## Third-Order Intercept

Recapping from our previous post on Amplifier Linearity: Amplifier linearity is focused on the amplifier's linear relationship of input power to output power. In the most optimal case, it would be directly related by the gain of the amplifier. Technically, this would mean an amplifier with a gain response of “X” dB across the frequency range of the amplifier would be consistent, but most lose gain with increasing frequency and inevitably suffer a gain loss at higher frequencies.

As we have discussed, there are two important measurements in determining power amplifier linearity: the third-order intercept (abbreviated TOI or IP3) point and the 1-dB compression (P1dB) point. These two elements allow you to evaluate and compare amplifier specifications and performance. In the first article, we discussed the P1dB, which you can read more about here. Let’s get to the Third Order Intercept.

### Third-Order Intercept

When an amplifier becomes non-linear, it will begin to produce harmonics of the amplified inputs. The second, third, and other harmonics are outside of the rf amplifier bandwidth, they are usually easy to filter out. However, non-linearity will also produce a mixing effect of two or more signals.

If the signals are close together in frequency, some of the sum and difference frequencies called intermodulation products produced can occur within the bandwidth of the amplifier. These cannot be filtered out, so they will ultimately become

interfering signals to the main signals to be amplified.Figure 2 shows two signals f1 and f2 occurring within the amplifier bandwidth. With distortion, new signals f1 – f2 and f1 +f2 are produced. However, these signals will also mix with the second, third, and higher harmonics to produce a wide range of potentially interfering signals within the amplifier pass band. The most troublesome are the third-order products, which are 2f1 ± f2 and 2f2 ± f1. Those possibly occurring in the amplifier frequency range are2f1 – f2 and 2f2 – f1.

If you plot the output power versus input power, you will get a 1-dB compression curve. This is the first-order signal plot. Note the flattening of the gain curve which shows compression. Also plotted on this same graph are the third-order product signal levels. These IM products increase at a rate three times that of the first-order products on a logarithmic scale because the mathematics of mixing indicates a 3:1 gain rate for the third-order products.

Now if you extend the linear portions of the two gain curves as shown in Figure 3, they will meet at a point where the third- order signals equal the first-order or input signals in amplitude. This is the third-order intercept point. It is a theoretical point that is never achieved. However, it is useful in determining the linearity condition of an amplifier.

The IP3 value can be read with reference to the input or the output. If you read the value from the output axis, it is called OIP3. Reading the value from the input axis, the value is IIP3.

The higher the output at the intercept, the better the linearity and the lower the IMD. The IP3 value indicates how large a signal the amplifier can process before IMD occurs. The IP3 point is typically about 10 dB above the 1-dB compression point.

### Summary

Third-order products are the most troublesome of the intermodulation effects caused by non-linear operation. The IP3 value is an imaginary point that indicates when the amplitude of the third-order products equals the input signals. This point is never reached in real testing, as the amplifier will saturate before this condition can occur. Nevertheless, it is a good indicator of amplifier linearity. This concludes our article on rf amplifier linearity and measurements via the third-order intercept (abbreviated TOI or IP3) point and the 1-dB compression (P1dB) point. For more information or reference material on rf amplifiers, such as rf calculators and many others, go to Eliterfllc.com.