# How does a frequency multiplier work?

1. Oct 6, 2009

### rjsalmon

Hi,

I'm trying to work out how frequency multipliers physically work. What processes go on in order to multiply an input signal to a desired amount (ie 2 or 3 times the original frequency). I am intrested in thier use to generate a terahertz signal though I assume they work the same at most frequencies.

I hope someone can help.

2. Oct 6, 2009

### vk6kro

I can think of two types of frequency multiplier.

The first uses an amplifier that is deliberately driven into distortion so that a complex waveform is produced.

This will contain output on multiples of the input frequency.

Tuned circuits are then tuned to the required harmonic to recover this harmonic and reject others.

This is typically done in receivers and transmitters where a known stable signal is available but a multiple of that frequency is needed as a local oscillator for a mixer.

The other type of frequency multiplier is one that uses a free running oscillator near the desired high frequency. This oscillator frequency is divided by some exact amount using a digital divider.
This divided down signal is then compared with a known reference in a phase comparator and an error signal is sent back to the oscillator to pull it onto an exact multiple of the reference signal.

I also saw a reference to someone multiplying the frequency of a red laser to get green laser output. I have no idea how they did that.

3. Oct 6, 2009

### waht

Multiplication occurs when a sine wave is subjected to a non-linear device such a as diode that has an exponential response

$$i \sim e^v$$

If you know calculus, you can expand the exponential using Taylor series:

$$i \sim 1 + \frac{v^2}{2} + \frac{v^3}{6} ...+ \frac{v^n}{n!}$$

Notice, we have the v^2 term - if you square a sine wave

$$v = \sin(\omega t)$$

$$\sin^2(\omega t) = \frac{1}{2}(1-cos(2\omega t))$$

and hence the frequency is doubled. Note, that the higher order terms are usually negligible. It is possible to optimize the diode for the 3rd order term to triple the frequency or quadruple it. But the power goes down quickly.

Last edited: Oct 6, 2009
4. Oct 6, 2009

### waht

The t-rays are primarily generated by multiplication, however, the expense and quality of components that goes in making these is huge. A simple set up could cost you as much as a new car.

Instead, consider working at lower frequencies in the KHz, and MHz range which is cheap to do.

Also as vk6kro, mentioned, the light in green laser pointers is actually derived from an infrared laser shining into a non-linear crystal that generates the 2nd harmonic (green light), you can experiment with that:

Here is an example of a laser doubler:

Last edited by a moderator: Sep 25, 2014
5. Oct 6, 2009

### rjsalmon

Brilliant, thank you both very much. Its too difficult to find this information out online.
Rob

6. Oct 6, 2009

### halajeeb

Thank you for sharing your information