CHAPTER 4 - Impedance Matching
156
4.2.2 Impedance & Series Elements
As explained in section 1.5.5, complex numbers, which are used to represent the impedance
of an electrical network, give us two main bits of information:
- the ratio of the amplitude of the voltage across the impedance and the amplitude of the
current through it
- the difference between the phase of the voltage waveform and current waveform.
This is shown in equation (4.2-1).
( )
In a Cartesian form the impedance may be written as
Where the real part is termed resistance and the imaginary part is termed reactance.
Representing a passive electrical network with impedances is especially appropriate when only
series elements are present. This is because whether they are reactive or resistive, we can just add
such elements together and easily obtain a single complex number which greatly simplifies the
analysis of the network. For example the series R-C combination shown in Figure 4.2-7
Figure 4.2-7 Series R-C
will be characterised (section 1.5.4.3) by an impedance
Let us now consider the series R-C circuit shown in Figure 4.2-8 and let us attempt to calculate the
impedance of this network by inspection of voltage and current waveforms alone!
Figure 4.2-8 R-C network schematic in MWO
R
C
ACVS
ID=V1
Mag=1 V
Ang=0 Deg
Offset=0 V
DCVal=0 V
RES
ID=R1
R=50 Ohm
CAP
ID=C1
C=5.6 pF
M_PROBE
ID=VP1
(4.2-1)
(4.2-2)
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