Impedance Matching


If you are into RF (radio frequency) design, or perhaps telecommunications, this becomes an important topic. For hi-fi and professional
audio, it is a meaningless concept and will actually cause an increase in noise. It has often been claimed that a 600 Ohm microphone should
be matched to a 600 Ohm input for best performance. This is simply wrong, and microphone manufacturers specifications will support me on this.


Imagine a 600 Ohm microphone with an open-circuit output voltage of 5mV. If the mic preamp has an input impedance of 600 Ohms, the microphone 
output is reduced by 6dB to 2.5mV because of the simple voltage divider created. It helps to use the engineering "model" for a signal source of
any kind, which is basically a "perfect" (meaning zero Ohms impedance) voltage generator, with a resistance + inductance or capacitance 
(sometimes in combination) in series with the output.


If the output is loaded, then the available voltage from the source drops, and that in turn means that more amplification is needed to obtain
the final voltage needed. If the output is reduced by 6dB, this means that an additional 6dB of gain is required to compensate - therefore the
circuit will have 6dB more noise.

The ideal for a microphone is to use a high impedance input, but this creates other problems, so a compromise is needed. Typically, a good mic
preamp (for microphones of up to 600 Ohms) will have an input impedance of between 1.2k and 3k Ohms. This causes far less loading, and does not
cause any problems for the microphone.

Generally, it is desirable that the output impedance is low, and the destination impedance high, and this is the case with the majority of modern
equipment. Preamps usually have an output impedance of less than 1k Ohm, and power amps will have an input impedance of at least 10k Ohms, but more
commonly 22k or 47k.


So why is impedance matching important for RF and telecommunications? The reasons are completely different, as we shall see.


Radio Frequencies: When an RF voltage and current are transmitted along a wire, the impedance of the cable itself becomes significant, and for any
distance that is "significant" - which is to say any distance greater than about 0.1 of the signal's wavelength - matching is necessary. The wavelength
is calculated from the speed of light (3 x 10 ^ 8 m/s, or 300,000km/s) multiplied by the "velocity factor" of the cable. This varies from
about 0.7 up to 0.9 depending on the dielectric constant of the inner insulator and cable construction, meaning that a signal travels more slowly
in a cable than in free air or space.


Wavelength = C / f         (where C = velocity and f = frequency)
A 1Mhz signal travelling in a typical coaxial cable (velocity factor of 0.8) will have a wavelength of ...

Wavelength = ( ( 3 x 10E8) x 0.8 ) / 1 x 10E6 = 240m
Based on this, any attempt to transport a 1MHz signal further than about 24m will start to cause problems unless the send and receive impedances are
properly matched - not only to each other, but to the cable as well.

In the hi-fi audio world, this is not an issue, since this is 50 times the highest frequency we can hear, and few instruments create appreciable
harmonics above 20kHz anyway. In theory, we could send an audio signal 12km without having to worry about impedance matching, although at extreme
line lengths matching can reduce high frequency signal losses. To understand the reasons is beyond this article, as it involves transmission line
theory - not one of the easiest concepts to grasp.

Telecommunications: Impedance matching is a requirement in telecommunications networks, but not for any of the reasons you might think. It is
actually rare for an analogue phone line to run more than about 5km from the exchange (Central Office in the US) to the user's location.
Impedance matching is required to enable the hybrid - a circuit that allows simultaneous transmit and receive on a single pair without interference
- to function properly. If the impedances are not properly matched, you will hear too much of your own voice when you speak, the far end speech will
be too soft, and both parties will very likely get lots of echo on the line.

Because of the distances involved, the telecommunications network is balanced, to prevent noise.


Extract by Rod Elliott of Elliott Sound Productions (ESP) :   http://sound.westhost.com/impedanc.htm