# Understanding RF power amplifiers

The following is excerpted from Chapter 7 from a new edition of the book, __ RF Circuit Design, 2e __ by Christopher Bowick. (*If you order a copy of this book before March 30, 2008 you can receive additional 20% off. Visit www.newnespress.com or call 1-800-545-2522 and use code 91603.* )

**Class-A Amplifiers and Linearity**

A class-A amplifier is defined as an amplifier that is biased so that the output current flows at all times. Thus, the input signal-drive level to the amplifier is kept small enough to avoid driving the transistor into cutoff. Another way of stating this is to say that
the conduction angle of the transistor is 360deg., meaning that the transistor conducts for the full cycle of the input signal.

The class-A amplifier is the most linear of all amplifier types. Linearity is simply a measure of how closely the output signal of the amplifier resembles the input signal. A linear amplifier is one in which the output signal is proportional to the input signal, as shown in Fig. 7-4. Notice that, in this case, the output signal level is equal to twice the input signal level, and the transfer function from input to output is a straight line.

No transistor is perfectly linear, however, and, therefore, the output signal of an amplifier is never an exact replica of the input signal. There are always spurious components added to a signal in the form of harmonic generation or intermodulation distortion (IMD). These types of nonlinearities in transistors produce amplifier transfer functions that no longer resemble straight lines.

Instead, a curved characteristic appears, as shown in Fig. 7-5A. The distortion caused to an input signal of such an amplifier is shown in Fig. 7-5B. Notice the flat topping of the output signal that occurs due to the second-harmonic content generated by the amplifier. This type of distortion is called harmonic distortion and is expressed by the equation:

The second term of Equation 7-1 is known as the second harmonic or second-order distortion. The third term is called the third harmonic or third-order distortion. Of course, a perfectly linear amplifier will produce no second, third, or higher order products to distort the signal.

Notice in Fig. 7-5, where the amplifier's transfer function is given as Vout =5V_{in} +2V^{2}_{in}, that the second-order distortion component increases as the square of the input signal. Thus, with increasing input-signal levels, the second-order component will increase much faster than the fundamental component in the output signal. Eventually, the second-order content in the output signal will equal the amplitude of the fundamental. This effect is shown graphically in Fig. 7-6.

The point at which the second-order and first-order content of the output signal are equal is called the second-order intercept point. A similar graph may be drawn for an amplifier which exhibits a third-order distortion characteristic. In this case, the third-order term is plotted along with the fundamental gain term of the amplifier. In this manner, the third-order intercept may be determined. The second- and third-order intercept of an amplifier are often used as figures of merit. The higher the intercept point, the better the amplifier is at amplifying large signals.

When two or more signals are input to an amplifier simultaneously, the second-, third-, and higher-order intermodulation components are caused by the sum and difference products of each of the fundamental input signals and their associated harmonics.
For example, when two perfect sinusoidal signals, at frequencies f1 and f2, are input to any nonlinear amplifier, the following output components will result:

fundamental: *f*_{1}, *f*_{2}

second order: 2*f*_{1}, 2*f*_{2}, *f*_{1} +*f*_{2}, *f*_{1} - *f*_{2}

third order: 3*f*_{1}, 3*f*_{2}, 2*f*_{1} ±*f*_{2}, 2*f*_{2} ±*f*_{1} +higher order terms

Under normal circuit operation, the second-, third-, and higher-order terms are usually at a much smaller signal level than the fundamental component and, in the time domain, this is seen as distortion. Note that, if f_{1} and f_{2} are very close in frequency, the 2 f_{1} - f_{2} and 2_{2} -f_{1} terms fall very close to the two fundamental terms. Third-order distortion products are, therefore, much more difficult to eliminate through filtering once they are generated within an amplifier.

The bias requirements for a class-A power amplifier are the same as those for small-signal amplifiers. In fact, the distinction between a class-A power amplifier and its small-signal counterpart is a hazy one at best. For all practical purposes, they are equivalent except for input and output signal levels.