26 www.rfdesign.com November 2007

Amplifiers

Extracting true PA input impedance for high-power RF signals The input impedance of a non-ideal power amplifier (PA) stage is determined using a source-pull measurement in a load-pull system, though this method does not account for inaccuracies caused by the impedance of the measuring equipment. However, a test methodology using multiple measurements and two-port S-parameter values for the source and load tuners can extract the true input impedance of the PA at the probe/device reference plane for RF signal power levels.

By Zhijian Xie

With the increasing interest in integrated RF power applications, accurately characterizing on-chip components becomes critical

for the success of integrated circuit design. The issue becomes even more severe when dealing with the PA. The high-power levels in this final stage of the transmit path determine the PA’s special properties. One of them is its low input impedance, which varies with power level. Usually, load-pull systems are used to measure the impedance of on-chip components, or other kinds of devices having impedances other than an ideal 50 Ω.

In a load-pull system, the source impedance with minimum return loss is typically regarded as the conjugate impedance of device under test (DUT). Using this value is accurate if the return loss is truly at the DUT reference plane. However, because the return power is measured at the source-tuner reference plane, different methodologies are implemented to extract, or “de-embed” the return power at the DUT reference plane from the measured return power at the tuner reference plane. Unlike power de-embedding for input and output power, return power de-embedding is phase sensitive. This makes de-embedded return loss only an approximation, though it is generally accurate when tuner losses can be omitted.

Analysis and methodologyFor simplicity, assume there is a perfect (i.e., purely resistive)

50 Ω source impedance at the tuner reference plane. Figure 1 illustrates the basic definitions to be used for the source-tuner reference plane, the DUT-input reference plane, the DUT-output reference plane, Γo, Γtuner, Γs, and ΓDUT. For convenience, the source-tuner reference plane is referred to as the “tuner reference plane” and the DUT-input refer-ence plane as the “DUT reference plane,” since only the input path will be analyzed here.

The mathematical relationships among reflection coefficients (Γ),

S-port parameters (S), impedances (z), and the return loss (RL) as shown in Figure 1 are as follows: RL

RLZ Z

Z Z

tuner tuner

dutdut s

dut s

dut s

dut s

=

=−+

=−

−

| |

* *

Γ

Γ ΓΓ Γ

2

2 2

1 The goal is to create a relationship between RLtuner and RLDUT:

Because

It follows that

Where Sij is the two-port S parameter of the source-tuner block, which connects between the tuner reference plane and the DUT reference plane.

After simplification,

RLS

S SS Sdut tuner=

−− −

1 22

2

12 2111 22

2

( ) *Γ

Obviously, this is a function of both magnitude and phase of Γtuner. This phase dependence does have a vanishing point, however, which occurs when:

S

SS S S S11

22

11 22 12 21* = −

Further analysis shows that this condition is equivalent to an ideal matched network (i.e., a conjugate match at the second port makes a perfect 50 Ω impedance at the first port). This condition cannot be maintained for the high-loss region toward the edge of the Smith chart due to the high loss of a tuner having an internal stub that is close to the center of the transmission rod.

Another approximation often made during these measurements is the assumption that return power is negligibly small. When this is the case, phase difference will not be a problem. However, return-loss values measured from a load-pull system are usually large enough to render this assumption invalid. Furthermore, return loss will vary with power, as the impedance of the DUT varies with power. Therefore,

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Figure 1. Two-port network illustration for load-pull measurement. Tuner two-port blocks represent a combination of tuner, connectors and cables, as well as probes (and bias tees, if applicable).

ΓΓΓtuner

DUT

DUT

SS S

S= +

−1112 21

221

Γ

Γ

DUT

tuner

SS S

S

=+

−

1

2212 21

11

[1]

[2]

[1]

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28 www.rfdesign.com November 2007

return loss will almost never remain small for the entire range of an RF-power-level sweep.

As shown in Figure 2, the blue circle at the center of the simplifi ed Smith chart represents the set of points for the refl ection coeffi cient for the 20 dB return loss at the tuner reference plane. The red circle near the edge of the chart is the set of all possible DUT refl ection coeffi cients at the DUT reference plane, and generates the set of points that defi ne the blue circle. That means the real DUT impedance resides at one point on the red circle. As can be seen in Figure 2, even though the second circle is quite small, it still represents a wide range of input impedance, because it is close to the edge of the chart.

To determine the exact input impedance of the DUT, additional information is required. Furthermore, Γs in Figure 2 shows the source impedance presented to the DUT, while the “+” mark in the red circle represents the required ΓDUT for the tuner to have an ideal 50 Ω input impedance. The discrepancy between the two points indicates non-ideal matching, which is caused by an invalid direct conversion of the return loss between the tuner and DUT reference planes. This discrepancy usually increases as the losses contributed by elements in the measure-ment path increase. These elements include the source tuner, adapter, cable and probes (and bias tee, if present).

