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The Analysis And Design Of Linear Circuits 7th Edition Roland E Thomas, Albert J Rosa, Gregory J Toussaint - Solutions

In Figure P16–64 the three buses are interconnected by transmission lines with wire impedances of ZW1 ¼120 þ j800 V=phase and ZW2 ¼ 200 þ j1200 V=phase. The source at bus 2 produces an apparent power of jS2j ¼400 kVA at a leading power factor of 0.9. The load at bus 3 draws an apparent power
In Figure P16–66 the three buses are interconnected by transmission lines with wire impedances of ZW1 ¼ 100 þj850 V=phase and ZW2 ¼ 50 þ j250 V=phase. The load at bus 1 draws an apparent power of jS1j ¼ 400 kVA at a lagging power factor of 0.85. The line voltage at bus 1 is VL1 ¼ 138
In Figure P16–67 the source at bus 1 supplies two load buses through transmission lines with wire impedances of ZW1 ¼ 6 þ j33 V=phase and ZW2 ¼ 3 þ j15 V=phase. The load at bus 2 draws an apparent power 4 MVA at a lagging power factor of 0.95. The load at bus 3 draws an apparent power of 3
Three-phase Voltages in the Time Domain A balanced 60-Hz three-phase system has a line voltage of VL ¼ 208 VðrmsÞ. Using ffVAB ¼ 0 as the phase reference, derive time-domain expressions for the phase voltages vANðtÞ, vBNðtÞ, and vCNðtÞ for a positive phase sequence.
Single-Phase Motor Power Factor When a 1/2-hp (1 hp ¼ 746 W) single-phase induction motor delivers its rated mechanical output it is 65% efficient and draws a current of 4.8 A(rms) from a 200 V(rms) line. Find the power factor of the motor.
Three-Phase Transformer Figure P16–70 shows three identical ideal transformers connected to form a three-phase transformer. The windings on the primary (source) side are D-connected and the windings on the secondary (load) side are Y-connected. On the secondary side of the transformer VL2 ¼ 830
Phase Converter Efficiency Three-phase motors are often used in equipment because they are more efficient and reliable than single-phase motors.Such equipment may be installed in locations where only single-phase power is available and the cost of installing three-phase service is prohibitive. The
Find the z-parameters of the two-port network in Figure P17–1. 11 12 ww + 100 2 www 400 + V1 600 2 200 V2 FIGURE P17-1
Find the z-parameters of the two-port network in Figure P17–3. + 11 Vi j50 2 -100 12 100 V FIGURE P17-3
Find the z-parameters of the two-port network in Figure P17–5. 11 + /1 R W Vi R R3 V FIGURE P17-5
In Figure P17–11 a load impedance ZL is connected across the output port. Show that the input impedanceZIN ¼ V1=I1 is ZIN ¼ z11 z12z21 ZL þ z22 11 +5 12 + Two Port V2 ZL FIGURE P17-11
Find the h-parameters of the two-port networks in Figure P17–13. V1 I Vi (a) Z (b) FIGURE P17-13 2702 Y V2 1 +02 V2
Find the h-parameters of the two-port network in Figure P17–15. 516+ 5 w R R BI FIGURE P17-15 h + R3 V
Find the h-parameters of the two-port network in Figure P17–17. 11 V R + FIGURE P17-17 w R 12 V2
The t-parameters of the two-port networks Na and Nb in Figure P17–29 are ta ½ ¼ 60 10 5 40 and tb ½ ¼ 10 10 2:5 5Find the t-parameters of the cascade connection. Na FIGURE P17-29 Nb
The two-port parameters of the series connection in Figure P17–33 are za ½ ¼ 60 10 10 10 V and yb½ ¼ 60 4020 80 mS Find the z-parameters of the series connection. Is the network reciprocal? No Nb FIGURE P17-33
The two-port parameters of the parallel connection in Figure P17–35 are za ½ ¼ 30 10 10 20 V and yb½ ¼ 60 4040 80 mS Find the y-parameters of the parallel connection. Is the network reciprocal? Na Nb FIGURE P17-35
Two-port Parameters of a Transformer In the phasor-domain the I-V relationships of a linear transformer with positive coupling are V1 ¼ jvL1I1 þ jvMI2 V2 ¼ jvMI1 þ jvL2I2 Find the phasor-domain transmission parameters of the linear transformer.
