Electronic – Why don’t we talk about a signal reflection when we treat a lumped element model of a circuit


I don't clearly understand why I have never seen a talk about a signal reflection in a lumped element model.

When there is a transmission line connected to circuits A (signal emitter) and B (signal receiver) at its ends, we talk about the signal reflection when ZA (Thevenin equivalent series impedance of A) and ZB (equivalent impedance of B) are not matched to a characteristic impedance of the line Z0.

However, when the line is so short compared to a signal wavelength on the line, we ignore the line and see the whole circuit as "A is directly connected B". This is a lumped element model of the whole circuit. In this case, we don't say there is the signal reflection when ZA and ZB are not matched.

It seems the signal reflections only occurs between the transmission line and circuits it connects to. Could you please tell me why?

Best Answer

Suppose we view the short transmission line as a two port network.

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The input voltage and current are the same as the output voltage and current (magnitude and phase relationship).

The input voltage (Vin) and current (Iin) will be determined by the termination load (ZL) and the source impedance (Zs). It doesn't 'see' the lumped LCR components of the transmission wire (or at most it sees the resistance of the wire), just the terminating load (ZL).

Its as if the transmission wire doesn't exist and you directly connect the load impedance to the source.

The output voltage (Vout) and current (Iout) are the values that would be obtained connecting the output impedance directly to the source.

Its when we increase the length of the transmission wire (in relationship to the wavelength of the signal) we start to see that Vout and Iout are no longer equal to Vin and Iin so the original simplification no longer stands.

Voltage and current change phase and reflection becomes more important on an unbalanced line.

We use the short wire approximation all the time without even realising it. Any cable connecting any form of AC is subject to the same basic physics. Its only at very high frequencies do the physical lengths of the cable start to become significant in terms of transmission line theory and we need to consider termination impedances (source and load).

As Andy correctly points out there are always reflections on a mismatched line but in the case of the short wire they are barely measureable.