Calculating output impedance?

[audioguy]

Is there a tutorial anywhere for figuring out the output impedance of pedals?

Thanks!

audioguy

[R.G.]

Place a variable resistor to ground from the output of the pedal. With the resistor opened, set some reference output voltage on the output of the pedal. Now connect the resistor and decrease the resistor towards zero. When the voltage is reduced to half the voltage it was at first, the resistor now equals the output impedance, by Ohm's law as applied to voltage dividers. Notice that if the output impedance is low, like the raw output of an opamp buffer, this may involve the effect putting out a destructive amount of current or going into self-limiting. But in most cases it works fine.

[audioguy]

set some reference output voltage on the output of the pedal.

You lost me there... will I need a scope and/or signal generator for this?

[R.G.]

Yes, you will need a signal generator to provide a steady signal. An o'scope would be nice, but a soundcard oscilloscope program will do. You can also use the "AC voltage" scales on your digital multimeter if they go small enough.

The definition of output impedance is the open circuit voltage divided by the short circuit current. The SCC is hard to measure easily, so the half-voltage external resistance is a sub for it.

[audioguy]

 I know I've seen tons of soundcard o'scopes floating around, so I'll go that route. thank you so much for the help!

[GibsonGM]

Get a free audio oscillator program.  I recorded a bunch of .WAV files to CD of 100Hz, 440Hz, 1000Hz etc sine waves.  Each lasts about 5 minutes.  I play it on my stereo, measure the output voltage with a DMM, note that, and feed it to the pedal.  There ya go! 

[Paul Marossy]

Hmm... so that Craig Anderton impedance tester circuit would work for either input or output impedance then?
http://www.diyguitarist.com/PDF_Files/ImpedanceTester.pdf

[alanlan]

It can also help just to look at the circuit diagram if it's available.  If you have an op-amp or emitter follower driving out directly (even if via a cap), then you can say it is low, relatively speaking of course.  If there is a 100K volume pot on the output, then the output impedance will depend on the volume setting and you may lose top end as you wind the volume down for example. 

[R.G.]

Hmm... so that Craig Anderton impedance tester circuit would work for either input or output impedance then?

Yes, and for the same reasons. However, The input impedances may well be in the megohm range, but output impedances will usually be from 10K on down to fractions of an ohm. If you get under maybe 50 ohms or so, do not proceed just to satisfy your curiousity without knowing what you're doing, as you can destroy things with low impedance tests even if you can complete them.

[Paul Marossy]

Hmm... so that Craig Anderton impedance tester circuit would work for either input or output impedance then?

Yes, and for the same reasons. However, The input impedances may well be in the megohm range, but output impedances will usually be from 10K on down to fractions of an ohm. If you get under maybe 50 ohms or so, do not proceed just to satisfy your curiousity without knowing what you're doing, as you can destroy things with low impedance tests even if you can complete them.

Thanks R.G., that's good to know!

[audioguy]

It can also help just to look at the circuit diagram if it's available.  If you have an op-amp or emitter follower driving out directly (even if via a cap), then you can say it is low, relatively speaking of course.  If there is a 100K volume pot on the output, then the output impedance will depend on the volume setting and you may lose top end as you wind the volume down for example. 

Im looking at some of the standard stuff we do here- BMP, TS, miniboost... things like that. So for a ballpark figure I can just look at the scheme and do some math?

[R.G.]

Im looking at some of the standard stuff we do here- BMP, TS, miniboost... things like that. So for a ballpark figure I can just look at the scheme and do some math?

Yes.

However, it is important to keep in mind that matching impedances is almost never what you want to do with audio. What you want is the proper mismatch, that being the driver/source having a lower impedance than the driven/load by at least 10:1. So yes, being able to thumbnail impedances from looking at the circuit and doing some quick series/parallel/Thevenin/Norton transformations is an important skill.

[grapefruit]

The output impedance of a common emitter amplifier is roughly equal to the collector resistor, so for the big muff it is 10k. With the volume control at full the 10k is in parallel with 100k so the output impedance will be a bit less than 10k.

For an op amp and (to a lesser extent) emitter follower the output impedance is low enough that you can say it is pretty close to zero. Often op amp circuits will have a series resistor on the output and the value of that resistor is equal to the output impedance. Of course, as RG said, you have to take into account any parallel impedances such us volume controls on the output.

Regards,
Stewart.

[oliphaunt]

The output impedance of a common emitter amplifier is roughly equal to the collector resistor...

Would that be true for a Mosfet as well?  I am trying to do a rough calculation of the output impedance this circuit snippet:

[R.G.]

It's lower than the drain resistor, 5.1K.

How much lower? I'd have to do some more elaborate calcs and know what's driving it. The feedback through the 1M/1M resistors and the output impedance of the stage that drives it have an effect.

[liquids]

I've found myself using op amp buffers all over the place since it's so useful to work with a signal that is low impedance between stages.   

I think I've always assumed that an op amp doing 'gain' had poor output impedance characteristics compared to a buffer.    The book I've been thumbing seems to be telling me something different, along the lines of 'as the gain of the stage increases, output impedance decreases.'  To me, that is great news.        Here I'm reading that it's typically no higher than 10k..... I'd like some confirmation and clarification if possible.

Lets say we have your 'typical' op amp gain stage, with a 'standard' type op amp, TL072 for example.  To be more specific, a schematic I'm thinking of and currently working with a lot is something like this Boss FA-1:  http://www.schematicheaven.com/effects/boss_fa1_fet_amp.pdf

What factors determine the output impedance after IC1, or of an op amp buffer or doing voltage gain?

