EEVblog Electronics Community Forum
Electronics => Projects, Designs, and Technical Stuff => Topic started by: T3sl4co1l on February 25, 2017, 05:13:31 pm
-
...You make a probe!
(https://www.seventransistorlabs.com/Images/HighVoltageProbe.jpg)
The usual drawing of a probe is first of all, a voltage divider. This is correct at DC.
I had enough 1M resistors on hand, so I stacked ten in series (which also gets a suitable voltage rating -- I'd be comfortable up to 2kV here). To get 100:1 ratio with a 1M scope, I need 100k on the bottom (actually 101k). The scope provides 1M of that, so I need 112.3k in parallel. (I actually used 100k + 10k, close enough.)
But a resistor divider is not correct at AC. The scope (1M || 15pF) and cable (1m length, 50 ohm) have around 150pF equivalent to ground, so the divider's Thevenin resistance of ~100k has a pole at 10kHz.
We put "speed-up" caps across the top divider resistor to correct this. We get a resistor divider at low frequencies, and a capacitive divider at high frequencies. This extends the bandwidth massively, to a few 10s of MHz.
But it's still not quite correct.
So let me introduce the most correct model:
The probe is a lossy impedance transformer. It converts a high impedance down to a lower impedance. Consider: if we had transformers that worked DC to light, at any impedance, we'd use them! What could be better? A 100:1 voltage ratio on 1Mohm is 10Gohm. That's a damn fine probe there! Alas, this is unreasonable, so we do it with resistors, and accept the losses.
So what are the circuit impedances we need to worry about?
- Let's assume the source impedance is zero. This is justifiable as we are measuring voltage; if the source is "squishy", we'll just have to assume it was...meant that way? This is a shitty excuse, but it's what all the other probe kiddies are doing.......
- The load impedance is a transmission line, with a bit of stuff at the end (i.e., 1M || 15pF in the case of my scope). But, that's likely a lie as well (why would they put 15 real pF there? surely they have termination or damping resistance inside?), so I'll just as well assume it looks like a meter of 50 ohm transmission line, and not much beyond that.
- There's 1M out there, at DC, so to keep the ratio constant at all frequencies, we need to transition from 1M down to 50 ohms.
And here lies the key insight: by realizing it is an impedance divider, not strictly a resistor and/or capacitor divider, we can extend the response as high as we care to (or, more accurately, as high as we can measure the cable + scope system).
What's the key result, then? We need to terminate that transmission line. We can't assume it's terminated at the scope end (if it is, that's nice, but there's not much reason to believe so). That means the impedance has to drop to 50 ohms at some high frequency, then stay there. 100x that means the probe tip will be 5kohms (not 10M) at the same frequencies.
To get that, we put resistance in series with the "speed up" capacitor.
Since everything's distributed already (the 10 x 1M's), these shall also be distributed. This helps swamp stray capacitance (which would otherwise cause "hook" in the step response), too.
This gives the circuit:
(https://www.seventransistorlabs.com/Images/HighVoltageProbe.png)
A bit too much "speed up" capacitance is used, so that the toe frequency (where the output reaches ~50 ohms) falls below the first resonant frequency of the cable (1 m, at c/c_0 = 0.67, quarter wave, is 50MHz). The excess is compensated with an R+C to ground. The C is adjustable, to trim the cable length.
I also added a 200V GDT (gas discharge tube), just in case the resistors break down and high voltage goes into the scope. GDTs don't respond instantly, but the overshoot should still be okay given the scope's ratings, and the low added capacitance (a couple pF) means I don't have to worry about it under normal conditions.
How's the result? Great! I measured a high voltage square wave down to ~70ns, which looks just fine. Down in the 10ns range (reading an avalanche pulse generator circuit), there is some ringing, because an R+C to ground isn't an adequate to terminate the line (it's not the correct impedance at all frequencies). This can be accounted for by increasing the divider capacitance further (i.e., placing the knee well below the line's resonant frequency), or by using a more complex RLC network.
Ideally, the top half of the divider would be a transmission line as well, but this would be rather impractical: it would need 100M (DC resistance), and 5kohm characteristic impedance, with equal length (i.e., 1m). You can't make a transmission line without having capacitance to the space around it, so you end up with a ton of common mode loading. And that's if you could make a 5kohm TL in the first place, which you really can't...
So, because of common mode limitations, and size, the ultimate compensation that is possible for this type of design is to use an RLC network with a high frequency constant-resistance property. Such networks were invented by Zobel (https://archive.org/details/bstj2-1-1) for equalizing telephone lines.
Note that the probe resistance is relatively small at high frequency: about 5kohms. Those resistors can only dissipate maybe 2W total, and that would likely be self-desoldering heat at that. This gives a corresponding voltage limit: 100V, starting from 16MHz. Ignoring other harmonics, and the slow cutoff of the RC filter, this suggests a full voltage (~2kV) square wave can be safely read up to 800kHz (i.e., the 20th harmonic has 1/20th or 100V amplitude, and lands at 16MHz). But that's a horrible lie (the lower harmonics will still count because of the slow cutoff), so let's suppose it's half that, or 400kHz. Still not too bad, and unlikely to be see in practice!
Tim
-
Nice work Tim, and about the only thing that will kill that is to try to see the output of a 10kW shortwave transmitter, and those will typically already have built in divider networks ( mostly capacitive ones, who cares about a few watts in a resistor when you have 10 000 on the input side) so makinbg the probe superflous.
In any case just having the scope in the same room will be signal pick up enough for there, just stick a 5cm length of wire into the BNC socket ;)
-
Looks good.
-
Tektronix gives a lot of detail about their old high voltage probes including photographs which appear to show a tapered horn around the high voltage input resistor to produce the controlled distributed capacitance. I wonder how well that would work with the serpentine element of a modern leaded high voltage thick film resistor .
Tektronix also shows the details of the more complex compensation circuit you mentioned if anybody is interested.
I was thinking of trying this with coplanar transmisson line construction but I think it would be unmanageably long to get enough capacitance. I like that your solution works so well.
This guy built a coaxial high voltage probe:
https://www.youtube.com/watch?v=_OuonC7KlVE (https://www.youtube.com/watch?v=_OuonC7KlVE)