Managing nonlinearities is all about managing the impedance of each device in a signal chain. Nowhere else is this more true than in power amplifier design, where a signal of typically injected into an amplifier very near the saturation level. Due to the nonlinearities involved, impedance matching in an RF signal chain can become difficult as the load’s output impedance now depends on the input voltage.

Due to this nonlinear dependence of output impedance on input signal level, this means the instantaneous impedance (i.e., impedance at any point in time) also varies with the input signal level. For DC this does not matter; your signal does not change in time, so the termination required for maximum power transfer in a linear system is fixed. For analog signals, you need to devise a complex impedance matching scheme for a load component connected to an amplifier to ensure maximum power transfer. The ideal analysis to perform here is load-pull analysis.

Your signal chain stops behaving in the typical manner when nonlinearities are present in the system or in a particular component. All power amplifiers used in RF signal chains are slightly nonlinear. When we say "slightly nonlinear," we mean that the output signal level eventually rounds off at some maximum value. At low signal levels, the nonlinear relationship between input and output may not be noticeable. However, at high input signal levels, the output signal level is not a linear function of the input.

With power amplifiers, the nonlinearity in the output signal arises due to saturation of the input signal. If you are familiar with load lines, then you know there is a range of input signals that will produce a linear output, i.e., the two are directly proportional. With power amplifiers, the signal level is often low and the amplifier is often designed to provide high gain while running near saturation. In other words, the amplifier is running close to the saturation level for the power transistor in the component.

Saturation leads to some important effects with different types of signals:

**Harmonic generation.**All amplifiers are slightly nonlinear, even below threshold. Once the threshold is exceeded, clipping occurs in the time-domain output signal, which will appear as harmonic generation in the frequency domain.**Frequency mixing in modulated signals.**FM signals can mix due to the nonlinear nature of a power amplifier. This causes intermodulation products to appear near the side lobes in the frequency domain. The most important products are the 3rd order intermodulation products as these are closest to the desired signal and are difficult to properly filter. They also tend to lie in the receiver’s passband.

*Intermodulation products generated in an RF signal chain with a power amplifier (harmonics are not shown).*

Harmonics generated from a harmonic signal are easy to deal with; these can just be removed with a higher-order low pass filter. Intermodulation products are more difficult. They require a higher-order filter that does not cutoff the desired sidelobes. One method to suppress these products is to use a bandpass filter that lies within the receiver’s passband and simply run the amplifier at a lower level. The appropriate range of input powers and acceptable level of intermodulation is determined by the amplifiers 3rd order intermodulation point. Acceptable differences between the desired bandwidth and the 3rd order intermodulation point depend on the particular application. For 5G devices, the acceptable difference is something on the order of -120 dB. While this may sound like an immeasurably small signal, intermodulation products stronger than this level can significantly decrease upload and download speeds.

The 3rd order intermodulation point could be determined analytically, although this is a difficult prospect, especially in multistage amplifiers. Normally, the output from a DUT is measured in the frequency domain, and the peak level of the desired signal is measured. The output with the 3rd order products increases at a rate that is a factor 3 larger than the output for the desired signal. This means you only need a single measurement to determine both input-output relationships. The 3rd order intercept point (called 3OIP or OIP3) is used to quantify the input signal level that leads to saturation. This is shown below.

*3OIP for an amplifier in an RF signal chain determined through interpolation.*

Once you’ve determined the acceptable input signal level and 3OIP point, your goal in RF signal chain design is to ensure impedance matching to the load. Unfortunately, due to the nonlinear nature of a power amplifier, the optimal impedance matching applied to the load is not a matter of setting the load impedance to the complex conjugate of the amplifier’s output impedance. The method used to determine optimal impedance is called load-pull analysis.

In load-pull analysis, the impedance seen by the load is varied iteratively, and the maximum power transferred to the load is determined. Alternatively, the gain, power-added efficiency (PAE), or any other parameter of the amplifier can be measured for each load impedance value. Load-pull is performed with the following procedure:

- Set the magnitude of the load impedance to a test value.
- Vary the resistance and reactance while holding the magnitude constant.
- Simulate and measure the desired output characteristics for each pair of resistance and reactance values chosen in step 2.
- Plot a contour for the characteristic measured in step 3.
- Choose a new load impedance value (magnitude) and go back to step 2. Repeat this until you have generated a series of contours and identified the load impedance that produces maximum power transfer, PAE, gain, etc.

This generates a set of contours for each characteristic you are measuring. The impedance contour that provides the desired output measurement is the optimally matched impedance for the load. You should then design a matching network that provides this impedance throughout signal bandwidth.

Note that, if you measured multiple output characteristics for the DUT, the region where different contours overlap tells you the acceptable impedance matching range that will produce output characteristics within your design range. This also allows you to qualify whether the input signal level will produce the desired power transfer, gain, PAE, etc.

*Example load-pull contours for power delivered and PAE for a 2.5 GHz 10 W Class F power amplifier [Image source].*

**RF signal chain design and load-pull analysis can be complicated techniques, but they are essential for any RF design. If you’re looking for a knowledgable firm that offers cutting-edge PCB design services and technology research services for innovative electronics companies, contact NWES for a consultation. We can help you with all aspects of RF system design and guide you through the manufacturing process.**