Maximum Power The y-parameters of a two-port network operating in the sinusoidal steady state are y11¼ 20 j15 mS, y12¼ y21¼j12 ms, and y22¼ 10 j20 mS. The input port is driven by an ac voltage sourceVS ¼ 120ff25 VðrmsÞ.Findthe output port load impedance ZLthat will draw the maximum
Input Impedance of a Two-port Network A load impedance ZL is connected at the output of a twoport network. Show that the input impedance ZIN ¼ V1=I1 ¼ ZLwhen A ¼ D and C ¼ B= ZL ð Þ2. Hint: the result shown in Problem 17–24 is the place to start.
Unilateral Two-port Network A two-port network is said to be unilateral if excitation applied at the input port produces a response at the output port, but the same excitation applied at the output port produces no response at the input port. Show that a twoport is unilateral if AD BC ¼ 0.
The h-parameters of a two-portamplifier are h11 ¼ 10 kV, h12 ¼ 0, h21 ¼ 40, and h22 ¼ 1 mS. Find the forward current gain of a parallel connection of two such amplifiers. Assume the connection does not change the parameters of either amplifier.
In Figure 17–33 the network Na is an active device with h-parameters h11 ¼ 20 kV, h12 ¼ 0, h21 ¼ 5 103, and h22 ¼ 50 mS. The network Nb is a resistive feedback circuit with z-parameters z11 ¼ 2R and z12 ¼ z21 ¼ z22 ¼ R. Find a value of R such that the voltage gain of the series
Find the voltage gain of the two-stage amplifier defined in Problem 17–31.
The cascade connection in Figure P17–29 is a two-stage amplifier with identical two-port stages each having the h-parameters h11 ¼ 1 kV, h12 ¼ 0, h21 ¼10, and h22 ¼ 1mS. Find the t-parameters of the cascade connection and then calculate the current gain of the two-stage amplifier.
The t-parameters of the two-port networks Na and Nb in Figure P17–29 are ta ½ ¼ 4 25 0:01 4 and tb ½ ¼ 10 500 0:2 10 Find the impedance looking into the input port of Na when a 50-V resistive load is connected across the output port of Nb.Note: the result in Problem 17–24 will prove
Starting with the t-parameter i-v relationships in Eq.(17–13), show that for V2 ¼ 0 the current gain is TI ¼ 1=D.TI ¼ I2 I1¼1 D
Starting with the h-parameter i-v relationships in Eq. (17–9), show that for I2 ¼ 0 the voltage gain is TV ¼ V2 V1¼h21 Dh
Starting with the t-parameter i-v relationships in Eq. (17–13), show that y11¼ D B; y12¼Dt B; y21¼1 B; y22¼ A BD where Dt ¼ AD BC.
Starting with the h-parameter i-v relationships in Eq. (17–9), show that:A ¼Dh h21; B ¼h11 h21; C ¼h22 h21; D ¼1 h21 where Dh ¼ h11h22 h12h21.
When a load impedance ZL is connected across the output port, show that the input impedance is ZIN ¼ AZL þ B CZL þ D
When a voltage VX is applied across the input port, the short-circuit current at the output port is I2SC. When the same voltage is applied across the output port, the shortcircuit current at the input port is I1SC. Show that reciprocity I1SC ¼ I2SC ð Þrequires that h12 ¼ h21.
The t-parameters of a two-port network are A ¼ 0, B ¼ j100 V, C ¼ j20 mS, and D ¼ 1 j0:25. Find the voltage gain V2=V1 when a 50-V load resistor is connected across the output port.
The t-parameters of a two-port network are A ¼ 2, B ¼ 400 V, C ¼ 2:5 mS, and D ¼ 1.(a) Find the output resistance V2=I2 when the input port is short-circuited.(b) Find the output resistance V2=I2 when the input port is open-circuited.
The h-parameters of a two-port network are h11 ¼ 6 kV, h12 ¼ 0, h21 ¼ 50, and h22 ¼ 0:2 mS. Find the voltage gain V2=V1 when a 20-kV load resistor is connected across the output port.
The h-parameters of a two-port network are h11 ¼ 500 V, h12 ¼ 1, h21 ¼ 1 and h22 ¼ 2 mS. Find the Thevenin equivalent circuit at the output port when a 12-V voltage source is connected at the input port.
Find the t-parameters of the two-port network in Figure P17–17.
Find the t-parameters of the two-port network in Figure P17–15.
Find the t-parameters of the two-port networks in Figure P17–13.
In Figure P17–11 a load impedanceZL is connected across the output port. Show that the voltage gain TV ¼ V2=V1 is TV ¼y21 YL þ y22
The y-parameters of a two-port circuit are y11¼ 15þj20 mS, y12¼ y21¼ j20 mS, and y22¼ 40 þ j20 mS. Find the short-circuit V2 ð ¼ 0Þ current gain TI ¼ I2=I1.
