Intercept Point
The intercept point, IPn = (IIPn, OIPn), is the point in the {Pin, Pout} plane where the (linear) fundamental output power (Pout) intersects with the (linear) output power of the intermodulation product of order n (IMn). In this sense, the IPn quantifies the linearity of the system against intermodulation distortion of order n, so, the higher IP, the higher system linearity.
It is important to note that the intercept point cannot be achieved in a real experiment since nonlinear devices suffer from AM/AM distortion (i.e. compression) and it becomes saturated at some high drive level. The idea is to ignore saturation and predict the intermodulation level based on the two-tone test done at certain S/I. Notice that this diagram only applies for one single frequency, so severals diagrams are needed for broadband systems.
The IPn method is a linear tool for solving a nonlinear problem, but it is simple and intuitive.
The power of the n-th intermodulation product at the output (Pout, IMn) is given by:
$$ P_{out, IMn} = {n·P_{in}} - { (n-1)·IIP_{n} } + G \tag{1} $$
and, obviously, the fundamental output power (Pout) is related to the input (Pin) as:
$$ P_{out} = { P_{in} + G} \tag{2} $$
The IPn can be estimated from the two-tone test as [1]:
$$OIP_{n} = P_{out} + {\Delta \over {n-1} } \tag{3}$$
$$IIP_{n} = P_{out} + {\Delta \over {n-1} - G} \tag{4}$$
where Pout is the power of the carrier, G is the (linear) gain of the amplifier and Δ is the level (in dB) between Pout and the power level of the intermodulation products of n order. Notice that OIPn = IIPn + G
Compression
The compression point indicates the output power at which the actual output power coming from the device deviates n dBs (typically 1, but also 3 or 5dBs) from its ideal linear gain. As an amplifier enters in the saturation region, the actual gain is reduced because of its AM/AM nonlinear behavior. It is important to note that this kind of nonlinerity is not related to the intermodulated distortion. Also notice that the IP3 is a fictitious point, but the P1dB can be measured with a network analyzer doing a power sweep.
Dynamic Range
The dynamic range is limited by the noise floor at the lower end and by the minimum S/I ratio required for demodulation at the higher end. In the latter case, the power of the intermodulation distortion rises N dB for the increase in 1 dB in the input power, so at some point the S/I turns to be unbearable for the system. In order to find that point, we need to find the input power for what the difference between the output power and the intermodulation products is equal to the minimum S/I., So, taking into account Eqs. (1) and (2), we get:
$$ SI_{min} = \color{red}{P_{out} } - \color{blue}{P_{out, IMn} } \tag{5}$$
$$ SI_{min} = \color{red}{(P_{in} + G)} - \color{blue}{({n·P_{in}} - { (n-1)·IIP_{n} } + G) } \tag{6}$$
After solving Eq. (6), we find:
$$ P_{in} = IIP_{n} - { {SI_{min}} \over {n-1} } \tag{7}$$
and, obviously:
$$ P_{out} = { P_{in} + G }= IIP_{n} + G - { {SI_{min}} \over {n-1} } = {OIP_{n} - { {SI_{min}} \over {n-1} }} \tag{8}$$
Usually, n=3, so
$$ P_{in} = IIP_{3} - { {SI_{min}} \over {2} } \tag{9}$$
Noise floor
As said, the lower end of the dynamic range is determined by the noise floor at the output of the amplifier. It can be calculated as follows:
$$ N_{o} = k·T·BW·10^{ {(NF + G) \over 10} } \tag{10}$$
where k is the Boltzmann's constant (1.3806503 · 10-23 m2·kg·s-2·K-1), T is the temperature of the environment, BW is the bandwidth of the amplifier (in Hz), G is the gain of the amplifier (in dB) and NF is the noise figure (in dB too).
Summary Table
n = 2 |
n = 3 |
|
|---|---|---|
| Pout, IMn | 2·Pin - IIP2 + G | 3·Pin - 2·IIP3 + G |
| IIPn | Pout + Δ - G | Pout + Δ/2 - G |
| OIPn | Pout + Δ | Pout + Δ/2 |
| Pout @ S/Imin | OIP2 - SImin | OIP3 - SImin/2 |
References
[1] P. Vizmuller, RF design guide: systems, circuits, and equations. Boston u.a.: Artech House, 1995.