RF Power Amplifiers

Iulian Rosu, YO3DAC / VA3IUL

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RF Power Amplifiers are used in a wide variety of applications including Wireless Communication, TV transmissions, Radar, and RF heating.

The basic techniques for RF power amplification can use classes as A, B, C, D, E, and F, for frequencies ranging from VLF (Very Low Frequency) through Microwave Frequencies.

RF Output Power can range from a few mW to MW, depend by application.

The introduction of solid-state RF power devices brought the use of lower voltages, higher currents, and relatively low load resistances.

Most important parameters that defines an RF Power Amplifier are:

1. Output Power

2. Gain

3. Linearity

4. Stability

5. DC supply voltage

6. Efficiency

7. Ruggedness

Choosing the bias points of an RF Power Amplifier can determine the level of performance ultimately possible with that PA. By comparing PA bias approaches, can evaluate the trade-offs for: Output Power, Efficiency, Linearity, or other parameters for different applications.

The class of the amplification determines the type of bias applied to an RF power transistor.
The Power Amplifier’s Efficiency is a measure of its ability to convert the DC power of the supply into the signal power delivered to the load.

The definition of the efficiency can be represented in an equation form as:

or Power Added Efficiency:

Power Classes

There are many different classes of amplification available:

Class-A

Is defined, as an amplifier that is biased so that the output current flows at all the time, and the input signal drive level is kept small enough to avoid driving the transistor in cut-off. Another way of stating this is to say that the conduction angle of the transistor is 360°, meaning that the transistor conducts for the full cycle of the input signal. That makes Class-A the most linear of all amplifier types, where linearity means simply how closely the output signal of the amplifier resembles the input signal.

Always have to remember this:

No transistor is perfectly linear, however the output signal of an amplifier is never an exact replica of the input signal.

Linear amplification is required when the signal contains AM – Amplitude Modulation or a combination of both, Amplitude and Phase Modulation (SSB, TV video carriers, QPSK, QAM, OFDM).

Signals such as CW, FM or PM have constant envelopes (amplitudes) and therefore do not require linear amplification.

The DC-power input is constant and the efficiency of an ideal Class-A PA is 50 % at PEP.

P_DC= V_CC x I_CQ and I_CQ~ I_MAX / 2

The amplification process in Class-A is inherently linear, hence increasing the quiescent current or decreasing the input signal level monotonically decreases IMD and harmonic levels.
Since both positive and negative excursions of the drive affect the drain current, it has the highest gain of any PA.
The absence of harmonics in the amplification process, allows Class-A to be used at frequencies close to the maximum capability (fmax) of the transistor. However, the efficiency is low. Class-A PAs are therefore typically used in applications requiring low power, high linearity, high gain, broadband operation, or high-frequency operation.
The efficiency of real Class-A Pas is degraded by the on-state resistance or saturation voltage of the transistor. It is also degraded by the presence of load reactance, which in essence requires the PA to generate more output voltage or current to deliver the same power to the load.
One important thing to mentioned is that: small signal S-parameters can be used in simulations if the large-signal amplifier is operating in Class-A.

Class-B

This is an amplifier in which the conduction angle for the transistor is approximately 180°.

Thus the transistor conducts only half of the time, either on positive or negative half cycle of the input signal.

The same as in Class-A, the DC bias applied to the transistor determines the Class-B operation.
Class-B amplifiers are more efficient than Class-A amplifiers. The instantaneous efficiency of a Class-B PA varies with the output voltage and for an ideal PA reaches π/4 (78.5 %) at PEP. However they are much less linear. Therefore a typical Class-B amplifier will produce quite a bit harmonic distortion that must be filtered from the amplified signal.

Common configuration of Class-B amplifier is push-pull amplifier. In this configuration one transistor conducts during positive half cycles of the input signal and the second transistor conducts during the negative half cycle. In this way the entire input signal is reproduced at the output.

A single transistor may be used in a Class-B configuration. The only requirement in this case is that a resonant circuit must be placed in the output network of the transistor in order to “reproduce” the other half of the input signal.

