# Does a RF frequency multiplier work with ultrashort pulse?

The question is, does a RF frequency multiplier work with ultrashort pulses?

In another words, does the frequency multiplier change the pulse width of input signal?

For example, suppose we have a analog signal oscillating at 100MHz and it was amplitude modulated to be a 50ns-width Gaussian-shape single pulse (note, there was only 5 periods of signal).

1. Will the output signal of frequency doubler/tripler be a 200MHz/300MHz gaussian pulse? What is the pulse width?
2. What if the signal was amplitude modulated to be 50ns-width square shape pulse?

【update】 To be more specific, my signal is a frequency modulated analog f0=100MHz pulse with pulse width of ~10μs, where the frequency modulation $\delta f=\delta f(t)$ is a function of time during the pulse width.

For example, $\delta f$ is about 1MHz at t<5μs, and $\delta f$ jumps right away to be ~10MHz at t=5μs, then at t=8μs, $\delta f$ jumps to ~15MHz.

I want to extract the frequency jumping curve $\delta f(t)$with high time resolution (say, at least with 100ns resolution), but as you can see, the oscillation duration is very short (a few cycles). A short time Fourier transform analysis can not resolve the frequency jump accurately.

So I wonder, can a frequency multiplication process enhance the frequency difference to $N\delta f(t)$, but also the frequency jumping curve shape is not changed? Then the core question is, will a frequency multiplier work with short signals with few cycles?

I have read papers that uses frequency multipliers to generate wideband linear frequency modulation (LFM,$\delta f=\alpha t$) pulse signal from a narrow band linear frequency modulated signal . I'm not familiar with electronics, but I guess a frequency multiplier will also work on a nonlinear frequency modulated signal? Am I right?

• I suspect a multiplier only works well over some limited bandwidth and a short pulse is composed of a wide spectrum so it probably wouldn't work all that well. – jramsay42 Feb 1 '18 at 0:52
• "A RF frequency multiplier" is too broad. There are many different technologies that can be used to multiply a frequency, ranging from simple passive harmonic generators to active circuits like PLLs. They have very different characteristics, so you'll have to be a lot more specific about what you're talking about. – Dave Tweed Feb 1 '18 at 4:41
• As other comments suggest, what kind of frequency multiplier? The classic tripler should be fine, as the input is rich in third harmonic; its output will be approximately sinusoidal. The XOR/delay doubler will give unsatisfactory mark/space ratio, for two examples. – Brian Drummond Feb 1 '18 at 10:47