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Is impedance matching a MUST in low frequency operation, or can we ignore impedance effects?
January 7, 2008

There are actually two questions here. The answers to both are “no.”

No, impedance matching is not an absolute must in low-frequency operation; and no, you can’t ignore impedance effects. If you do, they’ll come back to bite you.

First, we need to talk about what constitutes “low” frequency. The signal’s wavelength provides a convenient yardstick for deciding what, in a particular situation, constitutes “low” frequency and what frequencies should be considered “high.”

The speed of an electrical signal on a transmission line is reduced from that of light in free space by a factor called the velocity factor. In general, the velocity factor for open-wire transmission lines is about 0.95. Following the usual wavelength/frequency relationship, that means a 300 MHz signal has a wavelength on the transmission line of about 95 cm.

If you’re dealing with a wire 9.5 cm long, only about a tenth of a 300 MHz wave will fit on it. That means the phase difference between the signal at one end of the wire and that at the other is about 36º. Standing waves cannot form on the wire, so it won’t resonate at that frequency, or any frequency up to the fourth harmonic. If such a wave is at its peak at one end of such a wire, its voltage will drop by only about 20% at the other end. Thus, 300 MHz is fairly low frequency to a circuit 9.5 cm across. 

What constitutes low frequency depends on the transmission line length.

Shifting to 1.5 GHz, however, drops the wavelength from 95 cm to 19 cm. Now, that 9.5 cm wire is a half-wave dipole and will radiate RF power away like gangbusters! It also will resonate very nicely, thank you. The phase change from one end of the wire to the other is 180º, and we know what happens then!

Thus, 1.5 GHz is not a low frequency to a circuit 9.5 cm across, while 300 MHz is.

In the low-frequency regime, we can treat the signal as effectively dc as long as the source and load impedances are purely resistive. How we match impedances now depends on what we’re trying to accomplish.

Suppose we’re trying to deliver maximum signal power. That’s usually the situation in powerline applications, as well as most audio and RF signaling applications.

Assuming the source voltage and resistance are fixed, if the load resistance is very low compared to the source resistance, all the power gets dissipated in the source and very little reaches the load. When, on the other hand, the load resistance is very high compared to the source resistance, the high load resistance chokes off current flow and, again, very little power is delivered. Maximum power arrives at the load when the source and load resistances are equal.

For a given source voltage and resistance, maximum power is delivered when the load resistance matches.

If, however, we have a measurement application, such as the feedback leg of an analog control loop, what we want most is voltage-signal fidelity. In that case, any voltage drop in the source resistance adds to the measurement error. What we want is maximum voltage delivered to the load with minimum current coursing through the signal leads. We achieve that by setting up a high impedance mismatch favoring the load.

When the goal is to transfer the source voltage to the load, as in a feedback application, maximize the load resistance.

That is why instrumentation amplifiers have very high input impedances and low output impedances. They load the sensor circuit as little as possible and present a low source impedance to the next stage.

Now, suppose we have a high-power motor/drive application. What we care about there is efficiency. That is, we want to maximize the ratio of power delivered to the load to the product of source voltage and current. That also occurs when the load impedance is much higher than the source impedance. 

When power transfer efficiency is important, maximize the load resistance.

Why not tune impedances to deliver maximum power? Because in that configuration, as much power gets dumped into source’s final amplier as heat as gets delivered to the load. Not only is it a waste of power, it is bad for the final amplifier.

So, in the end we can never ignore source, load, and transmission line impedances, but matching them is not always the right thing to do.

Control Engineering offers other impedance and power-related coverage.

Posted by Charlie Masi on January 7, 2008 | Comments (0)