EC-22.4 Amplifiers, Mixers and Oscillators

What this is and why it exists

Three blocks make a radio: something that makes a signal larger, something that moves it to another frequency, and something that provides the reference.

Each has one central difficulty, and knowing what it is makes the rest of the design legible.

The amplifier cannot have its best gain and its best noise at the same time. The mixer produces an unwanted response as well as the wanted one. The oscillator is never quite at one frequency, and that impurity limits the whole system.

The vocabulary

• Stability — whether an amplifier will oscillate for some source and load impedances.
• Stability circle — the boundary on the chart between safe and unsafe impedances.
• Noise match — the source impedance giving the lowest noise figure.
• Power match — the source impedance extracting the most power.
• Efficiency — the fraction of supplied power that becomes output signal.
• Back-off — operating below compression to keep distortion low.
• Mixer — a component whose output contains the sum and difference frequencies.
• Local oscillator — the reference signal a mixer multiplies the input by.
• Image frequency — a second input frequency that maps to the same output.
• Phase noise — energy spread around an oscillator's nominal frequency.

The mental model

A transistor characterised as a two-port can be matched for maximum gain using its scattering parameters. The same data also says which source and load impedances would make it oscillate. Checking stability before matching is not optional, and the stability circles drawn on the chart show which regions to avoid.

Then the central trade. The impedance that extracts the most power from a transistor is not the impedance that gives it the lowest noise. A first stage is therefore deliberately mismatched for power in order to be matched for noise. That is the most consequential decision in receiver design, and it follows directly from the cascade formula.

Power amplifiers face the opposite problem. A transmitter spends most of a system's energy, and an amplifier run near compression is efficient and distorting. The operating classes are different answers to that same conflict, trading linearity for efficiency in different proportions.

A mixer is a multiplier. Multiplying two sinusoids produces components at the sum and difference of their frequencies. That is how a signal is moved to a frequency where it is easier to filter, amplify and digitise. Everything else about mixers follows from that one fact.

The unavoidable consequence is the image. Two different input frequencies, one above the local oscillator and one below it by the same amount, map to the same output. Only one is wanted. There are three standard answers. A filter before the mixer, an intermediate frequency high enough to make that filter practical, or an image-cancelling architecture.

Finally the oscillator. A real one does not produce a single frequency; it produces a peak with skirts. Those skirts mix strong neighbouring signals onto the wanted channel exactly as the carrier does. Phase noise is therefore often the limit on how closely two channels can be spaced. That makes it a system parameter rather than a component detail.

What you should now be able to explain or do

• Check an amplifier for stability before matching it, using its parameters.
• Explain why the noise match and the power match are different impedances.
• Say why a transmitter amplifier trades linearity against efficiency.
• Describe a mixer as a multiplier and derive the two output frequencies.
• Explain the image and name the three standard ways of removing it.
• Say what phase noise is and why it limits channel spacing.

Check yourself