# Mixer Performance Metrics

Mixers are characterized by the following performance specifications, and here they are defined for down-conversion mixers.

1. Conversion Gain
2. Noise Figure
3. Gain Compression or 1dB Compression Point 4. Third-Order Intermodulation Distortion 5. Port Isolation
6. Efficiency
7. Port Return Loss
8. Supply voltage

### Conversion Gain

Conversion gain is the ratio of desired output signal to input signal. It can be either voltage, current or power.  Consider the example of a down-conversion mixer whose output voltage is given by

(1) IF component is the desired component of mixer output. High Frequency(HF) component is undesired and filtered out.

#### Voltage Conversion Gain

(2) From the above equation can observe that Conversion Gain is  a function of LO amplitude.

#### Power Conversion Gain

(3) The gain of the mixer must be adequate in order to suppress the noise contributed by the subsequent stages in Rx chain

### Noise Figure

The noise at the output of mixer is mainly due to down-conversion of  input noise at the RF signal frequency and image frequency. Noise in mixers is characterized by Noise Figure. Noise factor is defined as the ratio of total noise at the output of the mixer to the noise at the output of the mixer due to  the input signal noise.  If is the noise at the input of mixer, is the noise adder by the mixer, then the total noise at the output is . So the Noise Factor of mixer is

(4) where, Conversion Gain of mixer.

If is expressed in dB, it is called Noise Figure.

(5) Depending on mixer, it  can be Single Side Band(SSB) NF or Double Side Band(DSB) NF.

In case of SSB mixer, data or information is present only on one side of LO, so noise in the RF band alone is considered as the input noise. But the output noise is due to RF signal band and image band.

(6) In case of DSB mixer, data is present on both side bands of LO. So  the input noise considers both RF and Image band noise. Hence NF is

(7) Therefore noise figure of SSB mixer is 3dB higher than DSB mixer under the cond., .

Noise Figure of mixer is typically vary between 10 to 15dB. The other sources of noise that contribute to output noise are switching elements, noise from transconductor, etc.,

### Linearity

Ideally the conversion gain of mixer should remain constant. But in reality the conversion gain deviates from the constant value as the signal power or voltage increases. So to measure the amount of linearity of a mixer and are used.

In ideal situation we expect the intermod components to be very less compared to fundamental components. The third order components are at and ### Port isolation

LO-RF isolation

• If of LNA is low, LO leakage to RF port can make its way to antenna and radiate.
• Self-mixing : LO signal that leak to RF port mixes with itself and reflected as DC at the output port. This results in DC offset errors.

LO-IF isolation : Due to high LO amplitude, LO leakage to IF port may saturate the down stream circuits.

RF-IF isolation : Since RF signals for receiver are small or weak, it is not a great problem.

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