1/4 Wave Length cables and the Duplexer

1/4 wave length cables and the duplexer

By Gary Schafer K4FMX
August 4, 2012

Some Background:
Have you ever cabled up a duplexer and the actual notch depths revealed were deeper than what the math added up to in that leg of the duplexer?

A quality high-band BpBr (pass/notch) cavity can give 35 to 43 dB of notch depth per cavity. If you take two cavities (with say 40 dB notch each) and cable them together the math adds up. However, let's cable the complete duplexer together (with the additional cavities for the other side) and the 1/4 WL cables to the T connector. When the notch is swept, it will be several dB deeper than what the simple math adds up to! Why? Each 1/4 WL cable can add 5.5 dB of additional notch depth because of impedance transformation from one cavity to the next, or the last cavity to the T.

It is not uncommon for a complete duplexer which has two cavities in each leg that have 40 dB of notch depth individually (total of -80 dB) to result in a total notch depth (per leg) of -91 dB (or more).
So, how can this be? Read on....

The Theory:
The 1/4 wave length cables between cavities in a duplexer are not there for impedance matching. They are there to transform the low impedance that the notch in one cavity presents, to a high impedance at the next cavity so that the notch in that cavity is more effective. Essentially it lets the notch pull a high impedance down rather than trying to pull a modest impedance down.

The impedance in the pass range of the duplexer is hopefully in the 50 ohm range and cable length makes no difference to the impedance in the pass range. The 1/4 wave length cables between the TX and RX to antenna T are critical not for impedance matching but to present a high impedance between TX and RX, to isolate one from the other.

The notch in the RX side is tuned to the TX frequency. With a 1/4 wave length cable between the cavity and the T, the notch looks like a short in the cavity at the TX frequency and a 1/4 wave away, at the T, it looks like an open circuit at the TX frequency. This effectively isolates the RX cavity from the T at the transmitter frequency.

The same thing happens in the TX side of the duplexer. The TX cavity notch is tuned to the RX frequency. The short circuit of the notch is transformed to a high impedance or open circuit a 1/4 wave away at the T. This isolates the transmitter from the receiver at the T junction. At frequencies away from the notch the cables act as normal 50 ohm cables to pass the wanted frequencies.

73
Gary K4FMX

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