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SEMI E115-0302 E © SEMI 2002 4 RLOAD = Re( Z ou t *) − 2 RLOS S (6) X LOAD =− Im( Z ou t *) (7) where Effc is the calculated power efficiency based on the measurement of Re( Zout * ) and Effm , RLO AD is the real part of…

SEMI E115-0302

8 Test Setup for Determining Load Impedance

and Efficiency

8.1 Two test methods are described for analyzing

matching networks. The first method for determining

the load impedance and efficiency measures the

complex conjugate of the load impedance and then

corrects for the matching network losses to determine

the load impedance and efficiency. A schematic of the

Test Setup is shown in Figure 1. The method uses a

Network Analyzer to measure the reflection coefficient,

which is related to the load impedance, and the

transmission coefficient, which is related to the

efficiency. The Test Setup for this approach consists of

the Network Analyzer, the matching network to be

tested (DUT), coaxial test cables, and the appropriate

adapters (if any) to connect the DUT to the Network

Analyzer.

8.2 The second method for determining the load

impedance and efficiency uses a Load Impedance

Simulator attached to the output of the matching

network. A schematic of the Test Setup is shown in

Figure 2. The Test Setup for this approach consists of

the Network Analyzer, the matching network to be

tested (DUT), the load simulator, coaxial test cables,

the appropriate adapter (if any) to connect the DUT to

the Network Analyzer, and the appropriate adapter to

connect the load simulator to the DUT.

8.3 Prior to making any measurements, the Network

Analyzer shall be turned on and allowed to warm up

before the testing is to take place. This time will allow

for electronics to come to a stable operating condition

for the measurements.

9 Test Procedure for Determining Load

Impedance and Efficiency

9.1 Two test procedures can be used to determine the

load impedance and efficiency of the matching

network. The first method is designed for “L” type

matching networks, where the losses are dominated by

the loss resistance of the inductor that is in series with

the load impedance. For the case where there are finite

losses in the shunt capacitor, the capacitor losses can be

lumped in with the inductor losses without introducing

significant error (usually less than 0.5% for typical

values of < 0.1 ohms). Lumping the total losses into an

overall series loss will also cause a slight shift in the

reactive part of the impedance, but the magnitude of the

shift is on the same order as the impedance

measurement uncertainty and can be ignored.

9.2 The second method is designed for other matching

network types and uses a load simulator to determine

the load impedance and efficiency.

9.3 Test Method 1 for Determining Matching Network

Load Impedance and Efficiency

9.3.1 This test method shall be used for “L” type

matching networks of the type shown schematically in

Figure 1, where the losses in the network are dominated

by the loss resistance of the inductor, RLOSS. The

efficiency for this type of matching network is given as

Eff =

RLOAD

RLOAD + RLOSS

(1)

where RLOAD refers to the real part of the load

impedance and RLOSS refers to the losses of the

matching network.

9.3.2 For this type of network, the real part of the

complex conjugate impedance, Re(Zout*), contains the

real part of the load impedance plus twice the loss

resistance, RLOSS.

Re(

RLOAD + 2RLOS

(2)

9.3.3 The load impedance, therefore, is equal to the

complex conjugate impedance less twice the loss

resistance (along with the sign change of the reactive

part of the conjugate impedance). For example, if the

conjugate impedance is measured as 3 + j20 and

RLOSS is determined to be 0.5 ohms, then the load

impedance is 2 – j20 ohms.

9.3.4 The efficiency of the matching network and the

loss resistance, RLOSS, can be determined by

measuring both the transmission coefficient, S21, and

the reflection coefficient, S11, in the Test Setup shown

in Figure 1. Note that the reflection coefficient

measurement, S11, is equivalent to measuring the

complex conjugate impedance. If the matching

network is considered as a test load with an impedance

equal to the complex conjugate impedance, then the

loss resistance is found by measuring the efficiency of

the test load. This efficiency, Effm, can be expressed as

Effm =

Re(

out*) − RLOSS

Re(Zout*)

(3)

where Re(Zout*) is the real part of the complex

conjugate load impedance, Zout*. The measured

efficiency, Effm, can be determined from the S21 and

S11 measurements (as shown later in this section).