In practice, the quiescent current is on the order of 10 % of the peak collector current and adjusted to minimize crossover distortion caused by transistor nonlinearities at low outputs.
In theory 6dB or more drive power is needed to achieve Class-B compared with Class-A. In practice this 6dB reduction in power gain is lower; for BJT amplifiers is lower than FETs, approximately 2dB.
The efficiency of the push-pull power amplifier is the same as that of the single ended power amplifier with the same conduction angle, and the output power capability of the push-pull power amplifier is twice that of the single-ended power amplifier (3dB higher).

Class-AB

This amplifier is a compromise between Class-A and Class-B in terms of efficiency and linearity.

· The transistor is biased typically to a quiescent point, which is somewhere in the region between the cutoff point and the Class A bias point, at 10 to 15 percent of I_Cmax.

In this case, the transistor will be ON for more than half a cycle, but less than a full cycle of the input signal.

Conduction angle in Class-AB is between 180° and 360° and Efficiency is between 50 % and 78.5 %
Class-AB has higher efficiency than Class-A at price of linearity.
Class-AB is not a linear amplifier; a signal with an amplitude-modulated envelope will be distorted significantly at this peak power level. The reason is in fact that in Class-AB operation the conduction angle is a function of drive level.

Experimentally was found that Class-AB often offers a wider dynamic range than either Class-A or Class-B operation. This is because gain compression in Class-AB comes from a different, and additional, source than Class-A. Saturation effects are primarily caused by the clipping of the RF voltage on the supply rails.

Linearizing the response of a BJT PA in Class-AB includes the use of specific, and very low, impedance for the base bias supply voltage. This is a very different bias design issue in comparison to the simple current bias used in small signal BJT amplifiers, or the simple high impedance voltage bias used in FET PA’s.

Running the PA in a mid-AB condition the power gain may be 3dB higher than Class-B.
Conventional Class-AB operation incurs odd degree nonlinearities in the process of improving efficiency. Theoretically to increases efficiency all the way up to 78.5 %, the device shall generate only even order nonlinearities. Such a device will not generate undesirable close-to-carrier intermodulation distortion.

Class-C

Is an amplifier where the conduction angle for the transistor is significantly less than 180°.

The transistor is biased such that under steady-state conditions no collector current flows.

The transistor idles at cut-off. Class C Amplifier

Linearity of the Class-C amplifier is the poorest of the classes of amplifiers.
The Efficiency of Class-C can approach 85 %, which is much better than either the Class-B or the Class-A amplifier.

In order to bias a transistor for Class-C operation, it is necessary to reverse bias of base-emitter junction. External biasing is usually not needed, because is possible to force the transistor to provide its own bias, using an RF choke from base to ground.

One of the major problems with utilizing Class-C in solid-state applications is the large negative swing of the input voltage, which coincides with the collector/drain output voltage peaks. This is the worst condition for reverse breakdown in any kind of transistor, and even small amounts of leakage current flowing at this point of the cycle have an important effect on the efficiency. For this reason true Class-C operation is not often use in solid-state at higher RF and Microwave frequencies.

Output waveforms and Efficiency vs Conduction Angle

Class-D

The voltage mode Class D amplifier is defined as a switching circuit that results in the generation of a half-sinusoidal current waveform and a square voltage waveform. Class-D PAs use two or more transistors as switches to generate a square drain-voltage waveform. A series-tuned output filter passes only the fundamental-frequency component to the load,

Class-D amplifier Class-D Voltage and Current waveforms

Class-D amplifiers suffer from a number of problems that make them difficult to realize, especially at high frequencies. First, the availability of suitable devices for the upper switch is limited. Secondly, device parasitics such as drain-source capacitance and lead inductance result in losses in each cycle. If realized, (they are common at low RF and audio frequencies) Class-D amplifiers theoretically can reach 100% efficiency, as there is no period during a cycle where the voltage and current waveforms overlap (current is drawn only through the transistor that is on).

