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A measurement method for scattering parameters (Sparameters) of high power transistors is presented. The proposed method directly determines the Sparameters of high power transistors by measuring overall gain, phase and Sparameters of input and output matching network when the transistor is operating normally. Using this method, the Sparameters of a smallsignal amplifier transistor, Motorola MRF581, and a commercial high power transistor, Motorola MRF6402, are obtained.
Seok Kyun Park, Ik Soo Chang,
Yun Seo Choi, Jun Won Huh
and Young Kim
Sogang University
Seoul, South Korea
To get the optimum performance of a high power transistor, it is essential to obtain the characteristic of the device, such as its Sparameters. In the case of designing a smallsignal amplifier, Sparameters are useful and sufficient; however, for a largesignal amplifier, they are no longer useful. This is because the method of measuring the Sparameters of a high power transistor presents a problem.^{1} Generally, S_{11} and S_{21} are measured by the reflection coefficient at the input port and the transmission coefficient at the output port when the input signal is injected at the input port. They are correct values because the transistor is operating normally. S_{22} and S_{12} are measured by the reflection coefficient at the output port and the transmission coefficient at the input port when the input signal is injected at the output port. In this case, they are incorrect values because the transistor is not operating normally.^{2,3}
The measurement method of Sparameters of a high power transistor under normal conditions is based on the port reduction technique. This method determines the Sparameters of high power transistors by measuring the overall gain and phase of the measurement system and the Sparameters of the input and output matching networks four times, while the transistor is operating normally unlike the existing method which measures S_{12} and S_{22} when the transistor is operating abnormally.
THE THEORY OF THE SPARAMETERS MEASUREMENT METHOD
The principle of measuring Sparameters under normal conditions using the port reduction technique can be derived as follows. Consider the block diagram of Figure 1.

[S_{T} ] is the Sparameter matrix of the device under test (DUT), and [S_{i} ] and [S_{o} ] are the Sparameter matrices of the input and output matching network, respectively. The Sparameter matrix of the fourport network (dashed line) is given by
If this 4 x 4 matrix is partitioned into 2 x 2 matrices then
B_{1 } = S_{11} A_{1 } + S_{12} A_{2}
B_{2 } = S_{21} A_{1 } + S_{22} A_{2} (2)
where
The Sparameter matrix of the transistor is represented by
That is
A_{2 } = S_{T} B_{2} (5)
Using Equations 5 and 2, B_{2} is given by
B_{2 } = S_{T} ^{1} A_{2 } = S_{21} A_{1 } + S_{22} A_{2} (6)
From which A_{2} can be obtained as
A_{2 } = (S_{T} ^{1 } S_{22} )^{1} S_{21} A_{1} (7)
Substituting Equation 7 in Equation 2 gives
B_{1 } = S_{11} A_{1 } + S_{12} (S_{T} ^{1} S_{22} )^{1} S_{21} A_{1} (8)
Therefore, the overall Sparameter between port 1 and port 2, S_{all} is given by
S_{all } = B_{1} A_{1} ^{1 } = S_{11 } + S_{12} (S_{T} ^{1} S_{11} )^{1} S_{21} (9)
The matrix of S_{all} can be written as
and
where
= S_{11t} S_{22t} S_{12t} S_{21t}
and from Equations 11 and 3
where
Combining Equations 12 and 3 gives
And from Equation 9
Equating S_{21} in Equation 14 gives
which can be rewritten as
S_{21all } = S_{21all} S_{22i} S_{11t }
+ S_{21i} S_{21o} S_{21t } + S_{21all} S_{11o} S_{21t } S_{21all} S_{22i} S_{11o} (16)
where
= S_{11t} S_{22t} S_{12t} S_{21t}
Therefore, if four different values of the overall S_{21all} are known as well as the Sparameters of the matching networks for the same S_{21all} , a new matrix can be constructed whose elements are S_{11t} , S_{21t} , S_{22t} and as shown in Equation 17.
and from Equation 17
Equation 18 can be solved without difficulty using the Sparameters of the matching networks (S_{21i} , S_{22i} , S_{11o} , S_{21o} ) and the overall network including the matching networks (S_{21all} ). finally, the Sparameters of the DUT, that is, S_{11t} , S_{21t} , S_{12t} and S_{22t} , can be obtained.
MEASUREMENT METHOD
Figure 2 shows a block diagram of the measurement system used for a largesignal device (MRF6402).