Thus, the measurements of Re(Zout*) and Effm can be

used to determine RLOSS as

)1(*)Re( EffmZoutRLOSS −×

(4)

and the load impedance and power efficiency of the

matching network can then be determined from

Effc =

Re(

out*) − 2RLOSS

Re(Zout*) − RLOSS

(5)

SEMI E115-0302

RLOAD = Re(

*) − 2RLOS

(6)

LOAD =−Im(

*) (7)

where Effc is the calculated power efficiency based on

the measurement of Re(Zout*) and Effm, RLOAD is the

real part of the load impedance, and XLOAD is the

imaginary part of the load impedance.

9.3.5 Calibrate the Network Analyzer at the desired

operating frequency (e.g., 13.56 MHz). The Network

Analyzer shall be calibrated for measuring the

reflection coefficient at test Port 1 and for measuring

the transmission coefficient at test Port 2 (see Figure 1)

using the calibration kit provided with the Network

Analyzer. This measurement requires measuring the

S11 and S21 S-parameters and requires a full 2-port

calibration. The calibration shall be performed at fixed

frequency (continuous-wave operation) using the

lowest bandwidth possible (typically 10 Hz). The

calibration for each port shall include the additional test

cables and any additional adapters.

9.3.6 After calibration of the Network Analyzer, the

cable connected to Port 1 of the Network Analyzer shall

be connected to the output of the DUT. The cable

connected to Port 2 of the Network Analyzer shall be

connected to the input of the DUT.

9.3.7 The tuning elements shall be moved to their

minimum positions before the measurement is initiated.

After all connections are visually inspected for proper

contact and the Network Analyzer has stabilized, the

value of the complex conjugate impedance (Zout*), the

magnitude of the reflection coefficient (S11), and the

magnitude of the transmission coefficient (S21) shall be

recorded.

9.3.8 The efficiency when the DUT is viewed as a test

load, Effm, is determined from both the reflection and

transmission coefficients. The efficiency can be

calculated by taking the ratio of the output power

divided by the input power. The output power is

simply (S21)

and the input power is (1-(S11)

()

111

Effm

−

Typically, the reflection and transmission coefficients

are expressed in terms of dB (decibels). The conversion

between dB and efficiency is expressed as

)10/dBin 11S(

)10/dBin 21S(

101

−

=Effm

For example, if the transmission coefficient is measured

to be –10.2 dB and the reflection coefficient is

measured to be –0.61 dB, then Effm would be 0.7288.

The efficiency based on this measurement can then be

used to calculate RLOSS, Effc, RLOAD, and XLOAD by

using the equations previously shown. All of these

calculated numbers using equations 3–6 shall be

recorded, as well as the positions of the tuning elements

of the matching network.

9.3.9 For the next measurement, Tune Position shall

remain fixed, and the Load Position shall be increased

by an increment equal to no more than 10% of the full-

scale range of the tuning element position. For

example, if the range of the tuning element is 10 volts,

then the tuning element should be moved in increments

of no greater than 1 volt. A smaller increment shall be

used for the case where the incremental change in Load

Position results in an incremental impedance change of

more than 20% of the total impedance variation

measured by the full-scale variation of the Load

Position. For example, if the real part of the load

impedance varies 15 ohms over the 10 volt variation of

the Load Position, then a smaller Load Position

increment shall be used if the real load impedance

varies by more than 3 ohms between increments (0.2 ×

15 = 0.3). After the tuning elements have been moved

to their new values, the previous measurement steps

shall be repeated.

9.3.10 After the Load Position has been varied over its

entire range, the Tune Position shall be increased by an

increment equal to no more than 10% of the full-scale

range of the tuning element position. The Load

Position shall be moved back to its minimum position

and the above steps shall be repeated until the entire

tuning range of the matching network is measured.

9.3.11 The data shall be recorded and then presented in

both graphical and tabular forms. An example of a

typical impedance range graph is shown in Figure 3 for

the real load impedance and in Figure 4 for the reactive

load impedance. An example of a typical efficiency

plot is shown in Figure 5. An example of data

presented in tabular form is shown in Table I.

9.4 Test Method 2 for Determining Matching Network

Load Impedance and Efficiency

9.4.1 This test method shall be used for matching

networks that are not necessarily dominated by a series

loss resistance as in an ideal “L” type network. This

method uses a Load Simulator(s) attached to the DUT

and assumes that the DUT has two tuning elements.

The Load Simulator(s) shall have a tuning range that

will cover no less than 80% of the tuning range of the

matching network. Details of a typical Load Simulator

can be found in the Related Information section of this

Test Method. The test method outlined here assumes

that the Load Simulator(s) contains variable tuning

elements with position indicators to allow the load

SEMI E115-0302

impedance to vary. An example of a load simulator

would be a matching network used in reverse, where

the output of the DUT would attach to the output of

another matching network.