No real amplifier can be a true Class-D, as non-zero switch resistances and capacitive as well as inductive parasitics restrict the shape of the drain voltage waveform.
A unique aspect of Class-D (with infinitely fast switching) is that efficiency is not degraded by the presence of reactance in the load.

Class-E

Class-E employs a single transistor operated as a switch. The collector/drain voltage waveform is the result of the sum of the DC and RF currents charging the drain-shunt capacitance. In optimum class E, the drain voltage drops to zero and has zero slope just as the transistor turns on.

The result is an ideal efficiency of 100 %, elimination of the losses associated with charging the drain capacitance in class D, reduction of switching losses, and good tolerance of component variation.

Class-E amplifier Class-E Voltage and Current waveforms

A Class-E amplifier will exhibit an upper limit on its frequency of operation based on the output capacitance required for the output matching circuit that produces the waveforms described and shown above. Specifically, a Class-E amplifier (see figure II-6) for optimum efficiency requires an upper limit on capacitance Cs.
If a given transistor has an intrinsic capacitance greater than Cp_max, it is not useable at the desired frequency. This Cs requirement implies that for high power at high frequencies, higher current densities are required, as the cross-sectional area of the switch corresponds directly to the device’s intrinsic capacitance.

Class-F

Class-F boosts both efficiency and output by using harmonic resonators in the output network to shape the drain waveforms. The voltage waveform includes one or more odd harmonics and approximates a square wave, while the current includes even harmonics and approximates a half sine wave. Alternately (“inverse class F”), the voltage can approximate a half sine wave and the current a square wave.

Class-F amplifier Class-F Voltage and Current waveforms

The required harmonics can in principle be produced by current source operation of the transistor. However, in practice the transistor is driven into saturation during part of the RF cycle and the harmonics are produced by a self-regulating mechanism similar to that of saturating Class-C. Use of a harmonic voltage requires creating a high impedance (3 to 10 times the load impedance) at the collector/drain, while use of a harmonic current requires a low impedance (1/3 to 1/10 of the load impedance). While Class-F requires a more complex output filter than other PAs, the impedances must be correct at only a few specific frequencies. Lumped-element traps are used at lower frequencies and transmission lines are used at microwave frequencies. Typically, a shorting stub is placed a quarter or half-wavelength away from the collector/drain.
Class-F amplifier designs intentionally squaring the voltage waveform through controlling the harmonic content of the output waveform. This is accomplished by implementing an output matching network which provides a high impedance ‘open circuit’ to the odd harmonics and low impedance ‘shorts’ to even harmonics. This results in a squared off (though for Class-F, truly squared) voltage waveform. The third harmonic only is peaked.
Class-F amplifiers are capable of high efficiency (88.4% for traditionally defined Class-F, or 100% if infinite harmonic tuning is used).
Class-F amplifier design is difficult mainly due to the complex design of the output matching network.

PA Linearity

When two or more signals are input to an amplifier simultaneously, the second, third, and higher-order intermodulation components (IM) are caused by the sum and difference products of each of the fundamental input signals and their associated harmonics.

When two signals at frequencies f1 and f2 are input to any nonlinear amplifier, the following output components will result:

Fundamental: f1, f2

Second order: 2f1, 2f2, f1 + f2, f1 - f2

Third order: 3f1, 3f2, 2f1 ± f2, 2f2 ± f1,

Fourth order: 4f1, 4f2, 2f2 ± 2f1,

Fifth order: 5f1, 5f2, 3f1 ± 2f2, 3f2 ± 2f1,

+ Higher order terms

The odd order intermodulation products (2f1-f2, 2f2-f1, 3f1-2f2, 3f2-2f1, etc) are close to the two fundamental tone frequencies f1 and f2.

The nonlinearity of a Power Amplifier can be measured on the basis of generated spectra than on variations of the fundamental signal. The estimation of the amplitude change (in dB), of the intermodulation components (IM) versus fundamental level change, is equal to the order of nonlinearity.

