Introduction to Electric Circuits

9. 11 Insertion loss 227

terminals of ZI~, and terminating the input port with Z~I results in an impedance

looking into the output terminals of Z~2. Then Z~I and Z~2 are said to be image

impedances. Networks are often designed on an image impedance basis in

order to take advantage of the maximum power transfer theorem. For a

symmetrical two-port network ZI~ = Z12 and is the characteristic impedance of

the network, Zo.

9.11 INSERTION LOSS

As we saw in Chapter 3, the maximum power transfer theorem tells us that
maximum power is transferred from source to load when the impedance of the
load is equal to the impedance of the source. When a network (an attenuator
pad, for example) is inserted between a source and a load, as shown in Fig. 9.20,
there will be a loss of power transfer due to the resulting mismatch, as well as
that due to the loss in the inserted network itself.

Figure 9.20

vs4

Zs

Inserted

2-port

network

IL

VL

O

Source Load

ZL=RL+ jXL

The insertion loss is defined to be

10 log (Pb//Pa) dB (9.67)

where Pb is the power in the load before the network is inserted and Pa is the

power in the load after the network is inserted. If the load resistance is RE, the

power in the load is P - I2RL, so

Pb// Pa = IbZRL// IaZRL - IbZ// Ia 2

where Ib is the load current before the network is inserted and I~ is the load

current after the network is inserted. It follows that the insertion loss is

10 log (Ib2/Ia2), SO

insertion loss - 20 log (Ib/la) dB (9.68)

Example 9.14

The network shown in Fig. 9.21 is inserted between the generator and the load

resistor shown in Fig. 9.22. Determine the insertion loss.