Finding the electrical length of the branches of an N type T – #2

Finding the electrical length of the branches of an N type T – #1 posed a problem, this article looks at one simple solution.

For convenience, here is the problem.

An interesting problem arises in some applications in trying to measure the electrical length of each branch of a N type T piece.

Let’s make some assumptions that the device is of quality, that the connection from each connector to the internal junction is a uniform almost lossless transmission line of Zo=50Ω. Don’t assume that the left and right branches above are of the same length (though they often are) and we should not assume that the nearest branch is of the same length as the others (and they are often not).

So, the problem is all the uncertain things that connect to the internal T junction. Lets connect a calibration quality 50Ω termination to the left hand port. We now know that the path from the male port to the remaining female port comprises lengths l2 and l1 of low loss 50Ω transmission line with a 50Ω resistor shunting at the junction of l1 and l2.

Now lets connect a calibration quality short (SC) to the right hand female port, and measure ReturnLoss (RL) looking into the male port. At the frequency where the right hand branch (l1) is exactly a quarter wavelenth electrically, the SC is transformed to an open circuit (OC) at the internal T junction and so it does not load the circuit at that point. So, the instrument measuring RL at the male connector sees two sections of low loss 50Ω line to the 50Ω load, and RL will be very high.

Above is a simulation in Simsmith. For the line dimensions used here, there it a distinct peak in RL at 2500MHz (and there will be more at odd harmonics).

So, having measured the frequency f where RL peaks, the length l1 is \(\frac {299792458} {4f} m\). Don’t forget to then adjust for the offset of the SC used.

You can then reconnect the parts to find the other two lengths one by one.

So, for typical sizes of N type T adapters, you need an instrument that can measure RL to say 3GHz. A scalar analyser or RL Bridge can do this, it does not have to be a 1 port or 2 port VNA.

There is at least one other solution.

So, put your thinking caps on.

Another solution to follow…