Parent Category: 2017 HFE

*By Boris Aleiner*

**Introduction**

RF Power Amplifier design is a complicated task, which very often involves a team of engineers working on its different aspects (system design, circuit implementation and testing, mechanical design, control circuitry – to name a few). In order to synchronize their efforts, all team members have to have a clear understanding of the common goals and methods of their solution.

These notes describe basic amplifier requirements, mention approaches for meeting them, and briefly discuss a design flow. To keep them useful for all team members (regardless of their specialty or experience), formulas were avoided in the text and just a few of them are given in the appendix. For the same reason references were deliberately omitted: those who are interested in them can Google the subject or request them from the author.

**Power Amplifier Requirements**

The RF Power Amplifier (PA) is the last component of a transmitter chain. The purpose of a transmitter is to deliver an RF signal with required properties and specified power level to the antenna; and the need for the PA is in amplification of that signal to the level expected at antenna port.

That is, in order to do the job, the PA has to meet the following requirements:

It has to have sufficient Gain – to amplify RF signal to the level expected at Antenna Port. It is expressed as the difference between input and output RF powers.

It has to have sufficient Power Handling Capability – to be able to sustain a RF power level expected by the Antenna Port. Sometimes it is expressed as “dissipated power”, however for high power RF transistors it is often given as “Saturated Power” level.

It has to be distortion-free – in order for a system’s receiver to be able to recognize radiated signal. It is expressed as a degree of linearity.

It has to be stable – to avoid a creation of oscillations over anticipated variations of external conditions (that is, changes in temperature, load, frequency, DC and RF powers)

In addition, it is preferable that PA requirements are to be met efficiently. It is needed to avoid wasting of DC power, and/or to preserve the battery drainage. The problem with efficient amplifiers though, is that they do introduce additional distortions which increase with increasing efficiency. In order to deal with this issue, a number of linearization techniques have been developed. Amplifiers are divided into different classes (Class A to C for controlled current source and Class D and above for switched mode amplifiers) and linearization, specific for a given class, is applied.

All these requirements have to be met over the frequency band of operation (which might be 3-to-5 times wider than the occupied bandwidths if linearization techniques are to be used).

A detailed description of requirements is given below.

**1. Gain**

For a Power Amplifier, gain is defined as the difference between the power of the RF signal applied to PA input and the one delivered to the antenna port. While this property is the most important for the PA (it is the purpose of Power Amplifiers to create Gain), its actual value is of a lesser importance. Really, the gain of a last stage could be easily increased by adding extra preamplifiers preceding the final stage of a Power Amplifier. That is, the value of the Gain could be reduced for the sake of achieving other parameters (better match, linearity or efficiency). Very often two Gain values are included on PA spec sheets – they are a small signal gain (that is, gain at the significantly reduced level of an input signal; expressed as S21) and a large signal gain (gain at 1 dB compression point).

**2. Output Power**

Power Handling Capability is defined as the maximum power that an amplifier can handle without damage. Its value depends on the size and configuration of a transistor’s die and the proper application of cooling. This parameter should be large enough to sustain an RF power level expected by the Antenna Port. Sometimes it is expressed as “dissipated power” (which is the product of a current flowing through collector/drain and the voltage across the device); however, for high power transistors it is usually given as “output power at 1 dB Compression Point” or “Saturated Power.”

**3. Linearity**

Linearity is the measure of an amplifier’s distortions. Distortions are happening when RF signals with variable envelopes are applied to a nonlinear amplifier; they have to be low enough for the system’s receiver to recognize what the transmitter is sending. Mathematically, the distortions are realized as an interaction between additional spectral components created by the amplifier’s nonlinear transfer function (I-V DC curves).

For CW signals their measure is Compression Point or Intercept Point; for digitally modulated signals the figures of merit are Adjacent Channel Power (ACP – the measure of out-of-band interference) and Error Vector Magnitude (EVM – the measure of in-channel distortions). Distortions can be compensated by the application of products with the same amplitude and the opposite polarity to undesirable ones – the process which is called “linearization.”

There are two basic approaches to linearization – one of them is called Feedback, where the corrections for creating a distortion-free operation are done at the amplifier’s input (predistorters are operating on this principle), and the other is Feed-Forward, where the corrections are applied to the output of the amplifier. The first approach is cheaper, however it cannot compensate for distortions from heavily compressed amplifiers (above 1 dB compression point).

Generic math formulas are given in the appendix.

