Power Amplifier Classes Based upon Harmonic Approximation and Lumpedelement Loading Networks
Ramon A. Beltran
Skyworks Solutions, Inc. Newbury Park, CA 91320; ramon.beltran@skyworksinc.com
Power amplifiers (PAs) are, in general, classified by their operating bias point and output network [1].
Different classes yield different characteristics of the amplified signal and device efficiency. In theory, class-AB, B,
C, E and F PA performance can be analyzed assuming an infinite number of controlled harmonics and their
respective ideal impedance termination to those harmonics.
At high frequencies, the device parasitic elements impose significant limitation for true-transient PA
operation. Therefore, harmonic approximation may be used which means using a finite number of controlled
harmonics [2]. In this paper an overview of PA classes employing a finite number of controlled harmonics is
discussed. It can be noticed that when the PA design is based upon a limited number of harmonics the peak
efficiency is substantially limited since it depends on the number of controlled harmonics whereas the impedance
presented to those harmonics define the PA output power capability and waveform shapes [2]. On the other hand,
controlling a finite number of harmonics typically requires less physical layout space for the output network
implementation making an interesting approach for efficiency enhancement. In this summary, impedances for
different PA classes are then discussed using the waveform factors as described in [3] for a supply voltage VDD=21
V, assuming a device effective drain voltage of Veff =0.956VDD= 20 V (RON=0.43 Ω.) and a target output power of
10-W, as a design example. Also, the simple lumped-element output networks are proposed.
The linear class-A amplifier does not require harmonic impedance since no harmonic content is generated,
so that the device drain (or collector) impedance is simply: RL=(γVVeff)2/2Pout= 20.15-Ω, where γV=1 [3]. Since
IOUT=IDC=1-A the DC power PDC=VDDIDC=21W and the efficiency is then 47.61%. A practical PA schematic with a
simple low pass matching network is shown in Fig. 1. Notice that higher values of RON yields lower efficiencies.
A case in between class-A and B is class-AB which some harmonic current at device drain is allowed and
we can use the same class-A PA impedance. A 2nd-harmonic short is optional depending on the clipping level of the
current waveform. The drain impedances are the same as class-A but the efficiency should be higher depending
upon the ICQ, which is lower than a class-A PA.
The class-B PA requires harmonic current at the device drain. Controlling only the 2nd harmonic the
impedance at the intrinsic drain is calculated so that; RL=(γVVeff)2/2Pout= 20.15-Ω which is the same as that of a
class-A PA at the fundamental-frequency since is γV=1 [3]. A short circuit at 2nd harmonic is required and it is
provided by a shunt connected series resonator, Fig. 2. The DC input current is then; IDC=IOUT/γI = 0.707 A and
PDC=14.85 W which yields 67.3 percent efficiency.
The class-C PA also requires harmonic current and it can be regarded as a reduced conduction angle classB PA with large harmonic content yielding higher efficiency [2], so that the drain impedance is the same as that for
class-B at the fundamental-frequency and 2nd harmonic. The same schematic can be used for implementation, Fig. 2.
The true-transient class-E amplifier is 100 percent efficient (ideally) and it can be approximated as depicted
in Fig 3 which is convenient at an IC level. However, when the device parasitic drain-to-source capacitance exceeds
the optimum class-E shunt capacitance, harmonic approximation can be used. When controlling only the 2nd
harmonic, the class-E PA waveform coefficients are [3] γV= γI=1.414 and δV=δI=2.912. The impedances, output
power and efficiency are found in a different fashion compared to other PA classes. Starting by computing the
fundamental-frequency component of the drain voltage that is V1m= γVVeff = 28.28 V. The output voltage is then
related to the waveform factors and load power factor by Vom=V1m/ρ=20 V, where ρ=1.414, [3]. Since this analysis
can be based upon iDmax =2.06 A, which is slightly higher than for other PA classes but still ensuring safe operation
mode for the transistor, the DC current is then related to the waveform coefficients by IDC=iDmax/δI=0.7074 A, and
the fundamental-frequency component of the drain-current waveform is therefore: I1m=Iom= γVIDC = 1 A. The output
power is P0= (V0mI0m)/2= 10 W, as expected, and the DC input power PDC=VDDIDC= 14.85 W, hence, the efficiency is
67.3 percent. For the 2nd harmonic approximation both the drain-voltage and drain-current waveforms are composed
of fundamental-frequency and 2nd harmonic components. Their shapes are ideally identical, but the phases are
shifted so that the second harmonics differ in phase by 90° and therefore consume no power. This causes the
fundamental-frequency component to differ in phase by 45°, therefore the impedance at device drain is Z1 =R1+jR1.
