# Output Power versus Input Power Characteristic

The output power versus input power (P_{out} vs. P_{in}) characteristic is commonly used to characterize the transfer function of amplifiers. This characteristic relates the input power of the device under test (DUT) at the fundamental frequency to its output power at the same frequency. When both power levels are expressed in watts, the slope of the P_{out} vs. P_{in} characteristic represents the linear gain of the system. Most commonly, the power levels are expressed in dBm. In such case, the slope of the P_{out} vs. P_{in }characteristic is equal to unity and the gain in dB corresponds to the y-intercept point (i.e., the value of the output power for a 0 dB m input power).

In the absence of memory effects, the P_{out} vs. P_{in} characteristic appears as a one to one mapping function that increases linearly with the input power. As the amplifier is driven into its nonlinear region, a gain compression appears as the actual output power becomes lower than the linearly amplified version of the input power. The amount of compression introduced by the amplifier increases until it reaches the saturation power. Figure 1.7 presents a sample P_{out} vs. *P _{n}* characteristic of an amplifier

**Figure 1.7 **Sample output power versus input power characteristic

optimized for linearity. One can observe that the gain compression of the amplifier becomes noticeable only a few dBs before the saturation for input power levels beyond 0 dB m. With amplifiers optimized for efficiency, the gain compression is observed over a wider input power range starting from as early as 10 dB below the maximum input power.

The P_{out} vs. P_{in} characteristic is straightforward to derive as it only requires scalar measurements both at the input and output of the DUT. This can be performed using a network analyzer or a set up that comprises a signal generation instrument and a power measurement instrument such as a power meter or a spectrum analyzer. The P_{out} vs. P_{in} characteristic can be measured under a wide range of drive signals such as continuous wave (CW), multi-tone, or modulated signals.