Effects of Matching on RF Power Amplifier Efficiency and Output Power
To date, one of the most important design methods for RF power amplifiers (PA) still consists of matching the large-signal input and load impedances of an active device. These large-signal impedances are supplied by the manufacturer of the active devices or are measured directly by the user. In both cases, the output power level and efficiency are associated with those large-signal impedances. Nevertheless, in practice, the output power, efficiency and even the operation mode depend not only on the large-signal impedances but also on the matching networks used to provide the recommended loads for the transistor. This phenomenon is caused by the high frequency behavior of the matching networks. The usual practice of using a short-circuited l /4 line located at the collector or drain of the transistor to supply DC power causes similar frequency-limiting effects due to the behavior of l /4 lines at harmonics of the fundamental frequency.
Francisco Javier Ortega Gonzalez and Jose Luis Jimenez Martin
EUIT Telecomunicación
Madrid, Spain
Alberto Asensio López
ETSI Telecomunicación (GMR)
Madrid, Spain
The most popular methods for designing RF PAs utilize load-pull techniques in different sophistication levels, techniques based on load-line theory and techniques based on nonlinear simulation. By far, the load-pull design techniques are still the most widely used by most engineers and, hence, are the focus of this article. However, this method’s popularity does not mean the other design techniques are not important.
Load-Pull Methods
The design methods of PAs based on load-pull measurements (matching of large-signal impedances) consist of providing a concrete load impedance at the output of a transistor and simultaneously matching the input
impedance of the device. The transistor’s large-signal impedances are provided by the manufacturer or are measured directly by the user. After the large-signal impedances are determined, it is necessary to employ matching networks to provide these impedances at the input and load of the active device.
In addition, it is important to determine the usefulness of the load and input impedances provided by the manufacturer or in-house measurements. Usually, these impedances are suitable for the operating conditions for which the transistor was designed. The impedances are selected to maximize features such as gain or output power. In most cases, other important features such as collector/drain or added efficiencies are secondary.
Large-signal impedances are typically measured only at the fundamental operating frequency. The data provided by the manufacturer always are measured at the operating frequency. Only sometimes does the manufacturer show the test fixture used to measure the large-signal impedances. This test fixture can provide insight into the high frequency behavior of the loads recommended by the manufacturer.
In most cases, the designer is able to measure the large-signal impedances of a device only at the fundamental frequency. Although an increasing number of papers about multiharmonic load-pull measurements appear in technical literature every day,1,2 these works are still a minority. In the near future, this situation most likely will change because some manufacturers are beginning to offer automatic multiharmonic load-pull measurement systems. Nevertheless, the cost of these systems is still high. In the end, the output impedance of the generator and the load must be transformed into the required large-signal impedances at the input and output of the transistor.
Matching
The problem of determining how to design the matching networks of any amplifier can be complex, particularly if wideband matching is required. Usually, the operating frequency determines the use of matching networks using descrete components (capacitors and coils) or transmission lines. During the 1960s and 1970s, various manufacturers published application notes and tables to design matching networks for RF power amplifiers.3,4 The results obtained for transmission line or descrete matching networks with regard to the focus of this article are exactly the same. Therefore, this work will concentrate on analyzing matching networks with descrete components. The results obtained can be extrapolated to any network with the same behavior in the frequency domain.
In his application note, Davis describes four matching networks consisting of three elements each.3 The three-element matching networks are useful for narrowband matching. For the same application, matching networks different from those described by Davis are necessary to match the large-signal impedances provided by the manufacturer. However, designers have found that the resulting output power and efficiency can be substantially different.
The efficiency and output power of RF PAs are not the only parameters that depend on the matching network used to match the large-signal impedances provided for the device. The mode of operation (C or C-E) also can change. Three of these matching networks, shown in Figure 1 , will be analyzed from this point of view, emphasizing their high frequency behavior.
Most PA devices use loads and have input large-signal impedances lower than 50 W . For this reason, the coil L1 should be attached directly to the collector/drain at the output or the base/gate at the input of the device. In this sense, network A begins with a coil. The first thing the transistor sees is a coil, which causes the high frequency performance of the matching network to be inductive and tending toward an open circuit. (An exception occurs if the coil exhibits self resonances near the operating frequency.) In this way, although the correct load can be achieved at the fundamental frequency, a high reactive impedance tending toward an open circuit is provided for the harmonics of the fundamental frequency.
