# P1dB vs TOI-1dB compression point,Third Order Intercept Point

This page compares P1dB vs TOI and mentions difference between P1dB (1dB compression point) and TOI (Third Order Intercept Point). It also describes IIP3,OIP3 etc.

## TOI | Third Order Intercept Point

As mentioned TOI refers to Third Order Intercept Point. As we know from our discussion in intermodulation distortion page, saturated or overdriven amplifier produces unwanted products of input signals. This is known as IMD (Intermodulation Distortion). When two or more signals are fed to the nonlinear device whether passive or active will generate many combinations of input signals produced at the output. These contain first order, second order and third order products. Out of these intermodulation distortion (IMD) products only third order products are vulnerable to interference due to its higher amplitude and close proximity with the desired signals. For f1 and f2 input signals, output third order products namely 2f1-f2 as well as 2f2-f1 lead to IMD interference.

Each P1dB increase results in 3dB increase in 3rd order IM (Intermodulation) power. TOI point is a figure of merit,
which characterizes a RF receiver's tolerance subjected to multiple RF signals outside passband of interest.
The TOI points on X-axis and Y-axis are designated as IIP3 and OIP3 respectively.

Refer IIP3 versus OIP3 which describes difference between IIP3 and OIP3.

The figure depicts IP3 measurement setup.

➤ OIP3 = P_{OUT} + ΔP/2

Where,

ΔP = P_{OUT} - P_{OUT_3}

Here P_{OUT} refers to power of fundamental signals when they are equal in magnitude

P_{OUT_3} refers to power of third order intermodulation products when they are equal in magnitude

Refer IIP3 calculator >> which calculates IIP3 and OIP3,
when powers of both fundamental signals are equal and when powers of IMD products are also equal.

Refer IM3 calculator which calculates third order intercept points at input (i.e. IIP3) and at output (i.e. OIP3) using IM3 formula mentioned above.

## P1dB | 1dB compression point

P1dB or 1dB compression point is the part of the curve where, 2dB change in the input power fed to the amplifier(RF circuit) results
into 1 dB change in the output power. The input and output powers are called as P1B_{in} and P1dB_{out} respectively.
In reality, Intercept point is usually about 10 dB higher value compare to P1dB (1dB compression point).

Both IIP3 and OIP3 are results of third order intermodulation distortion products.
RF circuit does not function correctly or amplify the input signal properly at the **IIP3** input level.

IIP3 mentioned above is the 3rd order intercept point at the input of the amplifier for OIP3 (Output third Order Intercept point).
Following equation mentions relation between IIP3 and OIP3 with respect to gain.

Gain + IIP3 = **OIP3**

The formula is useful in order to characterize linearity of a RF receiver for signals below the saturation level.

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