Matching Impedance of Capacitor in Coaxial Line at a given Frequency - Page 1
Forum section: electronics / beginners

author: The13thParish
author_rank: Contributor
timestamp: May 20, 2020, 08:57:48 pm
content: Hello everyone,We're always told to match our impedances. In particular, the importance of terminating open coaxial lines with the correct 50 or 75 ohm impedance BNC terminator is often stressed to prevent standing wave formation interfering with your signals. I further understand that the impedance of a cable is frequency independent, so that when buying '50 ohm impedance cable', one does not need to ask at what frequency this 50 ohms is defined at.I have a decoupling capacitor downstream of a coaxial cable*. Since capacitor impedance does depend on frequency, do I now need to consider choosing the impedance of the capacitor such that at the signal frequency, the impedance of the capacitor matches that of the cable. i.e. with a signal frequency of 1 MHz, the capacitor has an impedance of 50 Ohms also at 1 MHz? If I do not match the impedance of such components, will I also get reflections as with incorrectly terminated BNC cable?Cheers,Ryan*I'm using this to detect electron arrival times at a micron-channel plate. This system has never worked correctly and I'm looking at all avenues of its original design such as reflections to discern why the signals look strange

author: bdunham7
author_rank: Super Contributor
timestamp: May 20, 2020, 09:11:14 pm
content: The short answer is probably "no", unless the wiring system "downstream" of the coax is also a transmission line, in which case the first termination is not needed. And if you do need to terminate it at that point, you need a resistor not a capacitor. Decoupling and termination are almost opposite concepts.Some more details about your setup, the nature of the signal and the devices that the coax is attached to would help.

author: jmelson
author_rank: Super Contributor
timestamp: May 20, 2020, 09:41:47 pm
content: Quote from: The13thParish on May 20, 2020, 08:57:48 pmFirst, your signal is probably not a single-frequency sine wave, so you CAN'T match the capacitor's reactance to a specific frequency.Second, the capacitor is not a resistor at any frequency, and it cannot absorb energy like a resistor. Therefore, it can't terminatea transient flowing down a cable.You DO need a resistive load to prevent a signal from bouncing off the destination end of the cable. I'm assuming this signal goes into some sort of amplifier. Just to throw out numbers, let's say the cable is 50 Ohm, and the amplifier receiving the signal has an input impedance of 20 Ohms in the range of frequencies involved. You would want to put a 30 Ohm resistor in series with the input to match the cable.Any decently sized capacitor in series with this would not affect the match. Just make the capacitor impedance at these frequencies low compared to the cable impedance and it will have no effect.(If the amp's input impedance is GREATER than the cable impedance, then use a parallel resistor to achieve the match.)Now, the trick is to accurately match the cable to the amplifier, and this is doubly important in many sensor applications as the source end is a pulse-like current source. If you get the match very accurate, no signal will bound off the downstream eand back to the source. If you CAN'T get the match very close, perhaps due to varying amp input impedance over frequency, then you may need to terminate the source end.Since the source end (microchannel plate) is likely to be high impedance, a parallel resistor equal to the cable impedance will absorb reflected energy coming nack at the source end. This, of course, reduces signal amplitude, but getting rid of reflections in fast signals may be much more important.Jon

author: The13thParish
author_rank: Contributor
timestamp: May 20, 2020, 11:11:53 pm
content: Thanks jmelson, that's very helpful.You are correct that the output from the anode goes into a preamp and then on to a digitizer.The preamp output and input are 50 ohm as indicated in the manual, but if I wanted to exercise my right to be curious, would the best way to measure this to use an LCR meter either side of the input and output and measure the impedance?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 21, 2020, 12:01:47 am
content: When the source/cable*/load is reactive, the ideal match is a conjugate impedance.*It is, actually, meaningful to ask at what frequency Zo is measured.We hope that our coax is reasonably flat over a wide range; but this need not be the case! Dispersive and lossy transmission lines can vary quite a bit, from microstrip's varying velocity factor (hybrid air and dielectric waves), or any TL simply long enough to drive up losses, or say a helical waveguide which makes quite a peculiar transmission line indeed. Not to mention pathological cases where the differential (RLCG) TL elements are reactances themselves (metamaterials and such).Since we only have R, L and C to work with, we can only make a conjugate impedance match at one frequency, or over some modest frequency range.If this is a baseband type of application, then you need bandwidth including DC, and it will extend up to some limiting HF cutoff.If the cable is properly terminated in the preamp, then it appears as a 50 ohm resistor at the MCP, regardless of length (assuming it's not shitty cable, and assuming we don't looktooclosely at the "50 ohms"!). The MCP has some capacitance, so together we get an RC single pole lowpass filter. Any current injected into the MCP, acts to charge that capacitance, then flows into the line.This gives a rough cutoff of F = 1 / (2 pi R C).We can introduce matching, to extend it a little further. Consider if we make an RLC circuit, where the C is the plate, L is in series with it, and R is the TL. If we set L = R^2 C (give or take), we peak the response, extending it a good, oh, 40% or so. (This is simple series peaking.) We can extend this even further, to a higher order network, and improving things with tapped coils; a bandwidth extension of 2-3x is feasible (depending on how poor the impulse response is permitted to be).This is the technique employed most famously by, well, everyone did it, but Tektronix is the exemplar I suppose, back in the days of the vacuum tube (and early transistors). Tubes are, well, unsurprisingly, they're plates in electron beams -- identical situation, a current flows into a largely capacitive plate, and further on into the rest of the circuit. Well, by using a tapped coil and the right combination of load resistances and capacitances (the capacitances typically being the driving plate, and the driven grid), bandwidth in terms of voltage or power gain can be extended by this amount.It seems even Tektronix didn't push much into higher order networks; presumably they're just too fiddly to tune. The 2nd order tapped coil is great though. For higher bandwidth, it seems they preferred distributed amplifiers.Which...If you're working with very fast pulses, by the way (as physics apparatus often is?), it may be meaningful to consider the MCP itself as a transmission plane. That is: a burst of charge in a given location will propagate out radially, then reflect off edges, and so on. Eventually the waves will find their way into the attached transmission line, but much energy will also go into modes trapped by, and absorbed by or radiated from, this resonator, reducing efficiency and smearing out what would otherwise be a sharp (~ps?) event into many humps.Perhaps this has been considered in the design already: I've heard of MCPs designed as a sinuous track, say. With a narrow width, waves (except for very high frequencies indeed) are confined to linear (transmission line) modes, and thus you have only one reflection from the end (which can be terminated if it is undesirable) and two pulses (or one) incident on the preamp. The delay between direct and reflected pulse can thus generate a position signal.Of course, neither matters if your preamp, and the rest of the signal chain, are unable to register such rapid events; system bandwidth is always limited by the weakest link. In that case, it is acceptable to model, for example, a sinuous-track MCP's unterminated reflection as a capacitance, for frequencies smaller than its electrical length equivalent; and then lumped-equivalent matching (peaking coils and such) might be used with it.Tim