Solved: a) Derive two equivalent circuits that are satisfied by the y-parameter

Find the v parameters for the circuit in Fig. 18.3

Find the g and h parameters for the circuit in Fig. 18.3.

The following measurements were made on a two-port resistive circuit. With 50 mV applied to port 1 and port 2 open, the current into port 1 is 5 /xA, and the voltage across port 2 is 200 mV. With port 1 short-circuited and 10 mV applied to port 2, the current into port 1 is 2 ^tA, and the current into port 2 is 0.5 ^A. Find the g parameters of the network.

The following measurements were made on a two-port resistive circuit: With port 1 open, V2 = 15 V, V1 = 10 V, and h = 30 A; with port 1 short-circuited, V2 = 10 V, 12 = 4 A, and /] = - 5 A. Calculate the z parameters.

The following measurements were made on a resistive two-port network that is symmetric and reciprocal: With port 2 open, V\ = 95 V and I{ = 5 A; with a short circuit across port 2, Vl = 11.52 V and I2 = -2.72 A. Calculate the Z parameters of the two-port network.

The a parameters of the two-port network shown are an = 5 X 10~4 , al2 = 10 ft, a2l = 10~6 S, and a22 = - 3 X 10~2 . The network is driven by a sinusoidal voltage source having a maximum amplitude of 50 mV and an internal impedance of 100 + /0 ft. It is terminated in a resistive load of 5 kft. a) Calculate the average power delivered to the load resistor. b) Calculate the load resistance for maximum average power. c) Calculate the maximum average power delivered to the resistor in (b)

Each element in the symmetric bridged-tee circuit shown is a 15 ft resistor. Two of these bridged tees are connected in cascade between a dc voltage source and a resistive load. The dc voltage source has a no load voltage of 100 V and an internal resistance of 8 ft. The load resistor is adjusted until maximum power is delivered to the load. Calculate (a) the load resistance, (b) the load voltage, and (c) the load power. /l ^- + za zc v, zb < za h ~*c + Vi

Find the a parameters for the circuit in Fig. PI8.8.

Use the results obtained in Problem 18.8 to calculate the g parameters of the circuit in Fig. PI8.8.

Find the h parameters of the two-port circuit shown inFig.P18.10.

Find the g parameters for the operational amplifier circuit shown in Fig. PI 8.11.

The operational amplifier in the circuit shown in Fig. P18.12 is ideal. Find the h parameters of the circuit.

The following direct-current measurements were made on the two-port network shown in Fig. PI8.13.Port 2 Open K, = 20 mV Is -5V /, = 0.25 juA Port 2 Short-Circuited lx = 200 fiA h = 50 fiA V{ = 10 V Calculate the g parameters for the network.

a) Use the measurements given in Problem 18.13 to find the y parameters for the network. b) Check your calculations by finding the y parameters directly from the g parameters found in Problem 18.13.

Derive the expressions for the h parameters as functions of the g parameters.

Derive the expressions for the b parameters as functions of the h parameters.

Derive the expressions for the g parameters as functions of the z parameters.

Find the ^-domain expressions for the a parameters of the two-port circuit shown in Fig. P18.18. Figure P18.18 *i 1F i k e : |(- 1 TVY-Y-V 0 ' ' :4H

Find the ^-domain expressions for the z parameters of the two-port circuit shown in Fig. P18.19. Figure P18.19

Find the frequency-domain values of the a parameters for the two-port circuit shown in Fig. P18.20.

Find the h parameters for the two-port circuit shown in Fig. P18.20.

a) Use the defining equations to find the s-domain expressions for the h parameters for the circuit in Fig. PI 8.22. b) Show that the results obtained in (a) agree with the /i-parameter relationships for a reciprocal symmetric network.

Is the two-port circuit shown in Fig. PI8.23 symmetric? Justify your answer.

Derive the expression for the voltage gain V2/V\ of the circuit in Fig. 18.7 in terms of the y parameters.

Derive the expression for the input impedance (Zin = Vj//i) of the circuit in Fig. 18.7 in terms of the b parameters.

Derive the expression for the voltage gain V2/Vg f the circuit in Fig. 18.7 in terms of the h parameters.

Derive the expression for the current gain I2/l\ of the circuit in Fig. 18.7 in terms of the g parameters.

Find the Thevenin equivalent circuit with respect to port 2 of the circuit in Fig. 18.7 in terms of the z parameters.

The b parameters of the amplifier in the circuit shown in Fig. PI8.29 are hn = 25; blx = -1.25 S; bl2 = 1 kO; b22 = -40. Find the ratio of the output power to that supplied by the ideal voltage source.

The y parameters for the two-port amplifier circuit in Fig. PI 8.30 are yu = 2mS; yn = -2 /xS; y2\ = 100 mS; y22 = - 5 0 JJLS. The internal impedance of the source is 2500 + /0 ft, and the load impedance is 70,000 + jO 0.. The ideal voltage source is generating a voltage vg = 80 V2 cos 4000r mV. a) Find the rms value of V2. b) Find the average power delivered to ZL. c) Find the average power developed by the ideal voltage source

For the terminated two-port amplifier circuit in Fig. P18.30, find a) the value of ZL for maximum average power transfer to ZL b) the maximum average power delivered to Zi c) the average power developed by the ideal voltage source when maximum power is delivered to ZL.