For example for 1dB increase of fundamental level (f1 and f2), the level of IM2 will go up with 2dB, the level of IM3 will go up with 3dB, and so on.

This is valid only for an amplifier that is not in compression.

As a relation between the degree of the nonlinearity (third, fifth, etc) and the frequency of the side tone (such as IM3, IM5, etc), can be mentioned that the IM5 tones are not affected by third-degree nonlinearities, but IM3 tones are functions of both third- and fifth-degree (and higher) nonlinearities. That means at low signal amplitudes, where the fifth-order distortion products can be neglected, the amplitudes of the IM3 tones are proportional to the third power of the input amplitude.

With a fairly large signal amplitude, fifth-order products (which are dependent on a power of five) will start to affect the IM3 responses. As a result, the 3:1 amplitude estimate will no longer hold,

If the phases of the third- and fifth-degree coefficients are equal, the fifth-degree nonlinearity will expand the IM3 responses. However, if the phases are the opposite, the IM3 distortion will be locally reduced. This explains why notches (sweet-spots) in the IM3 (and high-order) sidebands have been reported at certain amplitudes of output power.

IM(n) products vs Input Power Second- and third-order input and output intercept points

Re-growth of harmonic content vs Conduction Angle

Since the amount of device nonlinearities cannot be changed much, distortion is most effectively minimized by optimizing the impedances seen by the distortion current sources.
In all the Power Amplifiers, the output level is a “compressive” or “saturating” function of the input level. The gain of the Power Amplifier approaches zero for sufficiently high input levels. In RF circuits this effect is quantified by the “1dB compression point”, defined as the input signal level that causes the small-signal gain to drop by 1dB. This can be plotted in a log-log scale vs input level.

Sometimes this Output Power vs Input Power characteristic is referred as AM-AM distortion.

The asymmetry of side-band intermodiulation products (IM) in a two-tone test is often dependent on the carrier spacing, but not in a monotonic fashion. The effect can be explained as an interaction between AM-AM and AM-PM distortion processes. On the other hand, the mere presence of both processes does not guarantee that asymmetry will occur.
If there is a time lag, or phase shift as measured in the envelope time domain, between the AM-AM and AM-PM responses, or their individual frequency components, IM asymmetry will occur.

In the same time, reduction of AM-PM in the PA design would alleviate this problem.

For RF power transistors, a primary cause of AM-PM effects appears to be the dynamic mistuning of the input match. Some deliberate mistuning on the high Q factor input match of RF power transistors might pay off in terms of improved AM-PM performance for the loss of a decibel or two of gain.

Memory Effect

In a two or multi tone IMD test if the amplitude and/or phase of the IM signals is affected by the tone difference, the amplifier exhibits memory effects.
Memory is caused by the storage of energy that has to be charged or discharged.
Memory Effect could be explained as a time lag between AM-PM and AM-PM response of the amplifier. The Electrical Memory Effect is introduced by poor gate/base and drain/collector decoupling at low frequencies causing a distortion of the envelope currents which results in IMD asymmetry.
Low frequencies mean baseband/video frequencies or the frequency spacing between two tones.
The most significant Memory Effect appears in Class AB amplifiers, with reduced conduction angle where drain/collector varies with output power. In Class A amplifiers the Memory Effect reduces.
Smooth memory effects are not usually harmful to the linearity of the PA itself. A phase rotation of 10º to 20º or an amplitude change of less than 0.5 dB, as a function of modulation frequency, has no dramatic effect on the linearity of the device,
There are two memory effects: electrical and thermal.