Network B starts with a capacitor connected to ground. Obviously, the reactance of this capacitor decreases when the frequency increases. This case is the opposite of the one mentioned previously. At high frequencies, this network tends toward a short circuit. The high frequency behavior of this network is completely different from the behavior of network A. Nevertheless, in many cases, this network is able to match the input and load impedances provided for the device. Network B is recommended to match tube amplifiers.3
Network C begins with a coil. It is different from network A in that it has two coils. In this sense, its high frequency behavior is similar to but better than the high frequency of network A and is said to achieve high collector efficiencies.3
Table 1 lists the frequency behavior of the three matching networks that are used to provide a proper load impedance at the output of a transistor. The quality factor Q of the three networks is 3. The load to be matched is ZLOAD = 12.5 + j9.
|
Table I | |||
|
|
Network A |
Network B |
Network C |
L1(mH) |
8.0 |
2.2 |
8.0 |
|
L2(mH) |
-- |
-- |
10.4 |
|
C1(pF) |
2.7 |
28.1 |
6.6 |
|
C2(pF) |
3 |
22 |
-- |
|
Local Impedence ( W ) | |||
|
At 900m MHz |
12.0 + j9.4 |
12.0 + j9.0 |
13.0 + j9.0 |
|
At 1800 MHz |
8.4 + j68.0 |
0.01 – j3.7 |
0.8 + j74.0 |
|
At 2700 MHz |
5.6 +j118.0 |
0 – j2.3 |
0.2 + j12.5 |
As can be seen, all the matching networks are able to provide the required load impedance at 900 MHz. Nevertheless, their high frequency behavior is completely different. Matching networks A and C tend toward high inductive impedances (open circuit) as the frequency increases. Network B tends toward a low capacitive impedance (short circuit). This high frequency behavior will influence not only the device’s output power and efficiency performance, but also the class of operation.
Figures 2, 3 and 4 show nonlinear time-domain simulations where the output waveforms of current and voltage of the same transistor matched with networks A, B and C are displayed. The behavior of the device loaded at the output is the only case addressed in this article.
Table 2 lists the performance obtained with networks A, B and C. It is apparent that the same load impedance at the fundamental frequency yields very different results.
|
Table II | |||
|
|
Network A |
Network B |
Network C |
|
Pout (W) |
8.87 |
4.71 |
8.20 |
|
Pin (W) |
1 |
1 |
1 |
|
Power gain (dB) |
9.4 |
6.7 |
9.1 |
|
Collector Effic. (%) |
77.0 |
20.0 |
88.5 |
|
Added Effic. (%) |
71 |
19 |
80 |
|
Pdc (W) |
11.47 |
24.00 |
9.25 |
In network A, the transistor used in the amplifier to perform this work has its base connected to ground. Many designers may think this configuration is equivalent to working in class C, but class C requires collector current flowing in less than 180° of the signal period as well as short circuits for harmonics of the fundamental frequency. The high frequency trend of network A is exactly the opposite of the required behavior for class C operation. The data show that the collector current and VCE are exactly opposite of what is required for class C operation. Rather, network A forces the transistor to work in a mixed-C mode5 or class C-E.6 The data show a very high efficiency for network A as a result of the mixed-C mode or class C-E amplifier performance.
The high frequency behavior of network B is the opposite of the high frequency behavior of network A. It offers short circuits at the harmonics of the operating frequency. In this way, the amplifier is expected to function in a true class C operating mode. The output waveforms of the amplifier are completely different from regular output waveforms of class C operation. This effect is due mainly to the nonlinear output capacitance of the device (apart from other considerations).5 Nevertheless, it is believed that the inductance of the package (bonding) plays a very important role in this effect, particularly at high frequencies. This effect tends to preclude the C operating mode because the conditions required cannot be achieved. In fact, it is almost impossible to achieve true class C operation with RF power bipolar transistors. The data show that the output power and efficiency for these networks are very low.
The high frequency behavior of network C is similar to but better than the high frequency behavior of network A (at least at the second harmonic). The output waveforms are also similar to the waveforms obtained with network A. The operation mode is also mixed C or C-E. Network C exhibits weak inductive behavior for the third harmonic. However, the resulting collector efficiency is the best of the three configurations. This result enforces the theory that the value of the load at the second harmonic is crucial for efficiency and the load at the third harmonic only refines the main performance.8
From these three examples, it is easy to conclude that the high frequency behavior of the matching networks causes not only important changes in RF PA efficiency and output power, but also that the operation mode depends on these networks. These results have been obtained for one load impedance only. It is useful to determine if these results can be reproduced for any load on the Smith chart. Figures 5, 6, 7 and 8 show load-pull diagrams obtained on the Smith chart that resulted from various loads provided by networks A and C. Not all of the loads could be matched with network B.
Analyzing these data, it is easy to derive constant output power and constant collector efficiency h c load-pull contours. The output power contours obtained with networks A and C are very similar. The constant efficiency contours also are very similar for networks A and C, but some differences in the maximum values exist. The collector efficiency obtained with network C is slightly better.
These results agree with the values obtained for efficiency and output power. Apparently, matching network C yields better collector efficiency as predicted.3 This result also confirms that the mixed-C or C-E mode is similar to class E.6,7 For this kind of amplifier operating in class E, C-E or mixed-C mode (from a frequency point of view), once the harmonic load impedance is set highly inductive the collector efficiency depends mainly on the load at the fundamental frequency.8 On the other hand, most of the so-called C amplifiers are actually E, C-E or mixed-C amplifiers. Many RF amplifiers function in this way, particularly at VHF and UHF. The test circuits of the manufacturers only need to be examined to confirm this fact.
