Mixer

A mixer is used for frequency conversion. For example, it is used in radio receivers to convert incoming signals at a high frequency to a lower intermediate frequency. And, in transmitters, it is used to convert low frequencies such as voice to high carrier frequencies.

The mathematical operation v_out = k*v_RF*v_LO accomplishes frequency conversion. v_RF and v_LO respectively denote the input and the local oscillator signals. If v_RF and v_LO are sinusoids at f_RF and f_LO, v_out will contain sinusoids at f_RF+f_LO and f_RF-f_LO. The desired component can be selected using a filter to attenuate one of them. (The terms v_RF and v_LO are carried over from radios where they stand for radio frequency input and local oscillator signal respectively)

For practical reasons, switching mixers are used instead of multipliers. These are described by v_out = k*v_RF*sgn(v_LO) where sgn() denotes the signum function. sgn(v_LO) where v_LO is a sinusoid at f_LO contains odd harmonics n*f_LO, n=1,3,5,… In this case, if v_RF is a sinusoid at f_RF, v_out will contain sinusoids at f_RF+n*f_LO and f_RF-n*f_LO, n=1,3,5,… As before, the desired component can be selected using a filter to attenuate one of them.

The above figure shows a mixer. The combination of Q₀ and R_E converts the input signal v_RF to a signal current i_RF riding on a bias current I_bias. The differential pair Q_1,2 is driven by v_LO which is a square wave or a sufficiently high amplitude sinusoid such that one of Q_1,2 is completely on at a given time and the other is switched off. The current I_bias+i_RF is steered to the two load resistors alternately. Consequently, the voltage at the collector will be a certain bias voltage plus k*(I_bias+i_RF)*sgn(v_LO).

In this mixer, if v_RF=0(i.e. i_RF=0), the output will contain a component proportional to sgn(v_LO). This also needs to be filtered out if only the sum or difference frequency component is to be extracted. This is known as local oscillator(LO) feedthrough and is a characteristic of this type of mixers which are known as single balanced mixers.

LO feedthrough can be eliminated as shown in the circuit below by having two mixers driven by +v_RF and -v_RF and taking the difference between them. It can be seen by inspection that the sum of currents through Q₁ and Q_2a is always constant as is the sum of currents through Q₂ and Q_1a. This is a double balanced mixer.

The above circuit is available in the form of an IC-the MC1496 double balanced modulator. Its internal schematic is shown below. Most of the circuitry including the biasing arrangements are inside the IC. Only R_E, the load resistors, and the bias current setting resistor need to be connected externally.

• Design a single balanced mixer using BC107 transistors. Use a 12V supply and about 1mA bias current. The mixer should be able to take in an input amplitude of 1V and have a conversion gain(ratio of f_RF+f_LO OR f_RF-f_LO component at the output to the input amplitude) of 2.
  • Drive the input with a low frequency v_RF(~ 1kHz) and a high frequency v_LO(~20kHz) and observe the output.
  • Drive the mixer with a v_RF and v_LO at close by, but not identical frequencies and observe the low frequency(f_RF-f_LO) output. For filtering out the high frequency component, use a capacitor of appropriate value across R_L which will short it out at high frequencies.
  • Remove the RF input and observe the LO feedthrough
• Design a double balanced mixer around the MC1496 IC. Use a 12V supply and 1mA current through the bias branch. The mixer should be able to take in an input amplitude of 1V and have a conversion gain(ratio of f_RF+f_LO OR f_RF-f_LO component at the output to the input amplitude) of 2.
  • Repeat the experiments you did with the single balanced modulator.

• Drive the lower input with audio, say from your computer or digital player. Drive the LO input with a sinusoid in the AM band(0.5-1.5MHz). You should be able to use an AM radio placed close by to receive the transmitted audio. You can use a short wire connected to the output node as an antenna.