High voltage amplifiers – How fast are they really?
The high speed, high voltage amplifier: performance criteria
High voltage amplifier performance in terms of speed is not only determined by the bandwidth and the slew rate, but also by the maximum sustainable current and the capacitance of the load. This article discusses the specifications of high voltage amplifiers required to determine whether they are suitable for a certain amplifier-load combination.
The basic specifications relating to speed of a linear high voltage amplifier like the Falco Systems WMA-300 are its large signal bandwidth, small signal bandwidth and slew rate. The large signal bandwidth shows what the output amplitude voltage of a high voltage amplifier is for a given input sine wave amplitude as a function of frequency that drives it to its maximum output voltage (Fig. 1). Because the output voltage falls off gradually above a certain transition frequency, a single magic number named “the bandwidth” being so-and-so many kHz is only useful if also the reduction of the full-power bandwidth of the high voltage amplifier at this frequency is also quoted. It is often expressed as the -3dB point, where the amplitude has fallen to 0.707 times the maximum amplitude at low frequencies, but this is not always the way it is specified, so one has to be careful with a single number. A graph showing the maximum output voltage versus frequency conveys much more information. The small-signal bandwidth (sometimes, confusingly, also called “the bandwidth”) is the frequency response of the high voltage amplifier at some very low output voltage like 1% of the maximum output. This bandwidth is usually larger than the large signal bandwidth by a significant amount.
The slew rate
The slew rate is a fairly subtle spec. It is the time an amplifier needs to go from 10% to 90% of the total output voltage in response to a step in voltage at the input (Fig. 2). It is given in V/µs, the number of volts that the output can rise (or fall) in one microsecond. This spec obviously limits the capability of an amplifier to generate high voltage pulses with sharp rising and falling edges (Fig. 3), but is also a bandwidth limiting factor for sine-wave or arbitrary signals. This can be seen as follows. The highest rate of change in the output voltage of a sine wave is at the 0V-crossing (Fig. 4). The higher the frequency, the faster the voltage has to rise there to prevent distortion of the sine wave. If the high voltage amplifier cannot follow due to its limited slew rate, the sine wave will be distorted and its amplitude is lower than at low frequencies. The maximum peak to peak sine wave output voltage Vpp is related to the slew rate S by Vpp = S/pi*f, where f is the frequency of the sine wave.
Slew rate vs current – capacitive loading
The discussion above assumed that the load at the output of the amplifier does not influence the behavior of the amplifier in any way. This is the case for very small capacitive or resistive loads. However, typical loads for a high voltage amplifier are highly capacitive, like PZT (piezo) transducers, EO (Electro-Optical) modulators, and, to a lesser extent, coaxial cables (a RG58 cable constitutes about 100pF per meter!). To be able to bring the output voltage of the high voltage amplifier to a certain level, this component at the output representing electronically a capacitor has to be charged to this voltage (Fig. 5). If the amplifier has a current limit of I amperes, it can charge up a capacitor C only with a certain maximum speed. The maximum rise in voltage per microsecond (again a slew rate, but now determined by the maximum current and the load capacitor, so we call it SI) is then SI = I/C, which can be significantly lower than the intrinsic slew rate of the amplifier S discussed above for large capacitance values. The bandwidth for sine wave signals is reduced correspondingly. Even worse: if the high voltage amplifier has a current limit but will overheat when the maximum current is drawn continuously, it will break down after a while when delivering a high frequency, high voltage output even though the load at low frequencies is negligible.
Instabilities and overshoot due to capacitive loading
Many high voltage amplifiers have an internal circuitry that looks like a high voltage version of the general operational amplifier (Fig. 6). A capacitor at the output of such a circuit creates a time lag of the output voltage, because the capacitor has to be charged first as discussed above. This means that the voltage at the (–) input of the opamp is delayed too, which can cause the signal at the (+) and (–) input at certain frequencies to be 180 degrees out of phase rather than in-phase. If this happens with certain capacitance value at frequencies well above the frequency where the opamp has an amplification smaller than 1, this is no problem, but when this happens at a frequency where the opamp is still capable of amplifying the signal, the circuit has been effectively turned into an oscillator. The result is then at least overshoot or ringing at the output, and in extreme cases sporadic or continuous oscillations (Fig. 7). If the capacitor value is chosen large enough, this effect disappears again (although with a dramatically reduced bandwidth as a result). This means that most amplifiers have a certain capacitive load value where they are most likely to generate spurious signals. Only by placing the output stage outside the feedback loop (Fig. 8) in a high voltage amplifier design, this effect is circumvented.
To select a high speed high voltage amplifier for a certain purpose, one has to look not only at the bandwidth and/or slew rate of the amplifier, but also at the expected capacitive load, the maximum sustainable output current and the possibility of overshoot voltages damaging the load. All of these are required for an optimal result.
Example with numbers, using the Falco Systems WMA-300
In the following section, we illustrate the principles discussed above by comparing them to specs of a real high voltage amplifier, the Falco Systems WMA-300 (Fig. 9). It is made for very high speed operation and hence has a very large bandwidth of DC – 5 MHz (50% of full output voltage) and a corresponding 2000V/µs slew rate. The main application is in MEMS (micro-electromechanical systems), where the connecting coax cables are usually the main capacitive load (~100pF), but it is instructive to see what happens when the capacitive load is increased to the values typical for piezo-transducers or EO-modulators (~nF). The large signal bandwidth of the WMA-300 with 300Vpp output voltage (the maximum) is given in Fig. 10. The slew rate is measured by monitoring the rise-time of a pulse on an oscilloscope (Fig. 11). The bandwidth and slew rate specs result in a nice 300Vpp 100kHz square wave (Fig.12) with fast rising and falling edges with no load. This waveform is distorted if we add a significant load capacitance (Fig. 13). For 150pF the effect is negligible, but when we drive several nanofarads, the speed is reduced considerably. The reason is the 300mA current limit of the WMA-300 that limits the speed at which the capacitor can be charged, and hence the loaded slew rate SA is smaller for the loaded conditions. Note that there is no capacitive load at which the system generates overshoot. Unlike in many other amplifiers, in the WMA-300 the configuration of Fig. 6 has been used, which effectively prevents any instability caused by the load.
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