Mixer

Goals:
- Understand the operation of a mixer used for frequency conversion
- Design and build a single balanced mixer

Principle:
- 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.
- A linear time invariant network cannot generate new frequencies. For frequency conversion, one needs nonlinearity or time variance. The mixer you'll build here is of the latter variety-i.e. its input signal will experience a time varying gain(controlled by another signal). In this respect, it'll be different from circuits you have studied so far, most of which have been linear. Be sure to go through the description and this lecture before the experiment.
- A message signal v_RF(t) has to be shifted in frequency by an amount f_LO while retaining its spectral shape. i.e. V_RF(f) has to be turned into V_RF(f±f_LO). Frequency conversion is accomplished by the mathematical operation v_out = k*v_RF*v_LO where v_LO is a sinusoid of frequency f_LO. Of the two components at f±f_LO, one of them can be selected using a filter to attenuate the other. (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. i.e. v_LO is a square wave of frequency f_LO instead of a sinusoid. 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, V_RF(f) is turned into V_RF(f±n*f_LO), n=1,3,5,… As before, the desired component can be selected using a filter to attenuate all but one of them.
- The figure below 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 only 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).
- One deviation of this circuit from the description in the previous paragraphs is the presence of I_bias in addition to i_RF. Therefore, 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.

Experiments: Design a single balanced mixer using BC107 transistors(you can of course use BC177 transistors and reverse the polarity of all voltages and currents). Use a 12V supply and about 1mA bias current. Use a voltage divider to generate V_bias1 and V_bias2. Remember to bypass the bias nodes to ground. The mixer should be able to take in an input peak of 1V and have a conversion gain(ratio of the sinusoidal component at f_RF+f_LO OR f_RF-f_LO at the output to the amplitude of the input sinusoid) of 2.
- Drive the input with a low frequency v_RF(~ 1kHz) and a high frequency v_LO(~10kHz) and observe the output. You can use the oscillator designed in the previous experiment as the 10kHz source.
- 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. Filtering will be a lot easier if you choose a higher f_LO, say 25kHz or 50kHz, and a difference frequency around 1kHz.
- Remove the RF input and observe the LO feedthrough

Questions:
- How will you get rid of the LO feedthrough?
- What happens in this experiment if you do not bypass the bias nodes V_bias1 and V_bias2 generated using a resistive divider?

Applications: This(modified to get rid of the LO feedthrough) is probably the most widely used topology for mixers. [An alternative is to use switches(MOS transistors or diodes) to direct the signal to the output and away from it.] It is used in both transmitters and receivers. Typically, in a receiver, a high frequency v_RF is mixed with a comparably high frequency v_LO to convert the signal to a relatively low intermediate frequency f_IF=f_LO-f_RF. In a transmitter, a low frequency “message signal” v_mod around zero frequency is mixed with a high frequency v_LO to convert the signal to the carrier frequency f_LO. Although in its native form it does amplitude modulation, combinations of mixers are used for other types of signalling that involve both amplitude and phase modulation. You will see this in your courses on communication systems.

Something to try on your own: 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.