# IIP3 vs OIP3 | difference between IIP3 and OIP3

This page compares IIP3 vs OIP3 and mentions difference between IIP3 and OIP3. The terms IIP3 and OIP3 stands for Input Third Order Intercept Point and Output Third Order Intercept Point respectively.

**Introduction**: When two or more than two signals are mixed in nonlinear component whether active or passive, other signals get generated as a result of product of these original signals. This condition is referred as IMD or Intermodulation Distrotion.
The frequencies which are generated due to intermodulation can be sum or difference of various IMD products. Based on IMD products which are generated there will be second order, third order, fourth order and so on.
These IMD products are shown in the figure-1 below.
As shown in the figure there are many IMD products,
but the major interference will be due to 2w1+w2 and 2w1-w2 as they exists near to desired frequencies (w1,w2)
in the frequency spectrum.

The intermodulation distortion is generated in the transmitter when two or more signals are mixed in nonlinear component of transmitter such as RF mixer, MMIC amplifier etc. The table below mentions third order intermodulation output frequencies due to application of two input frequency channels (f1 and f2).

As mentioned above, only third order products at the output are higher in magnitude and closed to the desired frequencies (f1 and f2). Hence these third order products cause interference to the desired signal frequencies. Let us understand terms IIP3 and OIP3 associated with third order IMD curve (with slope 3).

## IIP3 | Input Third Order Intercept Point

Each 1dB increase in input power results in 3dB increase in the output power. Hence slope of 3 is achieved as shown in the figure-2. Third order intercept point is result of third order IMD products viz. 2w1-w2 as well as 2w2-w1 as shown in the frequency spectrum of figure-1. TOI point is called figure of merit. It characterizes RF receiver's tolerance subjected to multiple RF signals which is outside of desired pass band. Due to third order IMD products, RF circuit does not function as desired at IIP3 input level.

1dB gain compression Point (P1dB point): It is the output point where 2dB increase in input power fed to the amplifier (or non linear
RF circuit) results into 1 dB change in the output power.
The 1dB curve shows IP_{1dB} and OP_{1dB} as Input and output 1dB gain compression points.

The extrapolated point where IM3 is equal to 0 dBc is known as the third-order intercept point IP3. The extrapolated point where the curves of the fundamental signal and third order distortion product signal meet is called Third order Intercept Point (IP3). At this point, the input power level is known as IIP3, and the output power when this situation occurs is known as OIP3 point. IIP3 mentioned above is the 3rd order intercept point at the input of the amplifier for OIP3 (Output third Order Intercept point).

The figure-2 shows IP2 point. This is result of second order IMD products (i.e. f1+f2 and f1-f2) and second order harmonic frequencies (2*f1, 2*f2). The extrapolated point where curves of fundamental signal and second order distortion product signal meet is called second order intercept point (IP2). The input power level is known as IIP2 and output power when this occurs is known as OIP2 point.

## OIP3 | Output Third Order Intercept Point

Output power of the non linear device when fed with input power having strength equal to IIP3 level is known as OIP3.
Ideally, OIP3 is usually about 10 dB higher than P1dB gain compression point (i.e. OP_{1dB}).

The figure depicts IP3 measurement setup.

➤ OIP3 = P_{OUT} + ΔP/2

Example: Let f1 and f2 signals are measured at power level of -10 dBm (this is P_{OUT}) and
2f1-f2 and 2f2-f1 are measured at power level of approx. -40dBm.

➤ ΔP = -10-(-40) = +30 dBc

➤ Now, OIP3 = -10 dBm + 30/2 dB or OIP3 = +5 dBm

➤ If gain of the device is say + 6 dB, then IIP3 = OIP3 - G

Hence, IIP3 = +5 - 6 = -1 dBm

## Relation between IIP3 and OIP3

Let x and y are input power and output power respectively.
Let A is transfer function between X and Y. ( A is "gain" if the device is an amplifier).

Y = A0 + A1.X^{1} + A2.X^{2} + A3.X^{3} +... + Ai.X^{i} +... An.X^{n}

Where, A0 constant term which is independent of value of X,

A1*X is linear portion

A2.X^{2} is quadratic term i.e. second order

A3.X^{3} is third order part

Following equation expresses relation between IIP3 and OIP3.

➤ Gain_{dB} + IIP3_{dBm} = OIP3_{dBm}

Where,

• IIPn for nth-order input intercept point, measured on the input power axis (i.e. X-axis)

• OIPn for nth-order output intercept point, measured on the output power axis (i.e. Y-axis)

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