Making half wave and quarter wave transmission lines using coaxial cables?

Hi guys,

I have two questions and I need urgent answers. I hope that someone among you may help me in this regard. The questions are

Firstly, how can I make halfwave length and quarter wavelength transmission line at 123 MHz frequency? (I have coaxial cables and I have to cut them in such a way that I get the desired electrical length). I actually need to know how long these wires should be in each case? Please mention formula or rule of thumb.
Secondly, how can I check whether the transmission line I am using is half wave length or quarter wavelength using network analyzer (I mean what are the positions for such transmission lines on smith chart)?

many coax dielectric constants yield propagation speed
c ≈ 2e8 m/s
now L=c/f choose L/2 and L/4 for a given wavelength, L. and make it long than necessary by 10% so you can tune it.

using a NA you can measure return loss of stub if just using it as 1 port device.

Of course you know quarter wave cables will transfer the inverse impedance to the source ,so a short and end will appear open at source and visa versa. THey are useful for impedance transformers and notch filters and passive splitter using 71ohm coax split to 50Ω networks. etc etc.

For an air-filled coaxial line, the half or a quarter-wave length is straightforward. For dielectric-filled coax cable, the propagation speed is lower, so the cable will be shorter. How shorter you can find from manufacturer's data.

If you cannot find the data, follow this procedure:

1. Take an approx. quarter-wave long coax cable to sacrifice by an experiment. Solder one end to make a good short (sheath to center conductor. ) Open the other end and separate sheath from the center conductor.

2. Take a RF signal generator with a coax output at the desired frequency (e.g.123 MHz). Connect a diode detector so that the live point is exposed. Connect an analog indicator (Vmeter. mA meter) to detector output.
Set the RF level to 1...10 mW, the detector output would be ~30-300 mV or so ( 0.1 - 1-3 mA) with nothing else connected to the RF output. If you touch the point by your finger, the output will drop a bit.

3. Connect the open end of your shorted cable to the "hot" point: the detected output can swing high or low. Cut the open cable end by one inch and repeat. After several trials, you will see NO change at all.
This makes your cable exactly a quarter-wavelength long; it has a very high impedance (in theory, infinite) compared to 50 or 75 Ohms of the cable.

4. If you try the same with a half-wavelength shorted cable, the detected voltage should show a perfect short like placing a screwdriver across the coax. Half-wavelength line repeats other end's impedance. If you leave the other end open, half-wave long cable will have again a high impedance (like the shorted quarter-wave long one).