Radio Frequency Mixers

Mixers

In communication systems transmission is at Radio Frequency(RF), which need to be translated to Intermediate Frequency(IF) to make signal processing easier. Mixer is a non-linear device which translates power at one frequency to another frequency. Functionally it is equivalent to a multiplier.

Let's say, if A₁ cos(ω₁t)and A₂cos(ω₂t) are the two input signals then the output is given as,

O/P =[A₁ cos(ω₁t)].[A₂ cos(ω₂t)]
=(1/2)A₁A₂[cos(ω₁t - ω₂t) + cos(ω₁t+ ω₂t)]

(1.1)

Out of the sum and difference frequency components, in the down-conversion application the difference components are utilized, whereas the sum components in up-conversion applications. The unutilized other component, in either of the applications, which is to be rejected is called image component and can be filtered using bandpass filter generally.


Figure.1. Mixer Block Diagram

As shown in Fig.1., Mixer is represented by the symbol consisting of three ports, namely RF, IF and Local Oscillator(LO) ports. In up-conversion application input port is called IF port and output port is called RF port, and in down-conversion application it is vice-versa.

Out of the two input signals one is fed to LO port and other to either RF or IF port. If LO frequency is greater than input frequency it is called High side injection, where as in Low side injection the opposite is true. LO injection side, whether high or low, is often dictated by the spurs and the desired RF and IF band of operation.

LO provides periodic hard limited switching waveform to mixer rather than sinusoidal.

These harmonics cause additional signal energy to be converted into unused spurious component called spurs unless supressed by mixer gain at high frequencies.

While selecting a mixer, the following specifications of the mixer(active)need to be evaluated.

Conversion Gain

The ratio of r.m.s voltage of a signal at the output port(RF/IF) to the r.m.s voltage of the signal at the input port(IF/RF) of a mixer is called voltage conversion gain. If the input and output ports are perfectly matched for impedance, voltage conversion gain and power conversion gain are equal. Figure.2.1. illustrates variation of Conversion Gain (dB) Vs. LO power(dBm). Higher the LO drive, higher the conversion gain.


Figure.2. Conversion Gain Vs Lo Drive

Higher the conversion gain lowers the noise impact on the following stages in the RF chain.

3^rd Order Intercept Point (IP3)

- It is a hypothetical point where fundamental and 3rd order gain term will meet when extrapolated. At this point if power is referred to input it is called Input IP3(IIP3), else if reffered to ouput it is called output IP3 (OIP3). In receivers it impacts receiver's blocking performance.

1dB Compression Point(P1dB)

It is the input power level at which the small signal conversion gain drops by 1dB. Gain compression degrades at large input levels. It limits the upper limit of dynamic range of a mixer. Figure.3. illustrates compression in gain with input power level.


Figure.3. Gain Compression Vs. Amplitude

Noise Figure

The ratio between the Input SNR and output SNR is defined as Noise Factor. If it is expressed in dB scale it is called Noise Figure and is given by the equation,

(1.3)

Noise Figure impacts sensitivity of a circuit.

Dynamic Range

Dynamic Range is the amplitude range over which a mixer can operate without degradation of performance. Upper limit of dynamic range is limited by P1dB and lower limit is determined by noise floor and min SNR required.

Port Isolation

LO feedthrough will occur from LO port to IF port due to parasitic capacitance and power supply coupling, etc.,
Reverse LO feedthrough will occur from LO port to RF input port due to parasitic capacitance, etc., Self-mixing of Reverse LO feedthrough with LO result in DC offset, which poses a problem in zero IF architectures.
RF to IF leakage determines the fraction of the signal in the RF path that directly appears in the IF path.

Spurs

Spurious products are mixing harmonic frequency components resulted due to Nonlinear distortion. Spur performance is often captured in spur table . The individual spurious components are presented in dBc, relative to fundamental RF input power.

ω_IF = | m ω_RF ± n ω_LO | or
ω_RF = | m ω_IF ± n ω_LO |

(1.4)

where m and n are integers. Spur performance also play role in determining the LO injection side.

Spurs : Any signal that is half IF away from LO frequency may be mapped on to the IF channel at the output. For example, consider a down-conversion of 1950MHz signal using a lowside LO to an IF of 70MHz. If an unwanted interfering signal is present at a half-IF below, say 35MHz, the wanted signal, than the 2 x 2 product could result in a interfering product at {2(1950-35) - 2(1880) = 70MHz }. In narrow band system this can be avoided by choosing high IF. In BB systems use balanced mixer topology to overcome this problem.
Image response : If an undesired signal present at IF away from LO frequency may map on to the top of on-channel IF frequency at output. Remedy for this problem is either to use Image Reject Filter or Image Reject Mixer.

WhatIF is a frequency planner developed by GENESYS. Mixer input (RF/IF) drive levels are used to determine the amplitude of the spurious responses. Spur frequency depends on RF Center Frequency, RF Bandwidth, IF Bandwidth, and mixer configuration (sum, difference low side LO, or difference high side LO).

RF Circuits & Systems