IEEE Microwave Magazine - June 2015 - 31

Dk = 1
- sum of all loops that do not touch path k
+ sum of all products of two nontouching
loops that do not touch path k
- sum of all products of three nontouching
loops that do not touch path k
...
With this rule, we can obtain the transmission coefficients t LG from the generator to load L = Gt LG and
t DG from generator to detector D = Gt DG . Looking
for the loops yields CG S 11, S 22 CL, S 33 CD, S 21 CL S 12 CG,
S 31 C D S 13 C G, and so on. We are looking to find the
relationship between the signal at the load L and the
signal at the detector D, which is kept constant by the
leveling loop
t
L = Gt LG = D LG .
t DG

To achieve this steady amplitude, part
of the signal from a sweep frequency
generator is detected with a detector
diode or a power sensor.
direct one, and S 21 CL S 32, the reflection at the DUT. Bear
in mind that the matching of the DUT is unknown and
the value of CL can be considerable, which is why the
effective source match is so important. The search for
nontouching loops produces S 22 CL for the first path
and no loop for the second path
t DG =

(2)

S 31 (1 - S 22 C L) + S 21 C L S 32
.
D

(4)

With these expressions, (2) yields

Because we are interested only in the ratio t LG /t DG,
and both of these quantities are inversely proportional
to D (1), we need not evaluate D. To find the transmission coefficients, we inspect the signal flow graph
(Figure 3). Looking for transmission paths from the
generator (port 1) to the load (port 2) reveals the direct
path S 21 and a path via the reflection at the detector
diode S 31 C D S 23 . The only loop that does not touch
S 21 is S 33 CD . The path S 31 CD S 23 touches all loops, and
thus, the transmission coefficient is
S 21 (1 - S 33 CD) + S 31 CD S 23
t LG =
.
D

L =D

(3)

Port 3
Port 1 S31
G

CG

S11

CD
S33

S13

S23

S32
S21

S22

S12

Power Leveling

Goal: C eff = S 22 - S 21 S 32 = 0.
S 31

(5)

The last step in obtaining the effective source match
Ceff compares this expression with the expression for

D

As shown in Figure 4, there are also two paths from
the generator (port 1) to the detector (port 3): S 31, the

A mismatch at port 2 repairs the corrupted leveling, as shown in Figure S1. The lack of isolation
of the coupling structure used in a leveling loop
compromises the power leveling but can be compensated by an intentionally introduced reflection
coefficient

S 21 (1 - S C ) + S C
33 D
23 D
S 31
.
1 - C L (S 22 - S 21 S 32 )
S 31

Port 2
L

CL

Figure 4. The signal flow graph for determining t DG .
The direct path S 31 from the generator to the detector
is shown in green, the loop S 22 CL not touching S 31
is shown in blue, and the path S 21 CL S 32 via the load
is shown in red. Note that the value of CL can be
considerably large.
Gconst.

TX

L

Leveling Loop

Input

1

Power Divider/Splitter
3
S31
Detector
S32
2
Output
S21

Ceff

CL

Ceff

Figure S1. C eff represents both S22 and the effect
of the corrupted leveling via S32.

June 2015

Figure 5. The signal flow graph of a two-port device
attached to a load with a reflection coefficient of CL . TX
denotes the transmission coefficient, and Ceff denotes the
reflection coefficient at the output of the two-port device.

31
Table of Contents for the Digital Edition of IEEE Microwave Magazine - June 2015