The linear transformer in the circuit shown in Fig. P18.32 has a coefficient of coupling of 0.75. The transformer is driven by a sinusoidal voltage source whose internal voltage is vg = 260 cos 4000^ V. The internal impedance of the source is 25 + ;0 ft. a) Find the frequency-domain a parameters of the linear transformer. b) Use the a parameters to derive the Thevenin equivalent circuit with respect to the terminals of the load. c) Derive the steady-state time-domain expression for ih.

The g parameters for the two-port circuit in Fig. PI 8.33 are 1 ! Q ^ = 6" ; 6 S ' 12 = -0.5 + /0.5; -/0.5; g22 = 1.5 + /2.5ft. The load impedance ZL is adjusted for maximum average power transfer to ZL. The ideal voltage source is generating a sinusoidal voltage of vg = 42V2" cos 5000* V. a) Find the rms value of V2. b) Find the average power delivered to ZL. c) What percentage of the average power developed by the ideal voltage source is delivered by ZL?

The following dc measurements were made on the resistive network shown in Fig. P18.34. Measurement 1 V, = 4V /, - 5 raA h = -200 mA Measurement 2 V! = 20 mV /, = 20 juA V2 = 40 V /2 = 0A A variable resistor R0 is connected across port 2 and adjusted for maximum power transfer to R(). Find the maximum power.

The following measurements were made on a resistive two-port network: Condition 1 - create a short circuit at port 2 and apply 20 V to port 1: Measurements: I: = 1 A; h = - 1 A. Condition 2 - create an open circuit at port 1 and apply 80 V to port 2: Measurements: V{ = 400 V; I2 = 3 A. Find the maximum power that this two-port circuit can deliver to a resistive load at port 2 when port 1 is driven by a 4 A dc current source with an internal resistance of 60 O.

a) Find the s-domain expressions for the g parameters of the circuit in Fig. PI 8.36. b) Port 2 in Fig. P18.36 is terminated in a resistance of 400 O, and port 1 is driven by a step voltage source vx(t) = 30u(t) V. Find v2(t) for t > 0 if C = 0.2 /xF and L = 200 mH.

a) Find the y parameters for the two-port network in Fig. PI8.37. b) Find v2 for t > 0 when v8 = 50u(t) V.

The h parameters of the first two-port circuit in Fig. PI8.38(a) are hn = 1000 O; hn = 5 x 10-4: /i2i = 40; h22 = 25 fiS. The circuit in the second two-port circuit is shown in Fig. P18.38(b), where R = 72 kH. Find va if vn = 9 mV dc.

The networks A and B in the circuit in Fig. PI8.39 are reciprocal and symmetric. For network A, it is known that a'n = 5 and a\2 = 24 O. a) Find the a parameters of network B. b) Find V2 when Vg = 75/CT V, Zg = 1/tT n , and ZL = 10/0 a .

Tlie z and _y parameters for the resistive two-ports in Fig. P18.40 are given by z\\ = -r-U; ); n = 200/xS; 3 100 <12 ft; y12 = 40 /x.S; z21 = -kO ; y2l = -800/xS Z22 = v ^ i i ; - y 22 = 4W A0 if 1? = 30 mV dc.

a) Show that the circuit in Fig. P18.41 is an equivalent circuit satisfied by the //-parameter equations. b) Use the /i-parameter equivalent circuit of (a) to find the voltage gain V^Vg in the circuit in Fig. 18.11. Figure P18.41

a) Show that the circuit in Fig. PI 8.42 is an equivalent circuit satisfied by the z-parameter equations. b) Assume that the equivalent circuit in Fig. PI 8.42 is driven by a voltage source having an internal impedance of Z? ohms. Calculate the Thevenin equivalent circuit with respect to port 2. Check your results against the appropriate entries in Table 18.2. Figure P18.42 /, I-, + -oh(Z[2 ~ Zl\) -II tl\ ^22 ^21 221 + V,

a) Show that the circuit in Fig. P18.43 is also an equivalent circuit satisfied by the z-parameter equations.b) Assume that the equivalent circuit in Fig. PI8.43 is terminated in an impedance of ZL ohms at port 2. Find the input impedance V\jl\. Check your results against the appropriate entry in Table 18.2. Figure P18.43 /. * - + v. ?11 - *12 z 12 II ^22 ~~ - l2 \ ^ + A(*21 _ ^12)

a) Derive two equivalent circuits that are satisfied by the y-parameter equations. Hint: Start with Eqs. 18.2. Add and subtract y2\V2 to the first equation of the set. Construct a circuit that satisfies the resulting set of equations, by thinking in terms of node voltages. Derive an alternative equivalent circuit by first altering the second equation in Eq. 18.2. b) Assume that port 1 is driven by a voltage source having an internal impedance Z? , and port 2 is loaded with an impedance ZL. Find the current gain /2//1. Check your results against the appropriate entry in Table 18.2.

a) Derive the equivalent circuit satisfied by the ^-parameter equations. b) Use the g-parameter equivalent circuit derived in part (a) to solve for the output voltage in Problem 18.38. Hint: Use Problem 3.65 to simplify the second two-port circuit in Problem 18.38.

a) What conditions and measurements will allow you to calculate the b parameters for the "black box" amplifier described in the Practical Perspective? b) What measurements will be made if the resulting b parameters are equivalent to the h parameters calculated in the Practical Perspective?

Repeat Problem 18.46 for the z parameters.