|
|
| |||||||
|
|
|
|
There are several things to consider when generating a pulse: Repetition Rate For example, if we want to generate one pulse every 25 milliseconds, that's a repetition rate of 40 Hz. To simulate this pulse, we would begin by using a fundamental signal of a 40 Hz sine wave, then add harmonics of that frequency in various starting phases until we get a waveform that is close to the pulse train we're after. Duty Cycle The duty cycle affects the number and frequency of all the sine wave components we have to sum in order to simulate the pulse train. For example, you can see by the above simulation that we need several sine waves per pulse in order to simulate a square top on the pulse. If we're trying to simulate a 40 Hz square wave, let's just say we need about 9 harmonics of the pulse repetition frequency to make a reasonable "top" on the square wave. That's 9*40=360 Hz. Now, if we change the duty cycle from 50% (A square wave) to 4% (a pulse train), how many harmonics do we need? Remember, we're talking about harmonics of the pulse repetition frequency. It seems intuitive that we need to have about 9 full sine wave cycles that fit within the smallest part of the pulse. So that's 9*40*(50% / 4%)=360*12.5=4500 Hz. So now we need not only a lot more harmonics of the pulse repetition frequency, but we also need an amplifier with a wider bandwidth. Actually, the problem is even more demanding than this, because the only signals that make a good square wave are the odd harmonics of the fundamental. If we really need 9 of these components to make the waveform, they are: fo, 3fo, 5fo, 7fo, 9fo, 11fo, 13fo, 15fo and 17fo. So for a fundamental, fo, of 40 Hz, the amplifier must pass: 17*40*(50%/4%)=8500 Hz." DC Component The output will have equal areas (a=b) above and below zero volts: Also, if the repetition frequency is low compared with the time constant of the input circuit, we'll see some "droop" in the waveform, indicating the discharging of the input capacitor. Risetime Pratical Considerations Design engineers have to study the effects of "EMI" (Electromagnetic Interference) on their circuits and their designs have to pass international standards to make sure they don't interfere with other electronic devices. A high percentage of EMI problems can be directly related to fast rise-time pulses. One of the lessons in this simulation is that engineering is comprised of a series of tradeoffs. If we want to design a "better" pulse train, we need to make practical compromises: How much bandwidth? How much EMI? What does an "acceptable" pulse waveform look like?
|
|