The magnitude of the fundamental-frequency impedance is │Z1│= V1m/I1m=29.6 Ω. Since ρ=│Z1│/R1 =1.414 [3],
the impedance at the device drain for fundamental and 2nd harmonic is ZVD  Z1  20.6  j 20.6 Ω
and
X 2   j 29.12 Ω, respectively. Measured data for this PA class is presented in [4].
For the class-F amplifier at least two harmonics need to be controlled for voltage and current waveforms.
The 2nd and 3rd harmonic control is typical for the class-F2,3 amplifier. The impedance at fundamental-frequency for
a class-F2,3 PA is then computed based on [3], RL=(γVVeff)2/2Pout= 26.66-Ω where γV =1.1547. Notice that there is
higher load impedance for the same output power compared to other PA classes. The 2 nd and 3rd harmonic
impedances are a short and open circuit, respectively. The IDC can be computed using IDC=γVVDD/γIRL=0.643 A and
PDC=13.5 percent which yields 74 percent efficiency. The schematic for the class-F2,3 PA is illustrated in Fig. 5.
Measured data for this class of operation can be found in [5] for a 20-W GaN FET.
The impedances for different PA classes are depicted on the Smith chart for illustration (Fig. 6). The
transition between different PA classes can be realized. Notice the limitation of peak drain efficiency due to the onresistance; also notice the efficiency calculations are the theoretical highest values for a given controlled harmonic.
In a practical circuit, the output network can introduce significant insertion loss decreasing the overall PA
efficiency. For instance, in a handset amplifier the output network insertion loss could be as high as 0.7 dB and this
represents around 10 percent efficiency reduction for a given output power. When transmission-lines are used, the
insertion loss is low and the drain efficiency is almost maintained as predicted when proper impedances are
presented to the intrinsic device drain.
Fig 1. Class-A or AB PA.
Fig 2. Class-AB2. B2 or C2 PA.
Fig 4. Class-E2 PA.
Fig 3. Class-E PA approximation.
Fig 5. Class-F2,3 PA.
Fig. 6. Impedances for different PA classes.
References:
[1] H. Krauss, C. Bostian and F. H. Raab, “Solid-State Radio Engineering”. John Wiley & Sons, 1980.
[2] F. H. Raab, “Class-E -C and F power amplifiers based upon a finite number of harmonics”, IEEE Trans. Microwave Theory
Tech., vol. 49, no. 8, pp. 1462 - 1468, Aug. 2001.
[3] F. H. Raab, "Maximum efficiency and output of class-F power amplifiers," IEEE Trans. Microwave Theory Tech., vol. 49,
no. 6, pp. 1162 - 1166, June 2001.
[4] R. Beltran and F.H. Raab, “Lumped-element Output Networks for High-efficiency Power Amplifiers,” MTT Int. Microwave
Symposium Anaheim, CA, May 23-28, 2010.
[5] R. Beltran, “Class-F and Inverse Class-F Power Amplifier Loading Networks Design Based Upon Transmission Zeros,”
MTT Int. Microwave Symposium Tampa, FL, June 2-6, 2014.