The y-parameters of a two-port circuit are y11¼ 4mS, y12¼ y21¼ 2 mS, and y22¼ 2 mS. A 15-V voltage source is connected at the input port and a load resistor RL ¼ 2500V is connected across the output port. Find the port variable responses V2, I1, and I2.
The z-parameters of a two-port circuit are z11 ¼ 80 kV, z12 ¼ 3MV, z21 ¼ 400 kV, and z22 ¼ 5 kV. Find the opencircuitðI2 ¼ 0Þ voltage gain TV ¼ V2=V1.
The z-parameters of a two-port circuit are z11 ¼ 1 kV, z12 ¼ z21 ¼ 500 V, and z22 ¼ 1:5 kV. Find the port currents I1 and I2 when a 12-V voltage source is connected across the input port and a load resistor RL ¼ 250V is connected across the output port.
Find the y-parameters of the two-port network in Figure P17–5.
Find the y-parameters of the two-port network in Figure P17–3.
Find the y-parameters of the two-port network in Figure P17–1.
Transformer Thevenin Equivalent In the time-domain, the i–v relationships for a linear transformer are v1ðtÞ ¼ L1 di1ðtÞdtþM di2ðtÞdt v2ðtÞ ¼ M di1ðtÞdtþ L2 di2ðtÞdt Assuming zero initial conditions, transform these equations into the s-domain and show that the s-domain
The self and mutual inductances of a transformer can be calculated from measurements of the steady-state ac voltages and currents with the secondary winding open-circuited and short-circuited. Suppose the measurements are jV1j ¼ 120 V, jI1j ¼ 120 mA, and jV2j ¼ 240V when the secondary is open.
The linear transformer in Figure P15–38 is in the sinusoidal steady-state with reactances of X1 ¼ 15V; X2 ¼60 V;XM ¼ 27 V. Find the transformer secondary response V2 and I2 when ZL ¼ 200 j100 V and VS ¼ 200ff0 V.
The transformer in Figure P15–36 is operating in the ac steady-state with a voltage source connected at the input and the output shorted. Show that the short-circuit current is ISC ¼ k2 1 k2!VS jXM Hint: use the result derived in Problem 15–36 to find I1.
Repeat Problem 15–30 with ZL ¼ 16 j12 V.
A transformer operating in the sinusoidal steady state with v ¼ 377 rad/s has self inductances L1 ¼ 200mH;L2 ¼ 400 mH, and k ¼ 0.95. The load connected across the secondary winding is ZL ¼ 75 þ j150 V. Find the transformer input impedance. Assume additive coupling.
A transformer has self-inductances L1 ¼ 200mH;L2 ¼ 200 mH, and a coupling coefficient of k ¼ 0.99. The transformer is operating in the sinusoidal steady state with v ¼ 500 rad/s with a short-circuit connected across the secondary winding. Find the transformer input impedance.Assume additive
Repeat Problem 15–26 with vSðtÞ ¼ 60 cos 500t V.
A transformer that can be treated as ideal has 480 turns in the primary winding and 240 turns in the secondary winding. The primary is connected to a 60-Hz source with peak amplitude of 440 V. The secondary winding delivers an average power of 5 kW to a resistive load. Find the amplitudes of the
The primary winding of an ideal transformer with N1 ¼100 and N2 ¼ 250 is connected to a 480-V source. A load impedance of ZL ¼ 150 þ j200 V is connected across the secondary windings. Find the amplitudes of the primary and secondary currents.
An ideal transformer has a turns ratio of n ¼ 10. The secondary winding is connected to a load ZL ¼ 600 þ j100 V.The primary is connected to a voltage source with a peak amplitude of 400 Vand an internal impedance of ZS ¼ j7 V.Find the average power delivered to the load.
In Figure P15–21 the impedances are Z1 ¼ 35 þ j20 V;Z2 ¼ 70 þ j20 V, and Z3 ¼ 270 j90 V. Find the average power delivered to Z3.
A voltage source with Thevenin parameters vTðtÞ ¼5 sin 1000t V and RT ¼ 25 V drives the primary winding of an ideal transformer with n ¼ 2. Write an expression for the instantaneous power delivered to a 300-V load connected across the secondary winding.
The primary winding of an ideal transformer with n¼1/5 is connected to a voltage source with a source resistance of 2 kV. Find the load resistance connected across the secondary winding that will draw maximum power from the source.
