Wilkinson Power Combiner

[Randy222]

The Wilkinson design is an interesting way to divide or combine signals.

So for the audience here, this Q is for the Rf guru's.

If you use the Wilkinson to combine signals of different fundamental frequencies, and the signals are not sync'd in any way (no phase control), what does the output look like?



Example:
P2 is 2.400GHz
P3 is 2.450GHz

What then does P1 look like?

[joeqsmith]

I'm not much of an RF guru, but I can try a simple search on Google.  My guess is you wondering what the difference between a mixer and a combiner is but were afraid to ask. 

https://www.electro-tech-online.com/threads/why-a-mixer-to-combine-two-frequencies.154622/

[G0HZU]

Assuming Zo = 50R... If freqP2 is 2.4GHz and freqP3 is 2.45GHz (and both ports can normally deliver 1mW into a 50R load), then you would see 0.5mW at 2.4GHz at P1 and there would also be 0.5mW arriving at P1 at 2.45GHz. There would also be RF power being dissipated in the 100R resistor. This would be at a power level of 0.5mW at 2.4GHz and at a power level of 0.5mW at 2.45GHz.

If you then consider the classic freqP2 = freqP3 case, (i.e both P2 and P3 are 2.4GHz) and both are in phase and both can normally deliver 1mW into a 50R load then you would see 2mW at P1 at 2.4GHz because the two signals are at the same frequency and they are in phase. There would be no power dissipated in the 100R resistor.

[kj7e]

We have many high powered wilkinson combiners in our commercial FM broadcast transmitters, without doing any math I can quickly tell you you will end up with about 6dB of power into your reject port.  The inputs must be in phase otherwise it just wont work.

[profdc9]

To combine two different frequencies at two different ports into a single port, you need a diplexer.

If the separation at 2400 MHz is 50 MHz, that corresponds to a minimum Q of 48. 

I suppose you could use a cavity resonator to achieve this.  The cavity would reflect one frequency and pass the other, thus combining them.  A resonator could be in principle made out of  coupled microstrip lines.

[fourfathom]

To combine two different frequencies at two different ports into a single port, you need a diplexer.

If the separation at 2400 MHz is 50 MHz, that corresponds to a minimum Q of 48. 

I suppose you could use a cavity resonator to achieve this.  The cavity would reflect one frequency and pass the other, thus combining them.  A resonator could be in principle made out of  coupled microstrip lines.

You can also use a broadband transformer hybrid divider/combiner (also called a "Magic-Tee").  Here's a good discussion: https://ka7oei.blogspot.com/2019/11/homebrew-construction-of-2-and-4-port.html
If the two inputs are in-phase (or 180 degrees out of phase, depending on the construction) all the power will be dissipated in the termination resistor, and none will appear at the output.  With the opposite phase relationship the inputs combine at the output with no loss (assuming ideal transformers).  With a 90-degree relationship, or with different frequencies, the output will be down 3dB, with the other 3dB dissipated in the termination.  This is also the case with the Wilkinson.

The Wilkinson is a great circuit, and can be built with lumped L/C or with transmission lines, but it is fairly frequency-sensitive.  There are variants that have a wider frequency range, but they are still much narrower than a transformer hybrid design.  At high frequencies you can implement the Wilkinson as microstrip, which can be a big plus.

[RFDx]

If you use the Wilkinson to combine signals of different fundamental frequencies, and the signals are not sync'd in any way (no phase control), what does the output look like?



Example:
P2 is 2.400GHz
P3 is 2.450GHz

What then does P1 look like?

Assuming the power at P2 is equal to that at P3, you get a 2-tone output signal at P1 with every tone at 1/2 of the applied input power. The envelope power of the 2-tone signal varies continuously between 0 and a PEP-value of P2+P3 with a frequency of f(P3)-f(P2). Same goes for the power in the 100 Ohm isolation resistor, just out of phase to the output power at P1.

[fourfathom]

I suppose you could use a cavity resonator to achieve this.  The cavity would reflect one frequency and pass the other, thus combining them.  A resonator could be in principle made out of  coupled microstrip lines.

If the frequencies are separated sufficiently you can do this with moderately low-Q LC filter circuits as well.  The trick is to use multi-stage series-resonant filters (these go high-Z away from their resonant frequency.)  I've got an application where I combine the low-power (about 1W) outputs of six or more transmitters into a common multiband antenna. Using medium-Q surface-mount inductors I can achieve less than 1dB loss, and better than -20dB port-to-port coupling.  The frequencies are octave-spaced or slightly closer.  With higher-Q toroid inductors I can get closer frequency-spacing and similar performance.

[Randy222]

Assuming Zo = 50R... If freqP2 is 2.4GHz and freqP3 is 2.45GHz (and both ports can normally deliver 1mW into a 50R load), then you would see 0.5mW at 2.4GHz at P1 and there would also be 0.5mW arriving at P1 at 2.45GHz. There would also be RF power being dissipated in the 100R resistor. This would be at a power level of 0.5mW at 2.4GHz and at a power level of 0.5mW at 2.45GHz.

If you then consider the classic freqP2 = freqP3 case, (i.e both P2 and P3 are 2.4GHz) and both are in phase and both can normally deliver 1mW into a 50R load then you would see 2mW at P1 at 2.4GHz because the two signals are at the same frequency and they are in phase. There would be no power dissipated in the 100R resistor.

Yes, two sine voltages arrive at P1, but certainly those voltages add and subtract from each other in weird ways depending on phase shift?

If there's a 2.4-2.5GHz antenna attached (assume ideal 1:1 vswr matched Z), You don't see two signals resonating out, you see just one, yes?

I wondering if LTspice can simulate it?

[T3sl4co1l]

Since after all, networks wouldn't be very useful if you could only send pure sine waves (exact frequency) through them.

You have some bandwidth, determined by network type, and acceptable limits of what you're doing; in this case, balance between the two legs, and differential-mode termination.

Roughly speaking, transmission line structures for general (non-precision) purposes have on the order of 10% bandwidth, but this varies from case to case for the above reasons.

LTspice can model it by explicit transmission lines or their LC equivalents.

Tim

[Randy222]

But when two signals hit each other at P1 port, they combine by simple math, then look funny, meaning no longer simple sine wave.

Hit the "y1 + y2" box then move the omega slider on one, change amplitude, etc. The two combine by addition. In this case, the benefit of Wilkinson is that P2 is not seen on P3 (and vice versa) by same concept?

https://www.geogebra.org/m/BOMfKCIK

[T3sl4co1l]

Signals don't care how they "look"... superposition works independent of whatever aesthetics we ascribe to it.

Tim