Electrical memory effects are produced by nonconstant node impedances within frequency bands as DC, Fundamental, and Harmonics. Most of these effects are generated by frequency dependent envelope impedance, and those within the DC band are the most harmful, because bias impedances are strongly frequency dependent.
Thermal memory effects are generated by the junction temperature, which is modulated by the applied signal.
Thermal effects will be much more prominent in a slow sweep, or a stepped CW test.
The analysis and simulation show that the drain envelope impedance is the most important factor for reducing the memory effect and nonlinearity. A new matching topology is proposed for minimizing the drain and gate envelope impedances. The matching topology consists of a series LC circuit for shorting the device at a low frequency while maintaining a matchable impedance at the operating frequency. The circuits are connected to the gate and drain terminals, rather than to the bias lines, since the circuit can produce a very low impedance, not limited by the quarter-wavelength bias line. The amplifier, with the reduced envelope impedances, provides drastically reduced memory effects and very linear amplification performance for wideband signals.
Simultaneous amplitude and delayed phase modulation does generate asymmetric sidebands.

Input Matching

The input matching configuration, including the bias circuit, has an important impact on the operation of an RF Power Amplifier.

The input match will show different optima for maximum gain, best linearity, and highest efficiency. Optimization of the efficiency may involve substantial reduction in power gain.
Correct handling of harmonics is a necessary feature on the input, as well as the output, match. Device used well below its cutoff frequency may require specific harmonic terminating circuit elements on the input.

Output Matching and Load Line

The performance of the output matching circuit is critical for a Power Amplifier.

In a PA, impedances control how much power is delivered to the output and how much gain and noise are produced in the process, therefore matching network is critical for maximum performance.

One aspect that's sometimes overlooked is the power dissipation in the output matching circuit.

This power is lost in the capacitors, inductors, and other lossy elements that are part of the matching network. This "dissipation loss" degrades the PA's efficiency and output power capability.

Different implementations of the output match result in different losses and there are still significant design tradeoffs to be made between bandwidth and dissipation loss. For a PA, the loss of the output match is always a concern because of the large power levels involved.
A capacitor's quality factor is reversal proportional to its capacitance. To minimize the dissipation loss of the output match, it's therefore necessary to design the output match with the lowest possible value of C₁. The tradeoff is between bandwidth and dissipation loss.
Different capacitor technologies give different losses when used in output matching circuits.
One way of understanding the loss mechanisms of an output match and to don’t mix up mismatch loss and dissipation loss, is to simulate the match with loss-less components, then introduce loss into one component at a time.

Mismatch Loss _[dB] = 10*LOG (1-G²)

where reflection coefficient G = (VSWR-1) / (VSWR+1)

Because the dissipation loss doesn't depend on the source impedance it's possible to use S21 to find the correct dissipation loss in a circuit simulation. The procedure involves using the complex conjugate of the simulated load line as the source impedance.
Running at a low efficiency not only reduces talk time in a portable device, but it also creates significant problems with heating and reliability.
The load line is set based on the needed Power Amplifier output power and available supply voltage. For example low voltage PA’s (~3.5V for mobile devices) have a load line ranging from 1 to 5 Ω.

R_L = V_max / I_max

Matching for maximum Gain occurs when the amplifier is unconditional stable and load impedance is equal to the complex conjugate of the same source impedance (conjugate matching). Complex conjugate simply refers to complex impedance having the same real part with an opposite reactance.

for example: if the source impedance is Zs=R+jX, then its complex conjugate would be Zs*=R-jX

Matching for maximum Output Power occurs when Optimum Load impedance (R_L) is equal to Source impedance (R_gen).

Smith Chart representation for maximum gain and power matching Load Line for different classes

Optimum Load Resistance

In the absence of collector output resistance information on the datasheet, it becomes necessary to make a simple calculation to determine the optimum load resistance for the transistor.

The value of load resistance is dependent upon power level required and is given by:

where,

V_CC = the supply voltage

V_SAT= the saturation voltage of the transistor

P = the output power level required in Watts

Note that this equation provides only the load resistance, when usually in the datasheets the manufacturer provides values of shunt output capacitance vs frequency for the RF power transistor.

Ways to Test a Power Amplifier Stability

Rollet K factor: K>1.0 is unconditionally stable, 0<K<1.0 is conditionally stable, and K<0 is unstable.
S11 or S22 greater than 1.0 (or positive if expressed in dB’s) is unstable.
Stability circles show unstable impedance regions.
Be sure to test Stability over a wide range of frequencies.

