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Ex1_9.CIR - z-parameter evaluation .PARAM I1value=1mA I5value=0mA I1 0 1 AC {I1value} R10 1 0 1Tohm ; Large resistor to avoid floating node Ci 1 2 100uF RB 2 3 10kohm VB 0 3 DC 10V R1 2 4 1kohm R2 4 0 5kohm C2 4 0 0.05uF Co 5 4 100uF I5 0 5 AC {I5value} R50 5 0 1Tohm ; Large resistor to avoid floating node .AC LIN 11 10kHz 100kHz .PROBE .END
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The values of R10 and R50 are su ciently large 1 1012  so that I"1 I"Ci and I"5 I"Co . If source I"5 is deactivated by setting I5value=0 and I1value is assigned a small value (i.e., 1 mA), then z11 and z21 are determined by (1.10) and (1.12), respectively. <Ex1_9.CIR> is executed and the probe feature of PSpice is used to graphically display the magnitudes and phase angles of z11 and z21 in Fig. 1-11(a). Similarly, I"1 is deactivated and I"5 is assigned a small value (I1value=0, I5value=1mA) to determine the values of z12 and z22 by (1.11) and (1.13), respectively. Execution of <Ex1_9.CIR> and use of the Probe feature of PSpice results in the magnitudes and phase angles of z12 and z22 as shown by Fig. 1-11(b). Example 1.10. Use SPICE methods to determine the h parameters suitable for use with sinusoidal excitation at a frequency of 10 kHz for the frequency-sensitive two-port network of Fig. 1-10(a). The h parameters of (1.16) to (1.19) for sinusoidal steady-state excitation are ratios of phasor voltages and currents; thus the values are complex numbers expressible in polar form as hij hij ij . Connect the sinusoidal voltage source and current source of Fig. 1-10(c) to the network of Fig. 1-10(a). The " netlist code below models the resulting network with parameter-assigned values for I"1 and V5 . Two separate executions of <Ex1_10.CIR> are required to produce the results needed for evaluation of all four h parameters.
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" " Through use of the .PRINT statement, both magnitudes and phase angles of V1 , V5 , I"Ci , and I"Co are written to <Ex1_10.OUT> and can be retrieved by viewing of the le.
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Ex1_10.CIR - h-parameter evaluation .PARAM I1value=0mA V5value=1mV I1 0 1 AC {I1value} R10 1 0 1Tohm ; Large resistor to avoid floating node Ci 1 2 100uF RB 2 3 10kohm VB 0 3 DC 10V R1 2 4 1kohm R2 4 0 5kohm C2 4 0 0.05uF Co 5 4 100uF V5 5 0 AC {V5value} .AC LIN 1 10kHz 10kHz .PRINT AC Vm(1) Vp(1) Im(Ci) Ip(Ci) ; Mag & phase of inputs .PRINT AC Vm(5) Vp(5) Im(Co) Ip(Co) ; Mag & phase of outputs .END
" Set V5value=0 (deactivates V5 ) and I1value=1mA. Execute <Ex1_10.CIR> and retrieve the necessary " values of V1 ; I"Ci ; and I"Co to calculate h11 and h21 by use of (1.16) and (1.18). h11 h21 Vm 1 0:9091 Vp 1 Ip Ci 0:028 08 909:1 0:028 Im Ci 0:001 Im Co 9:08 10 4 Ip Co Ip Ci 1808 08 0:908 1808 Im Ci 1 10 3
Set V5value=1mV and I1value=0 (deactivates I"1 ). Execute <Exl_10.CIR> and retrieve the needed values of " " V1 ; V5 ; and I"Co to evaluate h12 and h22 by use of (1.17) and (1.19). h21 h22 Vm 1 9:08 10 4 08 08 0:908 08 Vp 1 Vp 5 Vm 5 1 10 3 Im Co 3:15 10 6 Ip Co Vp 5 84:78 08 3:15 10 3 84:78 Vm 5 1 10 3
INSTANTANEOUS, AVERAGE, AND RMS VALUES
The instantaneous value of a quantity is the value of that quantity at a speci c time. Often we will be interested in the average value of a time-varying quantity. But obviously, the average value of a sinusoidal function over one period is zero. For sinusoids, then, another concept, that of the root-meansquare (or rms) value, is more useful: For any time-varying function f t with period T, the average value over one period is given by 1 t0 T F0 f t dt 1:20 T t0 and the corresponding rms value is de ned as s 1 t0 T 2 F f t dt T t0 where, of course, F0 and F are independent of t0 . gathered from Example 1.12.
1:21
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