A preamplifier stage is needed to drive the main amplifier. The output power of the driving amplifier was 27 dBm. However, the output power of the DUT is too high to measure the Sparameters directly with a network analyzer; therefore, a directional coupler (30 dB) is used at output port. In the case of a smallsignal amplifier (MRF581), the Sparameters can be measured directly with the network analyzer.
A circulator was used to prevent the driving amplifier from being affected by the reflected signal from the DUT while being tuned.
The tuner was composed of a 3 dB directional coupler and variable sliding shorts. It is possible to realize every point on the Smith chart with this tuner.
The measurement proceeds as follows. The S_{21all} of the overall network that includes only the input and output matching networks can be obtained by compensating the Sparameters of the drive amplifier and output coupler. Then the Sparameters S_{21i} , S_{22i} , S_{11o} and S_{21o} of the matching networks must be measured. This procedure is repeated four times for four different S_{21all} . With this data, the required Sparameters of DUT can be obtained by solving the matrix Equation 18.
EXPERIMENTAL RESULTS
In order to illustrate the capability of this method, experimental results are presented which are obtained from the 1.0 GHzcentered smallsignal amplifier (MRF581) biased in class A and the 1.855 GHzcentered largesignal amplifier (MRF6402) biased in class AB (MRF6402, typical output power = 4.5 W, V_{CE } = 26 V, V_{BE } = 0.78 V, I_{CQ } = 40 mA).
Table 1 shows the Sparameters of MRF581 obtained from solving Equation 18 and measured with a network analyzer. Table 2 shows the Sparameters of the MRF 6402 device obtained by solving Equation 18.

To verify the validity of the Sparameters, the gain characteristic of the amplifier is obtained by matching the device using tuners and compared with that of the amplifier matched using the Sparameters from Table 2.
Figure 3 shows the gain characteristic of the amplifier matched with tuners. Figure 4 shows the gain characteristics of the amplifier matched using the measured Sparameters.

As can be seen, there was only 0.8 dB difference between the two data. When designing the amplifier, the design technique used the constant gain circle of the smallsignal amplifier. As the constant gain contour of the high power transistor is not a circle, the difference between the two approaches is an allowable error.^{4}
CONCLUSION
A novel method for the measurement of the scattering parameters of largesignal transistors has been proposed. Usually, S_{12} and S_{22} parameters are respectively obtained with a network analyzer by measuring the reflection coefficient at the collector port and the transmission coefficient at the base port when the input signal is injected into the collector port. This method does not satisfy the transistor's normal operating condition. Therefore, S_{12} and S_{22} are not the correct values. However, the method proposed in this article uses only the measured data while the transistor is operating normally. Using this method, the Sparameters of a MRF581 and MRF6402 are obtained, and the validity of this method is verified in each case by comparing the Sparameters measured with the network analyzer with those obtained from the proposed method, and by comparing the gain characteristics of amplifiers using tuners and using the obtained Sparameters. *
References
1. Guillermo Gonzalez, Microwave Transistor Amplifiers Analysis and Design, Prentice Hall, New Jersey, 1997, pp. 212283.
2. S.R. Mazumder, "Twosignal Method of Measuring the Largesignal Sparameters of Transistors," IEEE Transactions on Microwave Theory and Techniques, Vol. 26, June 1978, pp. 417420.
3. Van Valkenburg, Reference Data for Engineers: Radio, Electronics, Computer & Communications, SAMS Publishing, Eighth Edition, 1995, pp. 1217.
4. Guillermo Gonzalez, Microwave Transistor Amplifiers Analysis and Design, Prentice Hall, New Jersey, 1997, pp. 352356.
Seok Kyun Park received his BSEE and MSEE degrees from Sogang University, Seoul, South Korea, in 1998 and 2000, respectively. He has worked for Samsung Electronics Co. Ltd. since 2000. His areas of interest are microwave integrated circuits, microwave communication systems and mobile phones. He can be reached at humblesk@samsung.co.kr. Ik Soo Chang received his PhD degree from Seoul National University, Seoul, South Korea, in 1982. He is now a professor at Sogang University. He has more than 20 years of experience in RF and microwave circuits design. He is a member of IEEE. He can be reached at ischang@ccs.sogang.ac.kr. Yun Seo Choi received his BSEE from Sogang University, Seoul, South Korea, and is currently working toward his master's degree. His research includes PA design and linearizer system design. He can be reached at yuier@hanmail.net. Jun Won Huh received his MSEE degree from Sogang University, Seoul, South Korea, in 1996. From 1996 to 1999, he was a PA design engineer at KMW, South Korea. He is now a PhD student at Sogang University. His research interests include PA design and linearizer system design. He can be reached at hjwioio@hanmail.net. Young Kim received his MSEE from Sogang University, Seoul, South Korea, and is currently working toward his PhD degree. He developed Cellular and PCS linear power amplifiers at Samsung Electronics Co. Ltd. His areas of interest are the design of high power amplifiers and linearization techniques, and RF and microwave circuit analysis and design. He can be reached at youngk@unitel.co.kr. 
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