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SEMI E115-0302 E © SEMI 2002 3 8 Test Setup for Determining Load Impedance and Efficiency 8.1 Two test methods are des cribed for analyzing matching net works. The first method for det ermining the load impedance a n d e…

SEMI E115-0302

complex conjugate of a load impedance of 2.0 – j20

ohms would be 2.0 + j20 ohms.

5.2.2 device under test (DUT) — the matching network

to be tested.

5.2.3 harmonic frequency — the harmonic frequencies

are defined as integer multiples of the fundamental

frequency. For example, the second harmonic of 13.56

MHz is 27.12 MHz.

5.2.4 “L” type matching network — this type of

network consists of a tuning element that is connected

to ground, which is often a variable capacitor, and

another tuning element that is in series with the output

connection. The series section of the “L” matching

network typically consists of an inductor and a

capacitor, one of which is variable.

5.2.5 load and tune position — for some matching

networks, the tuning elements are referred to as the

Load Position and the Tune Position. This terminology

is common for “L” type matching networks, which

have a tuning element that is connected to ground and

another tuning element that is in series with the output

connection. The Load Position corresponds to the

tuning element that is grounded and is associated with

matching to the real part of the load impedance. The

Tune Position corresponds to the tuning element that is

in series with the output and is associated with

matching to the reactive part of the load impedance.

5.2.6 load impedance — the load impedance is the

impedance to which a matching network is matched.

5.2.7 load impedance simulator — the Load

Impedance Simulator is a device that presents a load

impedance to which a matching network can match.

Details of a typical Load Simulator can be found in the

Related Information section of this test method.

5.2.8 matched input impedance — a matched load

impedance is defined as typically having a magnitude

of 50 ± 3.3 ohms at a phase angle of up to ± 3.8

degrees. In other words, the load is considered matched

if the reflection coefficient is no greater than 0.032 at

any phase angle.

5.2.9 matching network — the device used to

transform the impedance of the load (chamber/chuck)

to match the impedance of the generator/cable

assembly, which is typically 50 ohms.

5.2.10 power efficiency — the ratio of the power

exiting the matching network divided by the power

entering the matching network.

5.2.11 S-parameters — the scattering matrix used to

describe a network. The reflection coefficient is the

S11 parameter and the transmission coefficient is the

S21 parameter.

5.2.12 tuning element position — the position of the

tuning element is defined as the output voltage or

output encoder value that corresponds to the position of

a variable tuning element in a Matching Network. For

example, the voltage from a rotary potentiometer on the

rotating shaft of a variable capacitor (the “Tuning

Element”) would be referred to as the capacitor’s

“Position”. In this example, the position/voltage

corresponds to a certain shaft location or position.

6 Test Apparatus

6.1 RF Vector Network Analyzer — The Network

Analyzer is used to measure the load impedance and

efficiency of the matching network. The Network

Analyzer requires vector capability so that both the

magnitude of phase of the reflection coefficient and

transmission coefficient can be measured at the

operating frequency. The Network Analyzer shall have

an up-to-date calibration per the manufacturer.

6.2 Coaxial Output Adapter — An adapter to convert

the output connection of the matching network to a

standard coaxial interface is required for some of the

tests.

6.3 RF Adapters and Terminations — Various adapters

may be necessary to convert between different types of

coaxial connectors (e.g., type N to type HN adapters,

etc.). All adapters used shall have the same nominal

characteristic impedance as the system, which is

typically 50 ohms. For some measurements, additional

coaxial cable assemblies are used. These cable

assemblies shall also be of the same nominal

characteristic impedance as the system. Standard

terminations are also used, such as shorts, opens, and

precision 50-ohm loads.

6.4 RF Load Impedance Simulator — A device that

can be attached to the output of the DUT to act as a

load for the DUT is required for some of the

measurements. The load simulator shall have an

impedance range to match a minimum of 80% of the

tuning space of the matching network to be tested.

7 Safety Precautions

7.1 Work should be conducted in accordance with local

safety requirements and test device manufacturer

recommended safety procedures. The tests described in

this document involve using low output power test

instrumentation (typically less than 10 milli-Watt).

7.2 The area immediately surrounding the Test Setup

shall be keep free and clear of unnecessary equipment

and materials.

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