### Section 2: Dividers

A Wilkinson divider is one many circuits which can divide the power incident at one port into two output ports. Dividers are generally reciprocal- they can also be used to combine the power from two input port into one output port. A number of concepts are important when dealing with power dividers/ combiners.

Match (S11, S22, S33): In general, one would like to have most of the power going through the divider, and not reflected back to the source.

Isolation (S23): When combining power, most of the power should go from the input port to the output port. However, some amount of power may go from one of the input ports to the other input port. The amount that the circuit suppresses energy going to the wrong port is the isolation.

Insertion Loss (S21): The amount of loss within the circuit, not caused by return loss. When the match is pretty good this is often approximated by S21; when the match is poor, or when being pedantic:

We will compare and contrast a few dividers: the T-junction, the Wilkinson, and the lossy divider.

#### T-Junction divider

The T-Junction divider is about as simple as it gets, three lines come together to form a junction with perhaps a matching element if needed. It only uses transmission lines (no resistors), requires less area than a Wilkinson, and has a low insertion loss. Unfortunately, some of the ports are not matched, and the isolation is poor.

In the circuit in Figure 5.1, the 50Ώ impedances of ports 2 and 3 are transformed into 100Ώ impedances by TL1 and TL2. These two 100Ώ impedances are in parallel with each other at port 1, which means that the impedance looking into the junction of TL1 and TL2 are 50Ώ, therefore port 1 is matched. However, the impedance that TL2 sees looking towards Port 1 and TL1 (which are both in parallel from TL2's perspective) is 33Ώ... which means port 2 (and port 3) are not matched.

Figure 5.1: Basic T-Junction

The return loss at Port 2 can be calculated using the following formula:

Questions:

5.1: Using Mason Plot, what is the bandwidth for S11 less than -20dB?

5.2: Using Mason Plot, how does the modeled S22 compare to the calculated Γ? Why might these two differ? What happens if the microstrip parameters of cu_sigma is changed to 10e9, and the loss_tan changed to 0?

5.3: Is there a relationship between the S22 (return loss) and the S23 (isolation)?

#### Wilkinson divider

The Wilkinson divider can be matched and provide good isolation over a narrow bandwidth. Specifically, a Wilkinson with one section has relatively low bandwidth, however more arms can be added to the Wilkinson to increase the bandwidth. The insertion loss is generally low. The circuit does take up more area than a T-junction.

Figure 5.2: Basic Wilkinson combiner

Questions:

5.4: Using Mason Plot, what is the bandwidth for S11 less than -20dB?

5.5: How does the S22 compare between this circuit and the T-Junction?

5.6: How does the S23 compare between this circuit and the T-Junction?

#### Lossy divider

The lossy divider is matched, has okay isolation, and operates over a wide bandwidth. It can be fairly small, made up of just a few resistors and no quarter-wave transmission lines. Unfortunately, as the name implies, this circuit has a relatively high amount of insertion loss.

For all ports having a common impedance, the resistor values are Z0/3. Because this circuit has no frequency dependent components, the S-Parameters do not change over frequency- this is what causes the circuit to have so broad of a band.

Figure 5.3: Lossy divider

Questions:

5.7: Using Mason Plot, what is the bandwidth for S11 less than -20dB?

5.8: How does the S23 compare between this circuit and the Wilkinson?

5.9: How does the S21 compare between this circuit and the Wilkinson?