The methodology that overcomes this drawback is to perform mea-surements on three tuner states in order to extract exact DUT input impedance. It can be applied for various power levels, and only three

steps are involved. First, fi nd the source-tuner state close to the low-est return power loss at the small-signal level, and then run a power sweep on the DUT.

Second, run two additional power sweeps on the DUT, but with the source tuner adjusted to produce a unique return loss value for each sweep. To get the best accuracy, the tuner states for these two additional sweeps should generate return-loss values that are slightly greater than that generated by the fi rst sweep, yet well separated from this fi rst value, and each other.

The third and fi nal step is to obtain the return loss for the same RF output power for the three tuner states using the sweep data together with the two-port S-parameters of the source tuner. Once these three steps have been completed, the previously described mathematical and graphical analysis can be performed on the new data.

The true DUT impedance at each power level is determined by the

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Figure 2. Relation between refl ection coeffi cient at tuner reference plane and DUT reference plane for a given tuner state. The blue circle near the center represents all possible values TUNER for RL = 20 dB; the red circle near edge represents all possible DUT values that satisfy the restriction for TUNER. The “x” mark is the value of s for the source impedance presented to the input of the DUT, and the “+” mark in the red circle is the required value of DUT (which can be adjusted by the source tuner) to obtain 50 at the tuner reference plane.

Pout (dBm)

Tuner State 1 Tuner State 2 Tuner State 3

Pin (dBm)

RL (dB)

Pin (dBm)

RL (dB)

Pin (dBm)

RL (dB)

12 dBm -6.2 18.0 -5.7 9.8 -8.0 22.6

16 dBm -2.4 17.0 -2.1 10.0 -4.2 19.8

20 dBm 1.5 15.8 1.6 11.4 -0.1 17.3

22 dBm 4.1 15.5 4.1 13.0 3.0 12.7

24 dBm 10.8 14.4 10.1 10.2 13.5 8.6

Table 1. Power sweep measurement data from input power sweep. Data in this table is extracted from linear interpolation.

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Figure 3. Result at output power level of 12 dBm: the black dot (Z = 12 + j108) represents the DUT input impedance at this power level.

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Figure 4. Result at output power level of 20 dBm: below 20 dBm, the DUT input impedance barely changes.

711RFDF3.indd 28 11/6/2007 3:25:21 PM

RF Design www.rfdesign.com 29

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Figure 5. Result at output power level of 22 dBm: the DUT input mpedance shifts from 12 + j108 to 12 + j98.

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Figure 6. Result at output power level of 24 dBm: the DUT impedance shifts to 15 + j91.

cross point of the three circles in the Smith chart for the DUT refer-ence plane. If these crosspoints are clearly distinguishable, it is an indication that the tuner states that generated the data were suffi ciently well separated.

Measured experimentVerifi cation experiments were performed on a silicon MOSFET having

a small-signal Γ of approximately 0.93 (when load matched for improved power-added effi ciency at high RF power level(s), and a maximum output power of about 24 dBm. The fundamental frequency of the RF signal was 900 MHz. For the experiment, the source impedance presented to the tuner is not an ideal 50 Ω. Return loss data were plotted according to the measured source impedances, so they became off-center circles.

Table 1 shows measurement data for output power from 12 dBm to 24 dBm. Figure 3 to 6 show results for output power levels of 12 dBm, 20 dBm, 22 dBm and 24 dBm. Measured return loss continuously changed with the output power level at all three tuner states. The extracted value for the true DUT impedance shifted with the power level, ranging from 12 + j108 Ω to 15 + j91 Ω.

As a basic accuracy check, the DUT was measured by a vector network analyzer (VNA) to obtain its two-port S parameters at 900 MHz at the small-signal level (-20 dBm in both directions). The two-port output impedance of the DUT was calculated as seen from the load-tuner input port. The impedance calculated from this VNA measurement performed at a low power level agreed with the extracted impedance derived from the three-step methodology. This methodology is also applicable to larger PA devices operating at higher RF power levels. RFD

Author’s noteThe author wishes to thank Harry Randall for taking the load-pull

measurements cited in this article, as well as Mike Carroll for provid-ing testing samples for this work.

References 1. Microwave Engineering, 3rd edition, David M. Pozar, 2005.2. Dean A. Frickey, “Conversions between S, Z, Y, h, ABCD, and

T parameters that are valid for Complex Source and Load Impedance,” IEEE Trans on Microwave Theory and Techniques, vol. 42, No 2, 1994.

ABOUT THE AUTHOR

Zhijian Xie has been a member of the Corporate Modeling and Characterization Group at RFMD for the past three years. Prior to joining RFMD, Zhijian was a member of the technical staff at Agere Systems working on LDMOS for base station applications. He graduated in 2001 with a Ph.D. in electrical engineering at Princeton University.

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