Just for variety, I used T networks (rather than your π networks) as transmission line simulators. In any case, this simulation shows the effect rather clearly.
The power through the transmission line is transformed in impedance and goes through a similar voltage divider action when it arrives at Port 3, but since it has been delayed by 180° it cancels the resistor power.Īgain, I haven't written out the full equations yet, but it seems like it should work out. I haven't worked out all of the math details, but I think it's going to be possible to show that if power is injected at Port 2, half of it flows through the resistor toward Port 3, and half flows down the transmission line to Port 1.Īt Port 1, this power divides further, sending 2/3 of it out Port 1, and the other 1/3 down the other transmission line to Port 3.Īt Port 3, the power through the resistor is attenuated by voltage divider action against the net impedance at that port. *It is impossible to construct a three-port lossless reciprocal network that is matched at all ports in general. This makes them a good candidate for use in solid state RF power amplifiers. It cannot combine independent signals losslessly*.
Assuming all ports are matches, this means the circuit can divide a signal losslessly (because the V2 and V3 will be equal and in phase) and can combine identical & in phase signals losslessly. If there are unequal voltages at ports 2 and 3 at any time power will be lost in the resistor.
The circuit is only lossless if all ports are matched. This circuit is the simplest way to achieve this property.Īnd wouldn't port 1 have some significance to the operation? The whole idea of the circuit is that it has the property that ports 2 and 3 are 180 degrees away (through the microstrips) and also 0 degrees away through the resistor. In this case he uses what is called Even-Odd mode analysis, which he explains pretty well since it is the first time it is used in the text.įor example, why split in half and not some other ratio which would not result in complete cancellation? For a more rigorous derivation of the scattering matrix you can read section 7.3 (page 328) of Pozar's Microwave Engineering. Microwaves101 provides a good qualitative and intuitive explanation, and you seem to understand the idea.
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