CHAPTER 4 - Impedance Matching
172
If the parallel R-C circuit that we have worked out is equivalent to the series one, our signal
generator should see the same impedance for both networks. This is indeed the case as shown by
the waveforms in Figure 4.2-36.
Figure 4.2-36 Voltage and current waveforms for series R-C in Figure 4.2-34 (left), Voltage and current waveforms for
equivalents parallel R-C in Figure 4.2-35 (right)
To summarise, for each series R-C network there exists and equivalent parallel R-C network and vice-
versa. The same applies to R-L networks. Table 4.2-1 and Table 4.2-2 give all the formulae that we
need to carry out these conversions.
R-L Circuits
Inductance
R-C Circuits
Capacitance
Parallel to
Series
( )
Series to
Parallel
( )
( ) ( )
Table 4.2-1 Formulae for parallel to series and series to parallel conversion of R-C and R-L circuits based on Q
R-L Circuits
Inductance
R-C Circuits
Capacitance
Parallel to
Series
Series to
Parallel
Table 4.2-2 Fomulae for parallel to series and series to parallel conversion of R-C and R-L circuits based on reactance
0 0.5 1 1.5 2
Time (ns)
Series to Parallel Conversion
-1
-0.5
0
0.5
1
-60
-30
0
30
60
p2
p1
0.5 ns
0 V
0.3239 ns
0 mA
1.25 ns
0.9999 V
1.07 ns
44.7 mA
Vtime(ACVS.V1,1)[*] (L, V)
series to parallel conversion
Itime(ACVS.V1,1)[*] (R, mA)
series to parallel conversion
p1: Freq = 1000 MHz
p2: Freq = 1000 MHz
0 0.5 1 1.5 2
Time (ns)
Series
-1
-0.5
0
0.5
1
-60
-30
0
30
60
p2
p1
0.5 ns
0 V
0.3237 ns
0 mA
1.25 ns
0.9999 V
1.074 ns
44.7 mA
Vtime(ACVS.V1,1)[*] (L, V)
series
Itime(ACVS.V1,1)[*] (R, mA)
series
p1: Freq = 1000 MHz
p2: Freq = 1000 MHz
Conquer Radio Frequency
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