#138: How to Measure Output Impedance

in this video we're going to address how to measure output impedance this has been requested a couple of times and this will work for you know many circuits but but certainly not all but this will kind of work in a general case and we're talking about output impedance that can kind of be modeled as kind of an ideal resistor in series with an ideal voltage source now and this might be buried inside or part of a function generator or signal generator or maybe other some other kind of circuit or amplifier or something like that and really all we need to do is to really measure how the output voltage changes as a function of the load applied and from there we can derive what the output impedance is now this is our test subject for today this is a function generator that I put together probably 25 years ago maybe even more maybe close to 30 years ago and I remember building a custom output amplifier for it where I could add DC offset in either direction and and I make that adjustable but I don't really remember what I designed in as the output impedance or if I did something specific or not this is a long time ago so rather than pull it apart I figured let's just go measure what that output impedance is so I've got the generator set up to generate a relatively low frequency about two kilohertz or so and that's kind of important because we want to ensure we're operating at a low enough frequency that we don't have to worry about reflections on a 50 ohm cable or anything like that now we generally want to use a sine wave so that we only have energy effectively at one frequency where if we'd use a square wave or a triangle wave we're going to have harmonic energy that extends up to high frequencies and the reflections that you get off the ends of improperly terminated cables and such might distract you from the actual results so we're just going to use a sine wave at about two kilohertz which will work just fine to characterize the output impedance of this device so in this first example we'll use the process of simply measuring the open circuit response out of the amplifier with effectively a very high impedance load and then measure the voltage that you get out without changing anything on the generator measure the voltage you get out with a load impedance applied and once you have those two voltages the open circuit voltage and the loaded voltage it's a simple matter of plugging them into this equation and the output resistance will simply be equal to the load resistance applied multiplied by this quantity the open circuit voltage divided by the load voltage minus one and so let's go run that example so the output of my home-brew signal generator is going into the oscilloscope here I've got the scope set to a one mega ohm input impedance which is going to give me a nice effectively open circuit load and I've got about a two kilohertz signal going in here and I can just simply use some cursors here to make a say a peak to peak voltage measurement for our open circuit measurement and I can see that it's really right at about 4 volts peak-to-peak so that'll be our V open of 4 volts peak-to-peak okay to measure the loaded voltage I'm just going to use a resistor substitution box here I've got this one doubt into 1 kilo ohms or 1000 ohms and I just have it connected up through a couple of banana leads into this adaptor which is going to allow me to plug it right into and load my signal generator with that so now with that loaded at a thousand ohms I can see my voltage is dropped as you'd expect it would so what we can do is go make a measurement of that peak to peak voltage in that loaded case where I've got a thousand ohms on the output and it looks like we're sitting right about two and a half volts so I know my unloaded voltage was at four volts and now my loaded voltage is at two point five so with that we can run calculation and see what the output impedance is okay so let's calculate our output impedance our open circuit voltage was 4 volts we divide that by our loaded voltage of two and a half volts subtract 1 from that and multiply our thousand ohm load resistance and we wind up with 600 ohms so and that makes sense when I designed this thing you know 25 or 30 years ago is probably looking at audio circuits that typically work with a 6 to 600 ohm impedance so that all worked out well now there is a special case of this scenario that if the load impedance equals the output impedance then the output or loaded voltage or loaded output voltage is going to be equal to half of the open circuit voltage so another way to measure the output impedance is to simply vary the load impedance until the loaded output voltage is equal to half of the open and then either you know measure the load opinions that you've applied or look at what what it is if you're using something like our resistor substitution box so let's do that all right we already know that our open circuit voltage was 4 volts peak-to-peak and we want to go down to 2 volts peak-to-peak because that'll be when the load impedance equals the output impedance I'm going to turn off the voltage cursors here because since we're sitting at 1 volt per division all I need to do is adjust my load until I get just to two divisions of deflection so I'm at 1k ohm impedance here drop it down to look I just made that 2100 but so it's going to go the other way here and push that up to let's make that 900 ohms okay see the voltages come down a little bit let's go down now it's that was zero let's go the other way about 800 700 600 right there at 600 ohms I can see my output voltage is now 2 volts peak-to-peak so now I know that's what the output impedance is and in many cases this is all you need to do but there are certain situations who this may not work now there are some circuits and other situations where the method we just followed may not work really well and some of those could be if the amplifier or circuit or generator that you're dealing with doesn't work well unloaded you know it might need some kind of a load to to work properly or it might clip or might do something weird if it's unloaded that would make it difficult or not possible to measure say the open circuit voltage or if the output impedance of the circuit changes with large changes in load alright if you go from an open circuit to some low impedance load that's a big change in load impedance and in many cases the output impedance of a circuit might change with such a large change in output impedance and what you're really interested in is what the output impedance is under normal operating circumstances so in those cases the method we used earlier where we measured the open circuit voltage and then the loaded circuit voltage might not be the best way so in those cases we can actually do another method very similar though is just measuring the output with two different load impedances connect up one load impedance measure the output voltage call that say v1 connect up another load called r2 and measure v2 and then once you've got that you can calculate the output impedance with this formula here let me set it that better on the screen here okay take a look at that and you might be able to kind of rearrange this in other ways but this form is reasonably easy enough to solve with a calculator so let's uh even though we already know the output impedance of my little homebrew generator let's try applying two different loads and seeing if we can calculate the load impedance this way all right we already know that with a 600 ohm load impedance I've got two volts peak-to-peak applied here let's just arbitrarily increase this to another value say sixteen hundred ohms and I can adjust these cursors here to measure the peak-to-peak voltage in this case and it looks to me that we're right around 2.9 or so right about two point nine volts peak-to-peak with a 1600 ohm load so we can use those two values two volts and 600 ohms and two point nine volts at 1600 ohms and calculate the output impedance from that okay we'll calculate with those values so r1 was 600 ohms I'll enter that in here again and multiply by 2 volts divided by 2.9 and subtract that from the original 600 and I'm also then going to take 2 volts divided by 2.9 and then my 600 divided by 1,600 subtract that multiply I'm left with about 592 ohms so I'm only about 8 ohms off out of the 600 but you can see that that method works as well and again this will work for situations where you want to put the amplifier or the circuit in a mode where it's operating close to its normal operating quiescent point so that the output impedance of the transistors and things like that or all would you expect them to be under normal operating conditions so this is a little bit more of a general case being able to just measure the output impedance or to me the output amplitude with two different load impedances and then calculating the output impedance from that you know I hope you found this video useful and enjoyable and got something out of it thanks again for watching and also later

Channel: w2aew

Views: 229,234

Keywords: W2AEW, Tek, Tektronix, Measure, How to, impedance, output impedance, resistance, divider, voltage divider, oscilloscope, scope, amplitude, voltage, load, load impedance, load resistor, sine, sinewave, sinusoid, termination, coax, function, generator, amplifier, function generator

Id: ieAhBejHe2M

Length: 10min 34sec (634 seconds)

Published: Sun Apr 06 2014