# What circuit to use to multiply 434 MHz by two?

I wanted to make an experimental simple 1296 MHz transmitter to have fun with my sdr dongle.

But after hours of googling I realised that there is no such thing as "simple 1296 MHz transmitter". Even though there is a "x3 varactor multiplier" it consists of old components that is rare and expensive. Which is strange since GSM uses multiple bands lower and higher than 32cm ham band.

But then I spotted a circuit called "diode odd-order frequency multiplier" which looks very simple.

Immediately I thought that 868 MHz ISM band is 2·434 MHz which is upper part of LPD band in europe.
So I can take my 70 cm radio, and connect this multiplier to its output.

What diodes can survive 1W @ 433 MHz and how to calculate rest of components (inductors and capacitors) used in said multiplier?

Or it also requires rare old components?

Edit: I'm using SDR to RECEIVE the 868 MHz signal, not to transmit. I want to create a 868 or 1296 MHz transmitter not create 868 mhz transmitter to use it as LO for 1296 MHz one. I planned to use non-sdr handheld radio as my transmitter.

• I know that it's nitpicking, but "Megahertz" is abbreviated "MHz", not mhz, or Mhz. So I went ahead and corrected that. Good question! – Marcus Müller Jan 11 '19 at 13:30

You don't usually produce microwave frequencies using frequency-doubling diodes (or any other nonlinear component) like that, that's why you can't find an "easy" circuit to do that.

Anyways, sure, any sufficiently robust semiconductor (all of which have nonlinear I/O curves) can do that. I'd frankly just go to e.g. mouser.com click through the semiconductors to the RF semiconductors and use a sufficiently fast transistor in a AC-coupled, biased common emitter configuration. 400something MHz isn't really "fast"!

The idea then would be that the mixing circuit itself behaves as an amplifier, greatly reducing the needed "transport" of energy from low to high frequencies.

The question still would be how to pick values for any circuit. The rule here really is that you want to pick an operating point for your semiconductors (which, for their full range, are exponential) that fulfills the mathematical operation you want it to perform as nicely as possible – for example, for an amplifier, you want the whole thing to operate as linearly as possible, whereas for a frequency doubler, you want the second-order intermodulation products to happen, which means you need quadratic behaviour: you'd bias your semiconductor so that around that bias point, its curve looks as quadratic as possible.

But, again, that's not how you typically generate RF signals, especially not in an SDR context!

You'd typically have a separate frequency synthesizer and a mixer. In your example, you say you already have a 434 MHz transmitter, but want to operate at 1296 MHz.

So, you need to shift that up by (1296-434)MHz = 862 MHz (and now I see where that number is coming from). In fact, you're building a heterodyne transmitter. So, aside from your 434 MHz IF signal, you'll need a 862 MHz LO.

And that is where things get more complicated than they need (at these frequencies) be if you use a high-powered IF:

For any mixer to work well, you'd want your LO to be at least at the same power as your IF signal – and suddenly you a) need to produce power at your LO frequency and b) need a mixer that can withstand at least twice the amount of power.

After mixing, you'll always need filtering to get rid of the unwanted intermodulation products; and mixers are optimized to produce at least one intermodulation product, and it's nontrivial to build them so that the others are well suppressed. Now these filters will also have to withstand power at unwanted frequencies! Power, that, by the way, you'll have produced only to have it dissipated in filters.

Compare that to a solution where you mix low-power signal + LO first, filter the result, and amplify the resulting RF signal (and then might not need to filter the PA output at all).

Which is strange since GSM uses multiple bands lower and higher than 32cm ham band.

And that's where a few things come to together:

GSM requires devices to be able to hop frequencies rapidly, over a relatively large range compared to the accuracy that these frequencies still need to have.

That's typically achieved using rational or fractional-N synthesizers. The idea is simple:

Instead of relying on the nonlinearity of some amplifier to produce a multiple of an input frequency (effectively, by letting that input mix itself up by itself, or by a mixed-up version of itself), you run a VCO (voltage controlled oscillator) at about the target frequency. The benefit of that is that this oscillator will be relatively "pure".

Then, you adjust your control voltage so that it's actually the frequency you want – and you do that simply by counting. For example, you want to generate 942 MHz for GSM operation. OK, so you take your 10 MHz reference source, and say: by the time this reference has fulfilled 10 cycles, the VCO has to have done 942 cycles (or, if you cancel out common factors: 10 cycles low should be 471 high). If the number of actual cycles is lower, increase the control voltage, and conversely, if its lower, decrease that.

Throw a bit of algebra at the problem, and you end up specifying slightly less intuitive numbers than the rational ratio between in- and output frequency, but can get a huge number of additional frequencies that you can synthesize (fractional-N synthesis).
Design an actual control loop (i.e. a PLL) instead of my vague "decrease or increase", and you end up with a synthesizer.

Such synthesizers can cheaply be built using bog-normal silicon digital logic – and that's a great advantage, because suddenly you're not depending on the hard-to-manufacture-exactly nonlinearities of some semiconductor to do your mixing, and you can account for the nonlinearities in the VCO's frequency-vs-voltage curve simply with the control loop that you've got in there, anyways.

Jumping to another frequency becomes as easy as adjusting the numbers "5" and/or "471" (or their fractional-N equivalents); that can be really fast-settling, too!

If you look inside post-GSM phones (i.e. 3G/UMTS and 4G/LTE/LTE advange/5G), you'll find that these aren't even heterodyne systems, but quadrature mixers – the standards are designed for complex baseband processing! Still, these systems use said fractional-N synthesizers to generate their target frequencies, and they do so to great accuracy; a relatively simple synthesizer like described above allows you to adjust frequencies on a very fine raster, so that you often don't even need correctable reference oscillators, which again decreases component cost in mass products.

So, you say, that's nice and all, but where do we go from here with my actual problem?

I'd say: whenever you're experimenting with mixing / frequency generation, the first thing you do is build a filter, as you don't want to get visited by your friendly neighbor, the national spectrum authorities (FCC, OFcom, BNetzA,…). You might be in luck, if distributors like mouser, digikey or arrow carry SAW filters, that might be easy to implement.

Put your tone-generating device in the lowest power setting.

Then, really, get a power rated transistor rated for bandwidths beyond your frequency of interest, and really just build a DC biasing network out of low-pass components (R's in series with L's) for that, so that you end up in an operation point of that transistor that has a quadratic curve. I find common-emitter circuits with NPNs to be easiest to build, so I'd go with that. Keep everything shorter than 1/10 of any wavelength involved, and matching becomes kinda optional¹. Make sure a mismatch can't damage your tone-generating device.

Filter the collector voltage, and do a spectrum plot of the result.

¹ very kinda. It's just that it's actually hard to actually match semiconductor circuits, so we need to simply be as robust as possible against mismatch.