9.4.2 Calibrate the Network Analyzer at the desired

operating frequency (e.g., 13.56 MHz). The Network

Analyzer shall be calibrated for measuring the

reflection coefficient at test Port 1 and for measuring

the transmission coefficient at test Port 2 (see Figure 1)

using the calibration kit provided with the Network

Analyzer. This measurement requires measuring the

S11 and S21 S-parameters and requires a full 2-port

calibration. The calibration shall be performed at fixed

frequency (continuous-wave operation) using the

lowest bandwidth possible (typically 10 Hz). The

calibration for each port shall include the additional test

cables and any additional adapters.

9.4.3 After calibration of the Network Analyzer, the

test cable connected to Port 1 of the Network Analyzer

shall be connected to the input of the matching network

to be tested (DUT). The Load Simulator shall be

connected to the output of the DUT. The cable

connected to Port 2 of the Network Analyzer shall be

connected to the output of the Load Simulator.

9.4.4 The tuning elements shall be moved to their

minimum positions (or the positions that can match to

lowest tuning point of the Load Simulator(s)) before the

measurement is initiated. The variable elements in the

Load Simulator shall be adjusted until the input

impedance of the matching network is matched (i.e.,

input impedance = 50 ohms). After all connections are

visually inspected for proper contact and the Network

Analyzer has stabilized, the value of the input

impedance and the magnitude of the transmission

coefficient (S21) shall be recorded. In addition, the

positions of the tuning elements of the DUT and the

Load Simulator shall be recorded.

9.4.5 The load impedance of the DUT corresponds to

the input impedance of the Load Simulator. At this

point in the process, the Load Simulator can be

disconnected and its input impedance can be measured.

Alternatively, the input impedance can be measured

later by moving the Load Simulator tuning element

values to the positions recorded in Section 9.4.4.

9.4.6 The efficiency of the Test Setup, which includes

the DUT and the Load Simulator, is determined from

the transmission coefficient. Typically, the

transmission coefficient is expressed in terms of dB

(decibels). The conversion between dB and percentage

is expressed as:

Efficiency(%) = 100 × 10

(loss in dB

10)

For example, if the transmission coefficient is measured

to be –3 dB, then the power transfer efficiency would

be 50.1%. In other words, 49.9% of the power is lost in

the Test Setup.

9.4.7 The efficiency of the DUT is determined by

dividing the efficiency of the Test Setup by the

efficiency of the Load Simulator. For example, if the

efficiency of the Test Setup is 70% and the efficiency

of the Load Simulator is 90%, then the efficiency of the

DUT is 77.8% (0.7/0.9). The efficiency of the Load

Simulator is typically determined separately (see

Related Information Section at the end of this Test

Method).

9.4.8 For the next measurement, one tuning element

(element 1) shall remain fixed, and the other tuning

element (element 2) shall be increased by an increment

equal to no more than 10% of the full scale range of the

tuning element position. For example, if the range of

the tuning element is 10 volts, then the tuning element

shall be moved in increments of no greater than 1 volt.

A smaller increment shall be used for the case where

the incremental change in tuning element position

results in an incremental impedance change of more

than 20% of the total impedance variation measured by

the full-scale variation of the tuning element. For

example, if the real part of the load impedance varies

15 ohms over the 10 volt variation of the tuning

element, then a smaller tuning element increment shall

be used if the real load impedance varies by more than

3 ohms between increments (0.2 × 15 = 0.3). After the

tuning elements have been moved to their new values,

the previous measurement steps shall be repeated.

9.4.9 After the tuning element (element 2) has been

varied over its entire range, the other tuning element

(element 1) shall be increased by an increment equal to

no more than 10% of its full-scale range. Tuning

element 2 shall be moved back to its minimum position

and the above steps shall be repeated until the entire

tuning range of the matching network is measured.

9.4.10 The data shall be recorded and then presented in

both graphical and tabular forms. An example of a

typical impedance range graph is shown in Figure 3 for

the real load impedance and in Figure 4 for the reactive

load impedance. An example of a typical efficiency

plot is shown in Figure 5. An example of data

presented in tabular form is shown in Table 1.

10 Reporting Test Results

10.1 Report the type of Network Analyzer and the

details of the Network Analyzer parameters used for the

tests, including the bandwidth, the number of data

points, and the test frequency. Also report which Test

Method was used.