**4. Efficiency**

Efficiency is a measure of DC energy loss when it is transferred to RF power. In hand-held units, an inefficient PA is draining the battery and producing excessive heat; in high-power stationary units it requires complicated cooling systems and increases the cost of operation.

However having ideal sinusoidal RF signal at an amplifier’s output (like in Class A amplifiers) makes the PA lose 50% of its DC power by repeating redundant (positive and negative) information about amplitudes of Voltage and Current; mathematically it is shown by calculating Average Powers, expressed as integrals of instantaneous powers for DC (which is constant) and RF (which is proportional to sin2[t]).

In order to increase efficiency, the redundancy of Voltage/Current amplitudes has to be eliminated, which is done with the introduction of a Class B amplifier. In this class a conduction angle is reduced by a biasing amplifier to the origin of its transfer function, which makes the PA transfer only half (positive OR negative) of input RF sinusoids. However, due to the nonlinearities of transfer function (especially pronounced at its origin) – maximum efficiency for this method would not exceed 78%.

A better method to increase efficiency is to use a switch modulated by input RF signal. The DC supply of that switch, expressed as Idc*Vdc, is providing a required value for RF output power (when the switch is opened – all DC power is applied to the output load, when it is closed – none is coming to that load; so all DC is applied to the load at intervals directed by input RF data stream). Theoretically this method provides 100% efficiency; the Gain in this model of operation is defined as before (the difference between input and output RF powers); it works because output DC power is higher than input RF one.

The obvious issue with this method, however, is that all variations of an input amplitude are lost – so for variable envelopes, one needs to use alternative means of their recovery. Examples of these means are LINC (“Linear amplification with Nonlinear Components” – a method based on idea that any amplitude-modulated signal can be expressed as a sum of two different constant-envelope but phase-modulated signals) and EER (”Envelope Elimination and Restoration” – a method which detects an amplitude of an RF signal, amplifies a phase portion of the RF input signal, and modulates the resulting signal by detected amplitude variation).

In order to keep an amplifier’s high efficiency over the range of output powers (vs. achieving it only at the highest level) a technique called Load Modulation is used. For switched amplifiers included in LINC system it is achieved by combining signals from each branch on non-isolated power combiners; however this technique is applied to non-switched amplifiers, too. It is called a Doherty amplifier (the idea of which is to combine very efficient and very linear amplifier on one modulated load), and it allows a reasonable compromise between linearity and efficiency.

**5. Stability**

The RF Power Amplifier has to be stable (that is, oscillation free) over its operational range (over variations in temperature, frequencies, and power levels). Oscillations are caused by a positive feedback from the amplifier’s output; one has to be careful to avoid them or to dump them with additional circuitry.

For small signal operations, stable conditions are found from so-called “Stability Factor,” which is a formula derived from S-parameters (parameters describing transfer characteristics of a linear circuit). However, for large signal operations (that is, the most important area of Power Amplifier’s operation) stability has to be determined from Load Pull measurements.

**Design Flow**

The typical design of an RF Power Amplifier for a Base Station starts from the requirements supplied by the customer. Based on power and frequency requirements, the output transistors (as a rule – it is a pair of transistors) are to be chosen. Then, based on a budget and requirements, the amplifier’s configuration and class are determined. Input and output matching circuits are designed from load-pull contours, either measured or provided with the transistor’s data sheets. Initial (small signal) simulation of matching circuitry is done based on ideal components and CW input signal. Initial verification of small signal simulations is done on demo boards, provided by the transistors’ manufacturers.

Customer requirements should also include a form factor for the amplifier which is a starting point for a mechanical team working on a design of enclosure. From this design an allocated room for a final stage of Power Amplifier is found. Knowing that, a preliminary layout is created and simulated using a large signal simulation with the input waveform supplied by the customer. The first round of simulations is done with still ideal components; at the next round – all known parasitics are to be included. The goal of this simulation is to come up with a PCB layout. When satisfactory results are achieved, EM simulation is conducted in order to include an influence of the enclosure (metal walls and cover) on the layout.

The control circuitry team applies their firmware and hardware to the amplifier’s prototype assembled on demo boards. They are to build their final version to the form factor given to them by the mechanical team.

Finally, the prototype of the amplifier is assembled into the required enclosure, fine-tuned and then tested using a customer-supplied waveform.

**Conclusion**

These notes were intended to help a team of engineers who work on an RF Power Amplifier design understand common goals in order to be more efficient as a team. The basic amplifier requirements were given, their meanings explained, and roles of team members in the design progress was described.

