Duplexer Basics: How Two Filters Share One Antenna

What a duplexer is

A duplexer lets a transmitter and a receiver use one antenna at the same time. It has three ports: a transmit input, a receive output and a common antenna port.

Inside are two band-pass filters. One passes the transmit band and rejects the receive band. The other passes the receive band and rejects the transmit band. Both connect to the antenna port.

The transmit signal is strong and the receive signal is weak. Without the second filter, a small fraction of the transmit power would reach the receiver and swamp it. The duplexer's job is to keep that leakage low while adding little loss to either wanted path.

Port numbering and the S-parameters you need

A three-port device has nine S-parameters. Only a few matter on a public data sheet. In this article the ports are numbered:

• Port 1: transmit input
• Port 2: antenna (common)
• Port 3: receive output

The numbering is a convention, not a law. Data sheets may use a different order, so always check the port table first.

The figure shows the two-port case. A duplexer extends the same idea to three ports, and each S-parameter is still "power or voltage coming out of the port named first, caused by a wave going into the port named second." If the notation is new, see S11, S21, S12 and S22 Explained for a Two-Port.

The useful parameters are:

• S21: transmit to antenna. This is the transmit-path insertion loss, read in the transmit band.
• S32: antenna to receive. This is the receive-path insertion loss, read in the receive band.
• S31: transmit to receive. This is the isolation.
• S22, S11, S33: reflection at each port, used for matching.

Insertion loss

Insertion loss in the passband is the negative of the through-path S-parameter in dB:

The same form applies to S32 for the receive path. Data sheets usually print S21 in dB as a negative number, such as -2. The insertion loss is then +2 dB. Do not mix the two signs in one calculation.

A loss in dB converts to a fraction of power passed:

For IL = 2 dB, this gives 10^-0.2 = 0.631. So 63 percent of the power passes and about 37 percent is lost, mostly as heat in the filter.

Read the loss at the right frequencies. S21 is only an insertion loss inside the transmit band. Outside it, the same curve describes rejection. Read S21 across the transmit band and S32 across the receive band, and note the worst point, not just the center.

Isolation

Isolation is the attenuation from the transmit port to the receive port. Using the numbering above, it is S31:

It is expressed as a positive number of dB. It is not S21 unless the ports are numbered so that transmit is port 1 and receive is port 2. This is the most common misreading on a data sheet.

Isolation matters most in the transmit band, where the strong transmit signal must be held back from the receiver. The receive filter's rejection of the transmit band sets that figure. Isolation in the receive band is a separate question and is set mainly by the transmit filter's rejection there.

This figure is a low-pass filter, not a duplexer, and it is computed from a circuit model, not measured. It shows the shape to look for: S21 stays near 0 dB in the pass region and falls in the stop region. A duplexer's two band-pass responses fall the same way on either side of their bands.

The phase match at the common port

Both filters connect to the same node. Each must look like a very high impedance, ideally an open circuit, to the other filter's band. Then the other filter does not load it, and the signal goes where it should.

This is set by the phase, or electrical length, of each filter as seen from the common port. The designer adds matching so that the transmit filter presents an open circuit across the receive band, and the receive filter presents an open circuit across the transmit band.

The reflection coefficient shows it. An open circuit has Γ = +1, so |Γ| ≈ 1 with the right phase. A filter far outside its passband reflects almost all power anyway. What the phase decides is whether that reflection looks like an open or like a partial short or reactance at the junction.

If the phase is wrong, the idle filter loads the node. The result is higher insertion loss in the band of the working filter and degraded isolation. This is why the S22 and the insertion-loss curves of a duplexer are tied together, and why you cannot judge the two filters on their own.

Worked example

Assume a duplexer with 2 dB of transmit insertion loss (S21 = -2 dB in the transmit band) and 20 dB of isolation (S31 = -20 dB). These are illustration values, not a real part. The transmitter puts 1 W into port 1.

1. Power at the antenna: 10^-0.2 = 0.631, so 0.631 W reaches port 2.
2. Power at the receive port: 20 dB of isolation is 10^-2 = 0.01, so 0.01 W (10 mW) leaks to port 3.
3. Heat in the filter: 1 − 0.631 = 0.369 W, ignoring reflection at the input.

Ten milliwatts is still huge for a receiver input, which is why real duplexers aim for much more isolation than this. The point of the example is the method: sign flip for loss, sign flip for isolation, then 10 to the power of minus dB over 10.

Checking a data sheet

For loss, find the transmit and receive band edges and read S21 and S32 across them. For isolation, read S31 in the transmit band. For match, check the reflection at the antenna port. If the data sheet gives a Touchstone file, the same S-parameters sit in its lines, one frequency per line.

In plain words · for students and beginners

Duplexers in plain words

An everyday picture

Think of a two-lane road that must pass through one narrow gate. One lane is for outgoing cars and one for incoming. A duplexer is the gate with two guards. One guard only lets outgoing cars through to the road. The other only lets incoming cars through to the parking lot.

The picture breaks down in one place. Real cars do not interfere with each other, but radio signals do. The outgoing signal is very loud and the incoming one very quiet, so even a tiny leak from the loud side can drown the quiet side.

The same example in simple steps

You send 1 W into the transmit port.

1. The filter loses 2 dB on the way to the antenna. A loss of 2 dB means 0.631 of the power gets through.
2. So 0.631 W goes to the antenna. The rest turns into heat.
3. The leak to the receiver is held back by 20 dB. That is a factor of 100, so 0.01 W leaks across.

Both numbers come from the same rule: take the dB value, divide by 10, and raise 10 to the power of minus that number.

Where to look on the data sheet

A data sheet often comes with an S2P file, a text file with one line per frequency. Each line holds the S-parameters for that frequency. Learn to find the right column first.

Then match the column to the right path: transmit to antenna for transmit loss, antenna to receive for receive loss, and transmit to receive for isolation.

Mistakes beginners make

• Reading the wrong column. Isolation is the transmit-to-receive path. It is only S21 if the ports are numbered that way.
• Mixing signs. A data sheet shows -2 dB. The loss is 2 dB. Isolation is also quoted as a positive number.
• Judging one filter alone. The two filters affect each other at the shared antenna point. Their phase must be matched, so a good filter on its own is not enough.
• Reading the wrong frequency range. The transmit curve is a loss only inside the transmit band.

Remember

• A duplexer is a transmit filter and a receive filter joined at one antenna port.
• Loss is the negative of S21 or S32 in dB, and 2 dB of loss passes 63 percent of power. Isolation is the transmit-to-receive S-parameter, shown as positive dB.
• Each filter must look like an open circuit to the other's band at the common port, and the phase match sets that.

Related pages on RF View

• S11, S21, S12 and S22 Explained for a Two-Port
• Return Loss vs Insertion Loss: What Each Number Tells You