Input and Output Impedance

by gaussmarkov

You have probably heard or seen it said that high input impedance and low output impedance are desirable properties for a circuit. Or at least something like that. 😉 Maybe it was the other way round, as in low input impedance and high output impedance? I found it hard to remember before I had some grasp on the concepts. This note describes the understanding that I have so far and a practical way to measure impedance.

The basic issue that motivates concern about input and output impedances is that circuits (and individual components) generally interact when they are connected. In other words, the signal at their junction, where the output of one circuit connects to the input of another, depends on both circuits—not just on the output.

It is tempting to think of a sequence of guitar stompbox effects as a sequence of unfolding events so that the first effect “happens” and is completed, then the second effect “happens” taking the first effect’s outcome as a given. This way of thinking isn’t necessarily correct and sometimes it is quite misleading. Instead, you might think of guitar effects as sensitive communicators that not only respond to what they hear but also respond to how they are heard.

Here’s an example. Suppose that you plug a Fender Stratocaster into a fuzz face pedal. Viewed sequentially, the clean Strat signal goes into the fuzz face which adds distortion and puts out the fuzzed signal into whatever comes next in the effects chain. That seems reasonable. But if you exchange the fuzz face pedal for a tube screamer and compare the clean Strat signal in both setups, you will find that they do not sound the same. So there really isn’t one initial, clean Strat signal. Actually, the Stratocaster is a sensitive communicator and its measured output responds to differences in the way fuzz faces and tube screamers “hear.” In other words, the Strat’s output impedance interacts with the the stompbox’s input impedance.

When Impedance Equals Resistance

The simplest analogy for explaining output and input impedances is to treat the output (or source) as a perfect AC voltage source in series with a resistor and to treat the input (or load) as a resistor connected to ground. Certainly stompboxes and guitars are more complicated devices than these, but this approximation can be useful. When this output circuit is connected to this input circuit, their junction is the junction of a voltage divider. So it is possible to explain impedance within the framework of a (resistive) voltage divider, where we focus on the signal at the junction.

Here is a schematic representation. Admittedly, stompbox signal chains usually go in the other direction. as in right-to-left. 😉

Impedance Divider
Photo credit: Gladmarr

R1 is the source (or output) resistance and R2 is the load (or input) resistance. We are concerned with the signal at the junction denoted by the red line.

First, consider two extremes. If we make the load (or input resistance) infinite, it is as though we remove that resistor altogether and leave an open circuit. In that case, the signal at the junction is exactly the output signal. On the other hand, if we make the load trivial so that the input resistor is just a wire (or a short), then the input signal goes straight to ground and there is no signal at the junction at all. In the first case, we have an input impedance that is high relative to the output impedance and the AC signal is preserved. In the second case, the input impedance is low relative to the output impedance and the AC signal is said to be loaded down.

Similar conclusions follow from extreme values for the output resistor. If the output resistor has no resistance, then the signal at the junction is exactly the output signal. On the other hand, if the output resistance is infinite then no signal reaches the junction of the voltage divider. As before, a relatively low input impedance (or relatively high output impedance) kills the signal and a relatively high input impedance (or relatively low output impedance) preserves the signal.

In between the extremes, we have a basic resistive voltage divider. In such voltage dividers, all that matters for voltage at the junction is the relative values of the resistors. The fraction of the original signal that appears at the junction is R2/(R1 + R2), as explained in Resistors in Series. If the input and output resistances are equal then the signal amplitude is cut in half by the interaction of the input and output resistances. The higher the input resistance R2, the greater the fraction of signal that appears at the junction. This formula gives precision to the basic lesson that low output and high input impedances are desirable.

More Generally . . .

Beyond the special case of a resistive voltage divider, the interaction of output and input depends on the particular AC signal. It’s really that complicated. To make the analysis tractable, electronic theory focuses on AC sine waves. In that case, there are only three characteristics of the signal to consider: amplitude, frequency, and phase. Impedance is a mathematical concept that is related to phasors, an algebraic device for solving a particular family of differential equations. If the input of a circuit does not preserve the sinusoidal character of a signal when connected to an ideal AC source in series with a resistor, then the input impedance is not even defined.

So what is the meaning of “impedance” in discussions about stompboxes? Often impedance refers to resistance that depends on frequency. An example is the behaviour of a capacitor, which actually fits into the sinusoidal electronic theory. An AC sine wave with frequency f through a capacitor with capacitance C has a resistance equal to 1/(2πfC), where resistance is the ratio of the amplitude of voltage to the amplitude of current. If you want to pursue the details, try reading Capacitors: Math.

More Practically . . .