The equivalent resistance in Figure P15–13 is REQ ¼ 15V. Find the turns ratio of the second ideal transformer.
The number of turns in the primary and secondary of an ideal transformer are N1 ¼ 50 and N2 ¼ 400. The primary winding is connected to a 120-V, 60 Hz source with a source resistance of 50 V. The secondary winding is connected to a 1600-V load. Find the primary and secondary currents.
The primary voltage of an ideal transformer is a 120-V, 60-Hz sinusoid. The secondary voltage is a 24-V, 60-Hz sinusoid. The secondary winding is connected to an 800-V resistive load.(a) Find the transformer turns ratio.(b) Write expressions for the primary current and voltage.
A pair of coupled inductors have L1 ¼ 3:6H; L2 ¼ 2:5H, and k ¼ 1:0. When the output terminals are open-circuitedði2ðtÞ ¼ 0Þ, the output voltage is observed to be v2ðtÞ ¼30 sin 1000t V. Find the input voltage v1ðtÞ for additive coupling.
In Figure P15–4 L1 ¼ 25mH; L2 ¼ 30 mH, and M ¼25mH. The output voltage is observed to v2ðtÞ ¼ 50 cos 1000t V when the output terminals are open-circuitedði2ðtÞ ¼ 0Þ. Find v1ðtÞ.
In Figure P15–1 L1 ¼ 10mH, L2 ¼ 10mH, M ¼ 7mH, i1ðtÞ ¼ 2 sin 1000t A, and i2ðtÞ ¼ 2 sin 1000t A.(a) Write the i–v relationships for the coupled inductors using the reference marks given.(b) Find the input voltage v1ðtÞ and the output voltage v2ðtÞ.
In Figure P15–1 L1 ¼ 10mH; L2 ¼ 5mH; M ¼ 7 mH, and vSðtÞ ¼ 100 sin 1000t V.(a) Write the i–v relationships for the coupled inductors using the reference marks in the figure.(b) Solve for i2ðtÞ when the output terminals are shortcircuited (v2 ¼ 0). Assume that i2ðtÞ has no dc
The portion of the radio spectrum shown in Figure P14–56 is the result you want after you design a suitable filter and amplifier. The passband gain desired is 100 dB and the‘‘shoulders’’ of your filter should have a roll-off of120 dB per decade. Design a wide-band filter and amplifier
Aamplified portion of the radio spectrum is shown in Figure P14–56. You want to select the signal at 1.22 MHz but it is barely above the background noise. Design a tuned filter that has a Q of at least 50 and amplifies the signal by 20 dB.Use OrCAD to validate your design.
Design an active high-pass filter to meet the specification in Problem 14–49. Use OrCAD to verify that your design meets the specifications.
Design an active high-pass filter to meet the specification in Problem 14–48. Use OrCAD to verify that your design meets the specifications.
Design an active high-pass filter to meet the specification in Problem 14–47. Use OrCAD to verify that your design meets the specifications.
Design an active high-pass filter to meet the specification in Problem 14–46. Use OrCAD to verify that your design meets the specifications.
A 10 kHz square wave must be bandwidth-limited by attenuating all harmonics after the third. Design a low-pass filter that attenuates the fifth harmonic and greater by at least 20 dB. The fundamental and third harmonic should not be reduced by more than 3 dB and the overshoot cannot exceed 13%.
Astrong signal at 2.45 MHz is interfering with anAM signal at 980 kHz. Design a filter that will attenuate the undesired signal by at least 60 dB. Verify your design using OrCAD.
Apesky signal at 100 kHz is interfering with a desired signal at 20 kHz.Acareful analysis suggests that reducing the interfering signal by 72 dB will eliminate the problem, provided the desired signal is not reduced by more than 3 dB. Design an active RC filter that meets these requirements.Verify
Design a low-pass filter with 10 dB passband gain, a cutoff frequency of 1 kHz, and a stopband gain of less than20 dB at 2 kHz. Overshoot is not a problem, but a low filter order, least number of parts, and a maximum of two OP AMPs is desired. Verify your design using OrCAD.
Design a low-pass filter with 0 dB passband gain, a cutoff frequency of 1 kHz, and a stopband gain of less than50 dB at 4 kHz. The filter must not have an overshoot greater than 12%. Verify your design using OrCAD.
Design a low-pass filter with 6 dB passband gain, a cutoff frequency of 2 kHz, and a stopband gain of less than14 dB at 6 kHz. The filter must not have an overshoot greater than 13%. Verify your design using OrCAD.
