In that case I would recommend building a few candidates and experimentally testing them with mock-up transmission line and plates. Your true goal may be stable response rather than speed, in which case I suggest you design for controlled dV/dt. (Normally dV/dt will be implicitly controlled by gate drive and device parasitics and drifts around a bit). Then again, if you don't have particle bunches going through the beam line at the time it won't really matter much, will it?
I would recommend making the driver stable and somewhat faster than needed, then tuning the output network to get the desired response.
The most important part will be reducing the dependency between rise time and semiconductor properties. Gate drive is a bad way to get this -- then again, if you add external Miller compensation capacitance (that is linear), you can swamp the transistor's capacitance, giving a more stable relation between gate drive current and output dV/dt.
And if efficiency is not required, it's not like there's anything wrong with brute-forcing this thing with a matched 50 ohm transmission line. Sure, it'll burn about a kilowatt, but it'll work, damn it!
A lot of responses are hinting at linear (class A or AB) amplifiers, as well, which may be more control than is needed here, and will definitely get hot -- but will absolutely do the job. (You also use a smaller fraction of the full operating range of the transistors, so the nonlinear capacitance is less significant.)
If some ringing / non-flat behaviour is allowed, a transformer-fed design might be possible. You might be able to use a 1:8 transformer near the deflection plates to adjust the plate impedance down to around j50 Ohms and then use a longer, terminated transmission line with series termination at source. Then the drive electronics could be driven from a 50V DC bus (but output 8A peak). But you would get at least some ringing.
Not so. At this bandwidth, a very clean transformer can be designed and built, and the circuit matched to eliminate ringing (\$\xi \ge 1\$). Or peaked (2nd or 3rd order, or even higher) to get a better step response (i.e., a Bessel response, most likely).
Example design:
Assume 50 ohm system.
Assume 2MHz +/- (low) dB, so that -3dB falls at 0.2MHz, say.
That sets Lp = (50 ohm) / (2*pi*(0.2MHz)) = 39.8uH minimum.
A half dozen turns on a large #43 ferrite bead will do the job there, so that's easy.
If t_r ~ 10ns, then Fmax ~ 100MHz (actually a bit under 50MHz). Let's say 200MHz or more to keep the response independent of the transformer (i.e., not relying on the transformer too much as a reactive component*).
*Which can be done, when using suitable designs (transmission line transformers). Or, in effect: the maximum bandwidth is simply made very, very high, so that the properties at modest frequencies are well controlled (i.e., it behaves as a transmission line).
200MHz at 0.67c velocity is a 1m winding length. "A half dozen turns" then needs to be under 160mm per turn, which is fine. (We don't even have to employ TLT design to implement this transformer, at least for the primary winding!)
Taking the load as a lumped capacitance (it's not, it has 250mm of coax and 15pF of plate; but for the above reason, we probably don't need to worry about the TL being too reactive), to achieve 200MHz frequency response it needs to be driven by a maximum resistance of 22.7 ohms. Or for the minimum response (tuning everything as a filter, for t_r ~ 10ns), 90.9 ohms.
Well, that's not very much ratio against 50 ohms, so that's kind of a downer.
Regardless, even a 1:1 transformer has leakage inductance*, so even if this ratio isn't as large as 1:8, the analysis can continue.
*Which is actually transmission line length. The asymptotic low frequency equivalent of a TL is stray inductance, or in a transformer, leakage inductance. But when working with RF, one must always keep in mind the assumptions they are using: in this case, the lumped LF model uses LL and Cp that arise from the TL characteristics of the winding(s). A conventionally wound transformer has poorly controlled TL characteristics, usually giving exaggerated LF parameters; but with only a little effort, we can control those characteristics, cleaning up the LF model (making it a better approximation to the real device) and making a simple TL model suitable above there.
To get a matched 90 ohm impedance, we need LL = 290nH (secondary referred). Then the equivalent circuit is:
(source) --- 50 ohms --- (transformer) --- (capacitor)
The source is 50 ohms matched. After the transformer, it's 90 ohms (secondary referred). The transformer has 290nH LL (which manifests as series inductance). The capacitor has 35pF (plus some TL, but we should be okay to ignore that here). This is a series RLC circuit, with Zo = sqrt(L/C) = 91 ohms, R = 90 ohms, and so Fo = 50MHz and Q = 1.0.
The step response will be critically damped, i.e., no overshoot. (Actually, it can be slightly underdamped, and still have no overshoot.)
If we add some CLC around the transformer, we can use the transformer as a series inductor, and the load as the final capacitor, of a ladder type filter network, with a suitable filter type (such as Bessel, Gaussian, or equiripple group delay). The filter will also be a source-terminated type, because the load resistance is ~infinite. (It's not well known that filters can be singly terminated, but yes, it works, and there are tables for them!
)
The transformer spec, 290nH, suggests a winding length around 0.6m, nicely in the ballpark of reasonable transformers. You'd want to use enameled magnet wire, winding one layer for the primary, then an extension winding on top of it (as an autoformer) for the 90 ohm secondary. The stray inductance of two adjacent cylindrical layers isn't too bad, and will probably come out close. (Ideally, you'd design it with less than necessary, then add inductance to bring it up.)
You need one of these. It should be a proper drawing with labeled axes and references to documents/design studies etc. You could ask the technical person responsible to try to come up with a 'we want' and 'we need' envelope. You should ask questions like 'when do the bunches go through the deflector exactly? Are there periods where you don't care about the voltage?' because the accelerator designers may be trying to make your requirements 'simpler' by not telling you everything.
If you can't get one, flag this to the project manager immediately but politely, because it would be evidence of communication problems.
As you can see from all the questions here, there are a lot of possibilities. Ultimately you're going to be spending a significant amount of time evaluating options and doing simulations.
I'm also very concerned that the OP is posting on the internet like a valid answer is expected here.
I mean, really. If you're not academic, then... you must be a professional with enough qualifications to figure this out yourself?
If you are academic, then it sounds like you're in a study position (grad or undergrad, perhaps?), and should have this kind of support from the curriculum and faculty. And if you don't -- that you've been burdened with this task, without the necessary knowledge and tools to create the solution -- it seems you've been set up to fail, and need to bring it to the department head, or registrar.
And if there's $10k's worth of downtime associated with failure of this device, one would hope it's at least reviewed by some or all of the above, especially if the designer has to resort to soliciting the internet for ideas.
Tim
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