The Short-circuited l /4 Transmission Line
Determining how to feed PAs is another routine problem faced by RF PA designers. l /4 transmission lines are used frequently at high frequencies (for example, 900 MHz). The transmission line is short circuited at one of its extremities. This type of line usually is located at the collector/drain of a transistor. The l /4 lines exhibit infinite impedance at the fundamental frequency and odd harmonics, and a short circuit at the even harmonics. This behavior at high frequencies influences the device’s collector efficiency and output power. Figure 9 shows the analyzed PA with a short-circuited l /4 line attached directly at the collector and at the output of matching network C.
The output waveforms (VCE/VDS and iC /iD ), shown in Figures 10 and 11 , were obtained using a coil to feed the collector of the transistor. The same output waveforms (VCE/VDS and iC/iD) are displayed when the coil is replaced by a l/4 line attached at the collector/drain or output of the matching network. Table 3 lists the performance of the amplifier using a l /4line at the collector to feed the amplifier (location a) or after the matching network (location b).
|
Table III | ||
|
|
Location A |
Location B |
|
Pout (W) |
3.84 |
8.43 |
|
Pin (W) |
1 |
1 |
|
Power gain (dB) |
5.8 |
9.2 |
|
Collector Effic. (%) |
17 |
91 |
|
Added Efficiency (%) |
16 |
87 |
|
Pdc (W) |
22.6 |
9.2 |
It is apparent that the first location of the l /4 line (at the collector) leads to a situation similar to using matching network B. This similarity occurs because the l /4 line provides a short circuit at the second harmonic of the operating frequency. If the l /4 line is located after the matching network (location b), the high frequency behavior of the matching network predominates over the high frequency behavior of the line. As a result, the performance is similar to that obtained with matching networks A and C. A similar situation occurs when the collector coil self resonates at frequencies lower than the third harmonic of the operating frequency.
The Transistor Package
Most PA designers use packaged transistors. Many packaged power transistors have built-in matching
networks to increase the operating bandwidth of the device. The behavior of built-in matching networks is similar to that of any matching network. Therefore, built-in matching networks can determine the operating mode of the final amplifier, limiting output power and, especially, collector efficiency. In this sense, a packaged transistor with a built-in matching network most often functions like an amplifier rather than a transistor. Furthermore, bonding and dynamic and stray capacitances of the device also limit the performance of the design. Figure 12 shows the area in which the entire Smith chart is converted when it is seen at different harmonics through the built-in matching network of a commercial power transistor.
Conclusion
The effects of matching networks on RF PA efficiency and output have been analyzed. The high frequency behavior of the matching networks influences not only the performance of RF amplifiers, but also their operating modes. It was determined from the high frequency behavior of the matching networks that the load at the second harmonic is crucial to improving efficiency. The load at the third and higher harmonics only contributes to refining the potential high efficiency behavior. As a result, the large-signal impedances offered by the manufacturers should be viewed with caution. In order to achieve the specified performance for any device, the design of the amplifier should closely resemble the test circuit recommended by the manufacturer. If this configuration is not possible, the high frequency behavior of the matching networks at least must reproduce as closely as possible the high frequency behavior of the networks used in the manufacturer’s test fixture (at the input and output of the transistor).
The effects associated with short-circuited l /4 lines used for feeding purposes also have been analyzed. The high frequency behavior of these lines modifies the efficiency and output power of PAs, depending on the location selected (attached directly to the collector or after the matching network). Again, the reason is due to the high frequency behavior of the l/4 transmission lines. Similarly, the package of the transistor and built-in matching network (if it exists) influences the operating mode and performance of the amplifier. Manufacturers usually offer little, if any, information about this important topic.
This article has analyzed only the problem at the output of the device. The effects of matching networks at the input of the device will be covered in future work.
Acknowledgment
The authors wish to thank Jose Manuel Ledo for the load-pull simulations described in this article.
References
1. J. Staudinger, "Multiharmonic Load Termination Effects on GaAs MESFET Power Amplifiers," Microwave Journal, April 1996, pp. 60–77.
2. F. Blache, J.M. Nebus, P. Bouysse and J.P. Villote, "A Novel Computerized Multiharmonic Load-pull and Power Measurement System," Proceedings of the Microwave Theory and Techniques Symposium (MTT-S), Orlando, FL, 1995.
3. F. Davis, "Matching Networks Designs with Computer Solutions," Application Note ANA267, Motorola Semiconductors.
4. R. Hejhall, "Systemizing RF Power Amplifier Design," Application Note AN282A, Motorola Semiconductors.
5. H.L. Krauss, C.W. Bostian and F.H. Raab, Solid State Radio Engineering, Wiley, New York, NY .