A low-pass filter is needed to suppress the harmonics in a periodic waveform with f0¼1 kHz. The filter must have unity passband gain, less than 50 dB gain at the 3rd harmonic, and less than 80 dB gain at the 5th harmonic.Since power is at a premium, choose a filter approach that minimizes the
Design an active low-pass filter to meet the specification in Problem 14–33. Use OrCAD to verify that your design meets the specifications.
Design an active low-pass filter to meet the specification in Problem 14–32. Use OrCAD to verify that your design meets the specifications.
Design an active low-pass filter to meet the specification in Problem 14–31. Use OrCAD to verify that your design meets the specifications.
Design an active low-pass filter to meet the specification in Problem 14–30. Use OrCAD to verify that your design meets the specifications.
Design an active low-pass filter to meet the specification in Problem 14–29. Use OrCAD to verify that your design meets the specifications.
The task is to design a second-order low-pass Filter using the three approaches shown in Problems 14–4, 14–5, and 14–6. The filter specs are a cutoff frequency of 100 krad/s and a z of 0.25. Using OrCAD, build your three designs and select the best one based on how well each meets the specs,
The circuit in Figure 14–9(b) has a high-pass transfer function given in Eq. (14–11) and repeated below TðsÞ ¼ V2ðsÞV1ðsÞ¼ mR1R2C1C2 s2 R1R2C1C2 s2 þ ðR2C2 þ R1C1 þ R1C2 mR2C2Þs þ 1 In Section 14–2, we developed equal element and unity gain design methods for this circuit.
The circuit in Figure 14–3(b) has a low-pass transfer function given in Eq. (14–6) and repeated below TðsÞ ¼ V2ðsÞV1ðsÞ¼ m R1R2C1C2s2 þ R1C1 þ R1C2 þ R2C2 mR1C1 ð Þs þ 1 In Section 14–2, we developed equal element and unity gain design methods for this circuit. This problem
Show that the circuit in Figure 14–17 has the bandstop transfer function in Eq. (14–20).
Show that the circuit in Figure 14–14 has the bandpass transfer function in Eq. (14–16).
Interchanging the positions of the resistors and capacitors converts the low-pass filter in Figure 14–3(a) into the highpass filter in Figure 14–9(a). This CR-RC interchange involves replacing Rk by 1/Cks and Cks by 1/Rk. Show that this interchange converts the low-pass transfer function in Eq.
For the circuit of Figure P10–3:(a) Find and express ZEQ(s) as a rational function and locate its poles and zeros.(b) Select values of R and C to locate a pole at 640 rad/s.Where is the resulting zero? 1 2R 2R 2 C ZEQ FIGURE P10-3
For the circuit of Figure P10–4:(a) Find and express ZEQ(s) as a rational function and locate its poles and zeros.(b) Select values of R and C to locate a zero at 33 krad/s. ZEQ 1 2R R C C/2 FIGURE P10-4
For the circuit of Figure P10–5:(a) Find and express ZEQ(s) as a rational function and locate its poles and zeros.(b) If R ¼ 2 kV and C ¼ 0.1 mF, select a value of L to locate zeros at j5000 rad/s.(c) Where are the poles located once you have selected the inductor in part (b)? 1 L R 2 C ZEQ
For the circuit of Figure P10–6:(a) Find and express ZEQ(s) as a rational function and locate its poles and zeros.(b) Select values of R and L to locate a pole at 150 rad/s.Where is the resulting zero? 500 1 2 20 w 2R L R ZEQ FIGURE P10-6
For the circuit of Figure P10–7:(a) Find and express ZEQ(s) as a rational function and locate its poles and zeros.(b) Select values of R and L to locate a pole at 2 krad/s.Where are the resulting zeros? 1 2L R2L 20 ZEQ FIGURE P10-7
For the circuit of Figure P10–8:(a) Find and express ZEQ(s) as a rational function and locate its poles and zeros.(b) If R ¼ 10 kV, select values of L and C to locate poles atj200 krad/s. Where are the resulting zeros? ww 1 R 2 Lsg ZEQ FIGURE P10-8 1/Cs
For the circuit of Figure P10–9:(a) If R ¼ 1 kV, L= 2 H, and C ¼ 0.5 mF locate the poles and zeros of ZEQ(s)?(b) If we were to increase the inductance to 5 H, how would the poles and zeros change? 1 L 000 20 R C ZEQ FIGURE P10-9
Find ZEQ1(s) and ZEQ2(s) for the bridge-T circuit in Figure P10–10. Express each impedance as a rational function and locate its poles and zeros. ZEQI w 2R 1 3 C C/2 R FIGURE P10-10 ZEQ2

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