The most general method: use a VNA with a bias tee.
The VNA (Vector Network Analyzer) measures the phase and magnitude of transmitted and reflected AC waves from a device under test (DUT), through as many ports as it is equipped with. In this case, we expect a capacitance at the end of a transmission line, so we merely need to use the equation for a transmission line with a capacitor load, at each frequency tested, and can solve for capacitance in that way.
We can also solve for resistance, and by varying frequency we can also synthesize an equivalent circuit for the DUT.
Now, a VNA is rather expensive, if you don't have access to one. But this highest-level perspective gives us insight into what methods might be applied.
A VNA is fundamentally a very precise
reflectance bridge. A bridge has already been mentioned above, and that is also a very nice, general method for lower frequency applications. (At high frequencies, it's desirable to do things in an RF-and-transmission-lines method, which means, using a reflectance bridge as such. But there isn't much operational difference between that, and the old fashioned e.g. Wheatstone bridge, as long as one understands the compromises of each).
We can also look at the fundamentals of what we're measuring. What is a capacitance? In AC steady-state, it is a reactance inversely proportional to frequency. This is actually a consequence of a more general statement, the fundamental capacitor equation: I = C * dV/dt. (If we have I and V as sinusoids at some frequency, then the AC steady-state condition follows instantly from this.
) We don't need to use sinusoids here; we can just as well use sharp, piecewise waveforms, that may be easier to measure with digital circuitry, for example.
Namely, if we apply a square-wave current, the time integral of that waveform is the voltage, a triangle wave. This is what most multimeters do: apply an alternating current (square wave), and measure the voltage. Typically the current will be switched when the voltage reaches a threshold, so the impedance (V / I) is held constant, and the frequency of oscillation is then inversely proportional to capacitance. Or the current is varied, in steps or continuously, to hold voltage and/or frequency in a typical range.
Note that such a method loses something: we expect to measure capacitance, but if we measure resistance instead, we get nonsense results. We're also testing with a wideband signal (assuming linear components (constant C), the usual analysis methods apply (superposition, Fourier transform, Parseval's theorem, etc.), and we note the transform of a square wave has many harmonics), which means we can get very weird results for complex (RLC) networks.
Some of this can be recovered (e.g., measuring the voltage waveform in quadrature with the current waveform, so we measure in-phase and out-of-phase components -- ESR and C), and some of it can be managed (modest size ESL can be avoided with a bandwidth-limited square wave test signal), but if you are expecting a network any more complex than that, a bridge or VNA method is probably best.
Tim
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