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 hotironsmoke 14th April 2013 12:43 PM

staging impedance ratio

I know these forums are not for electronic tutorials, but with moderator indulgence, it might help with a commonly posed question.
I have been confused by staging problems for many years. Last week the principles finally fell into place,.
If it is obvious to you, you can skip this post. I hope it might help other confused souls.

Consider two consecutive stages,S1 and S2 with impedances R1 (out) and R2 (in) at a stated frequency.
We can define a parameter "Staging Impedance Ratio" at that frequency such that (ignoring cable effects),

SIR = R2/(R1+R2)

This ratio will be constrained between 0 and 1.
Remember that the two stages are in a series circuit, so that the same current flows in both.

If a voltage,V, (eg signal) is applied to the circuit (say at the output of stage1), the voltage V2 developed across stage 2
input is given by SIR multiplied by V.
For audio voltage amp. stages we prefer a high SIR, say 0.9 (impedance bridging). We do this by trading off against power transfer.

For all signals, the maximum total circuit power can be shown to occur when R1 = R2 and SIR = 0.5
Accept that differential calculus shows S1 plus S2 circuit current (and power) are maximum at this point. (efficiency 50%).
However, for a voltage amp stage we do not want S2 input signal volts to be half applied signal volts.
This is not the maximum electrical efficiency which is found as R1 approaches zero.(ie SIR approaches 1)
Power and efficiency can be traded off to suit circumstances.
Thus we can lower R2 by connecting a current driven device (eg loudspeaker), where current is the large component of power.=Vi.
The SIR will be a small value and the resulting voltage developed across S2 lower. The S1S2 circuit power may be too low to allow
sufficient current through (source and) load S2.
Highest circuit power is by matching impedances eg in this case using a step-down transformer connection. If there is still too little
circuit power, you must consider lowering R1 eg by feedback or adding a buffer amp stage etc.
If you apply amplification to S2 to restore low circuit signal power without changing R2, you risk higher distortion and altered frequency/power curve.
If R1 or R2 include high reactance (complex) components, the frequency/power curve can show large changes,peaks or notches.

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