Potential Variables I'm thinking of that may or may not have an impact:
1) Inverting vs non - inverting configurations (i.e. cap to Vref in non-inverting feedback loop?)
2) Value of resistance in the feedback loop from inverting input to the output
3) Diodes/caps/etc in the feedback loop
4) Op amp type
5) Voltage

It may be because I understand so little of what they say, but it seems few if any datasheets mention impedance.

I realize this is probably op amps 101, but that is where I'm at right now (though I'm using them anyhow!   ), so any help is appreciated.   

[PRR]

> The book ... 'as the gain of the stage increases, output impedance decreases.'

Uh, that just looks wrong.

It may be true is "gain of the stage" means "gain of the opamp", NOT "gain of the final circuit". It may be true for some uncommon topology. But otherwise it appears the printer mangled the words (easy to do).

> that an op amp doing 'gain' had poor output impedance characteristics compared to a buffer.     ....Here I'm reading that it's typically no higher than 10k.....

10K?? No, not in real life.

The TLO72 is crude. The open-loop (no NFB, useless as-is) output impedance is dominated by a couple hundred ohms stuck on the end. Say it is 300 ohms.

The closed-loop output impedance is the open-loop output impedance divided by the amount of gain applied to NFB.

The open-loop gain of a TL072 (any amplifier) varies with frequency (proof: no amplifier has gain at infinite frequency). General-purpose opamps have high DC gain which falls all across the audio band. But let us "pretend" that a TL072 has gain of 1,000 all across the audio band.

If we wire it unity gain, all 1,000 of gain is available to reduce errors, including output impedance. So the 300 ohms is divided by 1,000, the closed-loop output impedance is 0.3 ohms.

If we wire for closed-loop gain of 10, we need gain=10 for the closed-loop gain. The other 100 of open-loop gain is available to reduce errors. Now 300 ohms divided by 100 is 3 ohm output impedance.

And if we want to arrive at gain of 100, the output impedance is 30 ohms.

Output impedance rises with gain.

However 0.3 or 30 ohms is much-much less than all other circuit impedances (including the lowest loads a TL072 can drive cleanly). So for all practical situations, we pencil the output impedance as "zero, near-enough" and move on.

LM741, 5532, most other audio-likely opamp chips have even lower open-loop output impedance, and are just "more nearly zero" output impedance.

For comparison, the output impedance of a BJT emitter follower working at 1mA is just about 30 ohms. A JFET source follower at 1mA will be several hundred ohms.

The output impedance of "plate loaded pentodes" including most MOSFETs and JFETs is, as Stewart says, dang-near the DC load resistance. Unless, as R.G. says, there's NFB around the stage, and whether it is current feedback or voltage feedback.

In EE school (at least the old days, before chips and SPICE), such puzzles appeared on quizzes and many students got it wrong. It is sometimes "obvious" and sometimes confounding.

[PRR]

> 1) Inverting vs non - inverting configurations (i.e. cap to Vref in non-inverting feedback loop?)
2) Value of resistance in the feedback loop from inverting input to the output
3) Diodes/caps/etc in the feedback loop
4) Op amp type
5) Voltage

You figure the open-loop gain (which is rarely known exactly), and the loss from output to inverting input. That covers 1), 2), and 3). Sometimes the calculations are easy, sometimes they are devious. And subtle: a unity-gain inverter has 2:1 loss for the NFB loop.

Oh, 2): the assumption for Voltage Feedback opamps is that the input pin is infinite impedance, therefore the feedback impedances are always "low" and do not affect results.

The typical gain is cited on the opamp data sheet. Pay no attention to the DC gain. Find the gain versus frequency plot. For nearly any general-purpose chip opamp, the gain plot is a straight diagonal line from some absurd high value at low-low audio frequency to cross unity-gain at something like 1MHz or higher.

Take LM741. Unity-gain frequency is 1MHz. Working backward we know the gain is:

1 at 1MHz
10 at 100KHz
100 at 10KHz
1,000 at 1KHz
10,000 at 100Hz
100,000 at 10Hz

WOW! What a lot of variation!! How can this work?

Put it in a gain-of-10 NFB loop. The excess gain, over 10, reduces error. Or conversely, the error is related to the excess gain.

BIG at 1MHz
100% at 100KHz
10% at 10KHz
1% at 1KHz
0.1% at 100Hz

In audio, a gain-error of 0.1% is "nothing". A gain-error of 10% is actually 1dB, which is a very small error. So we see that a LM741 can be wired for gain of 10, and will do it, within 1dB all the way to 10KHz. Error at 20KHz is about 2dB, not a big deal. (But not negligible, especially in large wide-range systems... this is one of the reasons '741 is no longer popular in audio.)

Notice that as long as you have a LOT of gain, you really do not care WHAT the exact amount of gain is. That was the original idea. A telephone amplifier might have a gain of 5 with one tube or a gain of 6 with another "same type" tube, and might sag to gain of 4 before you got out there to replace the tube. Long lines might have dozens of amplifiers. If you got a load of "hot" tubes", or a load of dull tubes, the level at the far end could be WAY out of whack. And manual trimming is tedious, especially up on a phone pole. While tubes vary +/-30%, resistors are easy to make to 10% tolerance, and two 1% resistors are quite affordable. Stack the amp up to gain of 50, use NFB resistors to force gain to 5, and it will always be 4.5 to 5.5. If you can build the amp with gain of 500 (not easy with telco-quality tubes), then gain can always be 4.95 to 5.05. Now that cheap chips give gains well over 1,000 all across the audio band, we can largely ignore the effects of chip-swap, voltages, impedances, and know our results in advance.