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(P_{\tiny 1dB})
  4. Third-Order Intermodulation Distortion(\mbox{IMD}_{\tiny3})
  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)   \begin{eqnarray*} v_{\tiny o} &=& V_{\tiny RF} \cos(\omega_{\tiny RF}t) . V_{\tiny LO} \cos(\omega_{\tiny LO}t) \\ &=& \frac{1}{2} V_{\tiny RF}V_{\tiny LO}[\underbrace{\cos(\omega_{\tiny RF} - \omega_{\tiny LO})t}_{\mbox{IF component}} + \underbrace{\cos(\omega_{\tiny RF} + \omega_{\tiny LO})t}_{\mbox{HF component}}] \end{eqnarray*}

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

Voltage Conversion Gain

(2)   \begin{eqnarray*}CG_v &=&\frac{\mbox{IF output voltage}}{\mbox{RF input voltage}}\\ &=&20.\log\left(\frac{V_{IF}}{V_{RF}}\right) = 20.\log\left(\frac{V_{LO}}{2}\right) \mbox{ (dB) } \end{eqnarray*}

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

Power Conversion Gain

(3)   \begin{eqnarray*}CG_p &=&\frac{\mbox{IF output power}}{\mbox{RF input power}}\\ &=& 10.\log\left( \frac{P_{IF}}{P_{RF}}\right) \mbox{ (dB) }\end{eqnarray*}

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 N_{\tiny i} is the noise at the input of mixer, N_{\tiny A}  is the noise adder by the mixer, then the total noise at the output is N_{\tiny o}= G N_{\tiny i} + N_{\tiny A}. So the Noise Factor of mixer is

(4)   \begin{equation*}Noise Factor = \frac{G N_{\tiny i} + N_{\tiny A}}{G N_{\tiny i}}\end{equation*}

where, G \rightarrow Conversion Gain of mixer.

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

(5)   \begin{equation*}NF = N_{\tiny o(dB)} - GN_{\tiny i(dB)}\end{equation*}

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)   \begin{equation*} NF = (2G N_{\tiny i} + N_{\tiny A})_{\tiny dB} - (G N_{\tiny i})_{\tiny dB} \end{equation*}

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)   \begin{equation*} NF = (2G N_{\tiny i} + N_{\tiny A})_{\tiny dB} - (2G N_{\tiny i})_{\tiny dB}\end{equation*}

Therefore noise figure of SSB mixer is 3dB higher than DSB mixer under the cond., N_{\tiny A}=0.

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 P_{\tiny 1dB} and IIP_{\tiny 3} are used.

In ideal situation we expect the intermod components to be very less compared to fundamental components. The third order components are at (2\omega_{\tiny LO}\pm\omega_{\tiny RF}) and (\omega_{\tiny LO}\pm 2\omega_{\tiny RF})

Port isolation

LO-RF isolation

  • If S_{\tiny 12} 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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