A practical way to deal with the complications introduced by impedance is to ignore phase shifts, forget about sine waves, choose a frequency for calculations and measurement, and focus on resistance again. Later, you can always change the frequency and recalculate or remeasure to see how sensitive your results are to the frequency.

Zachary Vex gave a nice practical (as in observable) description of impedance in a post on Aron’s diystompboxes forum. The basic idea is that when R1 equals R2 in a voltage divider the voltage at the junction is half the voltage at the source. As a result, you can measure one resistor using a potentiometer (as a variable resistor) in place of the other and finding the setting that produces half the source voltage at the junction.

So let’s say you want to measure the input impedance of your effect pedal.

  1. Create an AC source and connect that in series with a 1M variable resistor and the pedal.
  2. Use a DMM to measure the frequency and amplitude of the source at the junction between the source and the variable resistor. Suppose you read 500Hz and 100mV rms
  3. Start measuring ACV rms at the junction between the variable resistor and the pedal’s input.
  4. Adjust the variable resistor until the ACV reading is 50mV at the junction.
  5. Now disconnect everything and use your DMM to measure the resistance in ohms of the variable resistor.

That resistance is a practical version of impedance at 500Hz. For comparison, repeat the measurement for lower and higher frequencies.

Measuring output impedance is similar.

  1. Create an AC source with a known frequency, say 500Hz, and connect that to the input of your pedal.
  2. Connect the the variable resistor to the pedal’s output and to ground.
  3. Use a DMM to measure the frequency and amplitude of the output of the pedal, say 500Hz and 100mV rms.
  4. Start measuring ACV rms at the junction between the variable resistor and the pedal’s output.
  5. Adjust the variable resistor until the ACV reading is 50mV at the junction.
  6. Now disconnect everything and use your DMM to measure the resistance in ohms of the variable resistor.

In this case, it is unlikely that your pedal will put out a sine wave even if you send one into its input. So remember that we are forgetting about sine waves. All we need is a steady AC source. Don’t have one? Guess what? You probably have the parts to build one. 🙂

An alternative, but similar approach is to replace the variable resistor with a fixed resistor (R) and measure the AC voltage across the resistor (VR) and across the source (VS). Then calculate the impedance as (VSVRR/VR.


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9 Responses to “Input and Output Impedance”

  1. plg said:

    … much compliments ! great article 😉

    Posted 05.02.2008 at 2:00 am

  2. jacker said:

    Very nice writeup. Couple of small things, no need to measure the frequncy is there?
    Also, I think the 1M pot needs or ought to be linear. I just “built” this and tested a few pedals which had specs in their user manual (Boss, Ibanez..) and measured an output impedance that is about 100k less tn spec in real life. I tried output impedance measuring but I wonder if 1M is too big? I can’t get it down to halfway… I also looked on a scope and the pot really rounds off the input signal (my input is more of a square wave, which may be messing wiith RMS values?) and there seems to be a second AC signal it rides on when it is at lowest, etc.

    Posted 20.08.2008 at 10:48 am

  3. jacker said:

    A little more testing…I find a couple of things. On non-true-bypass pedals, it is interesting to measure input and output impedances both with pedal on and with it off. They change on many pedals. Also, with a 1Mohm pot it is extremely inaccurate or difficult to adjust, it would be smart to use a 100kohm pot for measuring output impedance.

    Wtih True Bypass, if you try to measure in or output with pedal off though you aren’t measuring the pedal but the signal generator source.

    You generally want

    Posted 22.08.2008 at 6:16 am

  4. Hugo Gutierrez S. said:

    Thanks for the circuit, I commit a great mistake, I do the circuit using the pattern reversed, this had as consequence to insert the IC in reverse mode. I had to invert the pins … but it works fine. I used a LM741 insted the LM308 (hard to find in my country) , If anyone wants to know how to change it, go to http:\\hugosworld0.tripod.com, soon I will pubish how to do it.

    Regards

    Hugo

    Posted 05.09.2008 at 2:13 pm

  5. Ankur said:

    It is really a awesome method to correlate and learn. I would recommend to read it once and make similar analogies for future reference.

    Thanks buddy.

    Posted 27.08.2009 at 11:25 am

  6. Vishy said:

    Superb compiled – thnx for d info

    Posted 21.10.2010 at 10:27 am

  7. Nguyen Dang Minh said:

    This is the lesson of resistance and impedance that having simple explanations. thank very much.

    Posted 23.01.2011 at 2:14 am

  8. John said:

    You prove again that teaching is an art. Great. Thanks.

    Posted 09.02.2011 at 7:13 am

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