Power Amplifier Linearity Metrics

Scaled Linearity = OIP3 – P1dB
Linear Efficiency = 10*LOG (OIP3/P_DC)
ACPR = (Main Channel Average Power) / (Adjacent Channel Average Power)

RF Power Amplifiers for Wideband Modulations

RF Power Amplifiers for wideband modulations as CDMA or WCDMA, which operate in the linear region, are not very efficient. Only a portion of the D.C. current is used to generate the RF power; a much larger portion turns into heat.

LDMOS and GaN (Gallium Nitride) devices are best suited for the output and driver stages because of higher gain, improved linearity, and very low on-resistance. High gain reduces the number of stages needed in the amplifier to attain the same output power, compared to the old generation systems built with bipolar transistors.

In a multi-stage linear power amplifier there are various factors that need to be considered for choosing the right transistor for each of the stages of the amplifier.

The pre-driver is biased Class A for attaining consistent performance for minimal effect on the linearity of the device due to minor changes in bias supply. Drain efficiency is not as much of a concern for the pre-driver as it is for the latter stages in the amplifier. The driver and the output stage for such a system are typically biased Class AB, for achieving best tradeoff between linearity and efficiency of the amplifier.
The most common method used to determine the linearity of a transistor is to characterize the Intermodulation Distortion (IMD) measured with two tones spaced. Typically, a tone spacing up to 20 MHz should be used while tuning amplifiers for wide-band modulation applications.
When transistors are used significantly backed-off from their peak power levels, it is all the more necessary that the IMD characteristics of the transistor at lower output power levels be taken into account. The profile of an IMD vs. Pout (drive-up) curve for a good transistor should have a large positive slope, even while attaining similar peak power capability, to get maximum Adjacent Channel Power Ratio (ACPR).
The transistor used in the driver stage has similar linearity requirements as the output stage. In terms of ACPR, it needs be operated at an output power that gives a margin of at least 4 dB from the maximum allowed value for the output stage. In addition, it needs to have an input bandwidth about 2 to 2.5 times greater than the bandwidth of the modulating signal in order to maintain constant group delay and flat gain.
One of the major factors determining the performance of the high power transistor in the wide modulation environment is the gain flatness. The transistor needs to have a flat gain across the band for its use in multiple channel amplifiers. Very flat gain response greatly simplifies the design of linearization schemes systems.
Fast roll-off of gain at the edges of the band causes deterioration in the ACPR performance.
To attain the intrinsic device linearity, the 3 dB bandwidth of bias networks needs to be at least two times greater than the modulation bandwidth.

For attaining best ACPR response, it is necessary to have an excellent decoupling network at the Drain of the transistor, down to very low modulation frequencies. This can be achieved by using a high quality shunt capacitor. This technique helps in achieving maximal gain flatness, which is very critical for wideband applications.
It is advisable to avoid ferrite components in the biasing network and to use a series resistor on the Gate bias network to prevent instability. To achieve flat gain response across the band, the traditional inductive feed should be avoided on both the Gate and Drain. Instead, a quarter wave line at the frequency of interest, properly decoupled with a chip-capacitor, has been shown to provide very flat gain across the entire bandwidth.

References:

RF Circuit Design – C. Bowick
RF Power Amplifiers for Wireless Communications – S. Cripps
Advanced Techniques in RF Power Amplifier Design – S. Cripps
Distortion in RF Power Amplifiers – J. Vuolevi
Circuit Design for RF Transceivers – D. Leenaerts, J. Tang, C. Vaucher
Radio Frequency Transistors - N. Dye, H. Granberg
High Frequency Current Mode Class-D Amplifiers With High Output Power and Efficiency - A. L. Long
Microwave Journal Magazine; 1996 – 2005
Portable Design Magazine; 2002 - 2005
High Frequency Electronics Magazine; 2002 - 2007

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