For additional comments or references one can contact the author.

**Appendix**

Distortions are happening when amplitude-varying signals are applied to nonlinear devices.

In the frequency domain the simplest representation of an amplitude-varying signal is given by 2 CW tone with the same amplitude and different frequencies, the situation mathematically expressed as

e_{in} = A{cos(α) + cos(β)}(1)

where

e_{in} - is a signal applied to the input of nonlinear device

A - is an amplitude of each of the tones

*α* and β - are frequency components of each of the tomes

At the same time any nonlinear system can be described as

e_{out }= k_{1}e_{in}+ k_{2}e_{in}2+ k_{2}e_{in}^{3}+…(2)

where

e_{out} - is a signal from the output of nonlinear device

k_{i} - are coefficients representing an order of nonlinearity (they can be frequency and level dependent)

That is, k_{3} is a 3rd order coefficient; k_{5} is a 5th order one, etc.

Substituting formula (1) into (2) and performing transactions with trigonometric identities shows that higher orders of (2) create frequency components in addition to initial two tones. Components appearing due to even orders are high-frequency ones (2nd harmonic and above) – so they can be easily filtered out. It is components from odd orders that create a problem, since they are happening to be within the operational frequency band. Their frequencies are (2α±β) or (2β ± α) – for 3rd order, (3α±2β) and similar – for 5th order, etc. Note, that the frequency difference between each of 2 tones is the same as between any tone and the nearest 3rd order IM product (and the same as between any order of IM product and the next one – for example, between 3rd order product and 5th order one, etc.)

For a perfectly linear system – all coefficients above 1st order (k_{2}, etc.) are zeroes; k_{1} – is a constant linear gain; no additional frequency components are created. However for the system with nonlinearity, gain is not a constant, but level dependent (proportional to the amplitude of input tones), and the amplitude of additional intermodulation components depends on the order of nonlinearity. It is seen when magnitudes of fundamental (at (α) or (β)) and intermodulation components (at (2α±β) – for 3rd order, etc.) are found when (1) is substituted into (2). In case of 3rd order nonlinearity those magnitudes are expressed as:

e_{fund} = k_{1}A + 9/4 k_{3}A^{3}(3)

e_{IM} = 3/4 k_{3}A^{3}(4)

To get rid of unwanted e_{IM}, one needs to add signals with the same amplitude and opposite phase to undesirable ones. Clearly though, if e_{IM} is large and the correction is applied to the input – it would lead to creation of additional distortions by correcting signals themselves. That is, input correction (based on feedback and called Predistortion) is good for mild nonlinearity (below 1-dB compression point); strong nonlinearities are to be corrected by Feed-Forward techniques (where the correcting signals are applied to the output). Besides that, from Parseval’s theorem, the signal’s spectrum is a constant, corresponding to its Average Power. It means that if one of IMD products is reduced – other products would increase (to keep an Average Power unchanged). That is, compensation should be focused not at the single IM product, but on all of them (which is done when Volterra Series is applied as a method of compensation).

Two-tone approach is good to figure out distortions at fixed frequencies. Digitally modulated signal though occupies a band of frequencies. Two-tone can give a general idea of the level of distortions for a digitally modulated signal, their actual value have to be calculated with the specific waveform at amplifier’s input. To evaluate the influence of distortions, consider a typical digitally modulated signal presented in the time domain by a periodic pulse train. Its frequency domain presentation is given by SINC function

e_{in} =AT{sin[(T(f-f_{c})]/[T(f-f_{c})]}= AT[SINC(T(f-f_{c}))](5)

Normalized graphic of SINC function is given at the top right.

Formula (5) is to be substituted into transfer function of a nonlinear system (2) and transactions with trigonometric identities are to be performed. It is not too hard to show that components appearing due to even order products do not fall into main lobe of the fundamental product, while odd order ones do, which is the same as in the case of CW two-tone signal. What is different from CW case is the spread at which distortions appear.

Comparing it to CW signals explained above, it is clear, that in this case instead of fixed two-tones the amplitude varies. If we choose any two-tone signals from the interval (-1, 1) then, from the note explaining the frequency intervals between tones and IM products (given in italic above) – 3rd order IM products would be anywhere between (-3, 3), 5th order between (-5, 5) etc.

An actual presentation of the products of a typical digitally modulated signal appears below.

**About the Author**

Boris Aleiner is an RF Engineer with many years’ experience at several telecom companies. He has published numerous papers and now serves as a consultant.

### January 2018

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