, and L = 10 mH, find C, Q, and the bandwidth of the circuit. + R C 36 cos (t + 45) V L Figure P12.49

A parallel RLC resonant circuit with a resonant frequency of 20,000 rad/s has an admittance at resonance of 1 mS. If the capacitance of the network is 2 F, find the values of R and L

A parallel RLC circuit, which is driven by a variable frequency 2-A current source, has the following values: R = 1 k, L = 400 mH, and C = 10 F. Find the bandwidth of the network, the half-power frequencies, and the voltage across the network at the half-power frequencies.

A variable-frequency voltage source drives the network in Fig. P12.52. Determine the resonant frequency, Q, BW, and the average power dissipated by the network at resonance. 12 cos t V 50 mH 100 5 F + Figure P12.52

The network in Fig. P12.53 operates at 200 Hz. Determine the manner in which the resistor bank should be connected to maximize the voltage Vo and determine the value of the maximum voltage (R1 = 12 , R2 = 6 , R3 = 4 ). 12 0 V 50 F 500 H Vo + R1 R2 R3 + Figure P12.53

A series RLC circuit is driven by a signal generator. The resonant frequency of the network is known to be 1600 rad/s and at that frequency the impedance seen by the signal generator is 5 . If C = 20 F, find L, Q, and the bandwidth

The network in Fig. P12.55 operates at a resonant frequency of = 2000 rad/s. Select the values for the unknown circuit elements so that the circuit has a Q = 40. Then find the value of the voltage across the capacitor. + 25 F R L 10 cos 2000t V Figure P12.55

The network in Fig. P12.56 operates at a resonant frequency of 7200 rad/s. If the Q = 60, find the values of the inductor and capacitor. + C L 6 Figure P12.56

Given the circuit in Fig. P12.57, determine the Q of the network and calculate the phasor voltage V0 as well as the voltage across each element in the network. + 100 F 2.5 mH 1 20 cos 2000t V o(t) + Figure P12.57

A series RLC circuit is required to have a resonant frequency of 1 MHz and a bandwidth that is 2% of the resonant frequency. If R = 100 , find the values for L and C.

Determine the expression for the frequency at which the input impedance of the network shown in Fig. P12.59 is real. L C R Figure P12.59

Consider the network in Fig. P12.60. If R = 1 k, L = 20 mH, C = 50 F, and RS = , determine the resonant frequency 0, the Q of the network, and the bandwidth of the network. What impact does an RS of 10 k have on the quantities determined? RS R L C Figure P12.60

Determine the equation for the nonzero resonant frequency of the impedance shown in Fig. P12.61. Z L R C Figure P12.61

Given the network in Fig. P12.62, find the frequency M at which the magnitude of impedance Z( j) is a maximum. In addition, determine the phase of the impedance at the frequency M. Z( j) C R L Figure P12.62

A parallel RLC resonant circuit has a resistance of 200 . If it is known that the bandwidth is 80 rad/s and the lower half-power frequency is 800 rad/s, find the values of the parameters L and C

A parallel RLC circuit, which is driven by a variablefrequency 4-A current source, has the following values: R = 2 k, L = 100 mH, and C = 10 F. Find the bandwidth of the network, the half-power frequencies, and the voltage across the network at the half-power frequencies

Determine the parameters of a parallel resonant circuit that has the following properties: 0 = 2 Mrad/s, BW = 20 rad/s, and an impedance at resonance of 2000 .

Determine the value of C in the network shown in Fig. P12.66 for the circuit to be in resonance. + C 6 4 4 H 4 cos 2t V Figure P12.66

The source in the network in Fig. P12.67 is iS(t) = cos 1000t + cos 1500t A. R = 200 and C = 500 F. If 0 = 1000 rad/s, find L, Q, and the BW. Compute the output voltage o(t) and discuss the magnitude of the output voltage at the two input frequencies. R L C o(t) iS(t) + Figure P12.67

Determine the new parameters of the network in Fig. P12.68 if new = 104 old. Z R = 2 L = H C = F 1 2 1 8 Figure P12.68

Determine the new parameters of the network shown in Fig. P12.69 if Znew = 104 Zold. Z R = 2 L = H C = F 1 2 1 8 Figure P12.69

Compute the voltage transfer function for the network shown in Fig. P12.70 and tell what type of filter the network represents. + R1 R2 C + i (t) o(t) Figure P12.70

Determine what type of filter the network shown in Fig. P12.71 represents by determining the voltage transfer function. o(t) + i (t) + C R1 R2 Figure P12.71

Given the network in Fig. P12.72, sketch the magnitude characteristic of the transfer function G( j) = ___ V0 V1 ( j) Identify the type of filter. o (t) i (t) + + 10 H 1 mF 100 Figure P12.72

Determine what type of filter the network shown in Fig. P12.73 represents by determining the voltage transfer function. o (t) i (t) + + L R1 R2 Figure P12.73

Given the network in Fig. P12.74, sketch the magnitude characteristic of the transfer function G( j) = ___ Vo V1 ( j) Identify the type of filter. 100 1000 F 10 H o (t) i (t) + + Figure P12.74

Given the lattice network shown in Fig. P12.75, determine what type of filter this network represents by determining the voltage transfer function. R1 R1 C R2 o(t) + i (t) + Figure P12.75

The circuit in Fig. P12.76 is a dual-T notch filter. It has an advantage over the filter in Example 12.21 in that it contains no inductors, which tend to be bulky and heavy. Derive the transfer function for this filter and verify your work for the component values C = 100 nF and R = 1590 . C C R R 2 C R 2 o(t) + i (t) + Figure P12.76

Design a low-pass filter with a cutoff frequency between 15 and 16 kHz

Design a low-pass filter using one resistor and one capacitor that will produce a 4.24-volt output at 159 Hz when 6 volts at 159 Hz are applied at the input.

Design a high-pass filter with a half-power frequency between 159 and 161 kHz.

Design a band-pass filter with a low cutoff frequency of approximately 4535 Hz and a high cutoff frequency of approximately 5535 Hz.

An engineer has proposed the circuit shown in Fig. P12.81 to filter out high-frequency noise. Determine the values of the capacitor and resistor to achieve a 3-dB voltage drop at 23.16 kHz. R C Figure P12.81