How do signal generators maintain a 50 ohm output impedance with varying frequency? Or do they?
Let's take a square wave as an example. If the output impedance is 50 ohm at the repetition rate of the square wave then I would expect it to be quite different at the harmonics which would result in distortion of the output signal. Or can you actually design a circuit that would maintain the 50 ohm impedance over a broad range of frequencies?
What? Err... I'm going to assume you're not trolling, and just have some basic misconceptions.
Points:
* The impedance of the output, ideally, is purely resistive. It's supposed to be equivalent to a zero-impedance signal source, with a 50 ohm resistor in series. In reality, it will be very close.
* So the signal shape, repetition frequency and 'harmonics' (energy spectrum) have no relationship to the impedance. The attenuation is very flat across the applicable spectrum, so there's very little distortion of even a square wave.
No, it's a valid question. If the output impedance varies, then the gain into 50 ohms varies, and therefore the frequency response; if it goes reactive, it starts ringing; if it goes negative (enough), it starts oscillating!
A typical op-amp (open loop) has an impedance that rises somewhat with frequency, maybe starting around a few ohms in the DC-kHz range, then rising into the 10s of ohms by 100k-1M and maybe into the 100s in the megs. This is due to the emitter (or source) follower equivalent output stage, bypassed at the input/base end with the internal gain node capacitance (usually also the site of the dominant pole / miller compensation capacitor). You'd expect it to fall with frequency because of the reflected capacitance, but "slop" across the several transistors in the signal path tends to add up and make a somewhat "squishy" or inductive characteristic. (This is required when the gain node is carrying microamperes, and additional current gain is necessary to bring the signal to the outside world in the ~10mA range. There is also often level shifting and current limiting circuitry as well.)
Rail-to-rail types lack the voltage follower design and typically have even higher open-loop output impedances. Same as LDOs, they are more like current sources (transconductance amps) with feedback to save them. Compensation is more difficult, especially if a capacitive load is required.
The output impedance under feedback is considerably reduced, but only in proportion to the loop gain. So it's mohm or even uohm at DC, but it rises sharply with frequency, until at fT, it's the same as the open loop condition (actually, it will be worse, because phase margin won't be exactly 180 degrees -- the difference will manifest as an inductive output, hence the sensitivity to capacitive loads that's characteristic of most amp designs).
So you can see, an op-amp of fT = 5MHz would be very poorly chosen for the present subject. But that's probably quite obvious. What may not be obvious is, it's probably desirable to use one that's about triple the bandwidth, or fT >= 60MHz, so that the phase margin at harmonic frequencies is still useable.
There is also some virtue in having an output impedance maintained well beyond the bandwidth of the instrument itself, as it could be connected to some equipment that's generating poorly filtered junk at much higher frequencies, which if allowed to reflect, could disturb itself. (An example: a 100MHz oscillator coupled to a one-transistor mixer. The mixer input port will then have a lot of 100MHz on it... For just a quick try, you might lash it up without the necessary filters. But if the FG is reflecting 100MHz plus phase shift due to its poor output impedance, the phase shift goes back to the oscillator and shifts its frequency. Maybe it doesn't want to oscillate at all, at some frequencies, due to magic lengths of the cable and stuff!)
There are many ways to skin this problem; another good one is intentionally building a transconductance amplifier, and driving its current output into a shorting resistor of 50 ohms: thus making a Norton current source, which is of course equivalent to the Thevenin voltage source we have currently in this thread. The nice thing about transconductance is, that's what transistors are, so give or take some compensation, you can get about all the gain that they're good for (a modest current gain of just a few will get you within fT of the transistor -- for 2N3904, that's in the 100MHz range!), and the output impedance will simply be 50 ohms plus a little capacitance (which can be kept minimal using the smallest, fastest power transistors possible). If you were really serious, you could partially cancel that capacitance with some inductance (Tektronix' famous T-coils), or build a distributed amplifier even (which they did, many times, because it was absolutely necessary with vacuum tubes!).
Tim
Home
Help
Search
Login
Register
