CHAPTER 4:
FREQUENCY CONVERSION
HF requires HF amplifiers, tunable filters: those are power hungry and expensive
Tunable filters are difficult to build, and have lower order
Superheterodyne receiver
Down converting receiver: converts the incoming HF signal (var) into a fixed lower IF
We mix the incoming RF signal with a local oscillator (LO) signal
ARCHITECTURE OF A SUPERHETERODYNE RECEIVER
Architecture
Preselector filter: suppresses unwanted input frequencies
Low Noise Amplifier: provides sensitivity (the mixer noise figure is quite high)
Mixer: converts wanted input signal into fixed Intermediate Frequency (IF) pass band
IF amplifier/filter: provides most of the gain and filtering (channel separation)
Demodulator can be digital in modern receivers (e.g. after IF sampling A/D conversion)
Local Oscillator: provides a high-purity sine or square wave at a well-known
frequency offset from the desired RF input frequency.
Max gain: 120 to 140 dB, but IF amplifier must remain linear with strong input signals
 for amplitude-sensitive modulation formats (AM,QAM…), so a gain control element
is placed upfront to reduce the gain for strong signals, and an Automatic Gain
Control (AGC) loop is closed.
Other control loops can be added, such as Automatic Frequency Control (AFC).
Amplitude-insensitive modulation (FM/FSK/PSK…) yields a more simple receiver:
 can be handled by a limiting IF amplifier, no AGC needed.
Super with single down conversion
fLO = fRF + fIF
 We want: LOW IF but not too low: beware of image at fRF + 2*fIF
We prefer fLO = fRF PLUS fIF => smaller relative bandwidth
Tune the preselector to reject the strong RF signal
Super with upconversion
When we have a very wide (relative) input f range (e.g. spectrum/network analyzer)
One uses a series down convertor to lower the f again
Image-rejection mixing
When using a low IF: or else the preselector has to
Be very narrow and steep
=>
Homodyne receiver
A super with zero IF frequency
Modulation formats with residual carrier (AM, DSB)
More RF gain needed 
BASICS OF MIXING
Non-linearity and time-variance
LTI cannot produce spectral components that are not present in the input signal(s)
A mixer is nonlinear and/or time-invariant
Multiplication of two sine waves in time domain => sine at sum and diff frequency
Conversion gain
Ratio of the IF amplitude to the incoming RF amplitude (proportional with LO level)
Mixer linearity
Invariability of the conversion gain
Mixer isolation
Caveat: LO signals are very strong, isolate them from IF and RF
Physically separate ports, filter signal (or avoid spectra overlap), balanced circuits
SSB vs. DSB noise figure/factor
Ratio of input to output SNR (RF => IF)
Mixer converts two input spectra into one IF spectrum
DSB: noise figure of manufacturer
SSB:
Low noise receiver; LNA with low NF and enough gain
High LNA gain : strong signals to be mixed => linearity 
Input spectrum is noisy: omit the LNA for highest linearity
Passive mixer
Stable, low NF  but attenuate 
Active mixer
Less LNA or IF gain needed, less noise at IF input  but noisier and less linear 
A NON LINEAR SYSTEM AS A LINEAR MIXER
Quadratic two-port as a linear mixer
Perfect mixing: only 1st and 2nd order harmonics and unwanted mixing product needs to
be suppressed.
When using a higher LO: higher order nonlinearities arise. => Conversion gain changes
Quadratic two-port FET mixer
A MOSFET in long-channel regime has a quadratic characteristic.
High ZL => better conversion gain
Low ZL => less Miller effect = better isolation = better linearity
Quadratic two-port FET mixer with source LO injection
Better LO-RF isolation
Same VGS but more LO power
Zsource is lower
=>
Quadratic BJT mixer
Becomes =>
MULTIPLIER AS MIXER
Better separation of RF, LO, IF
Balanced mixer has a better isolation suppress even order products
Switching mixers: square wave LO => tolerant for LO noise and amplitude variation
Active single balance mixer
M3 must be very linear: vRF to iRF
Diff pair M1/M2: each takes the full tail current during half LO per.
Transformer: recombines both output currents to the load
Mixer transconductance
Use lowest order IM = IF
Port isolation
Check RF->IF isolation
 Remove the LO signal
 Short LO port, without
disturbing the bias
 High inter-port isolation
Increase mixer linearity (M3)
Use feedback around M3
Check LO->IF isolation
 Short the RF port using couple capacitors
 Mixer is diff amplifier for LO signal

 “Single balance”
ACTIVE DOUBLE BALANCE MIXER
Apply a second level of symmetry => we have a virtual ground!
LO in parallel, IF in anti-parallel
Linearization, differential RF
Use inductive source degeneration
Low VDD circuit
LC tank is in “series” with the output=> suppresses unwanted
Output frequencies
Gilbert cell: 4 more linearization techniques
LO input level
high enough for switching with short transitions
not too high can cause voltage peaks CS/E points
1. Pre-distortion
Create pre-distorted RF signal: compensate for the
exp BJT VBE-IC law
Diode makes a log(vRF) voltage input for B3
2. Positive feedback
CROSS QUAD circuit
If iIN increase: M4 & M2 more I_D
So a higher VGS
But voltage on A and B is the same
RF signal feels virtual short between A & B
3. Feed forward
CASCOMP circuit: cascade diffpair M1-4
Extra diff pair M5,6 (more parasitic)
4. Piecewise linearization
 Diffpairs show good linearity for VB, 0, -VB
More parasistics!
DIODE MIXERS
No DC power supply, GC < 0 dB, stable
Schottky diode: Majority carrier device => fast!,
low parasitics
Single diode mixer
VIN = RF + LO + Bias voltage
Used for EHF
AM envelope: drop L, use RC time constant
No isolation and poor linearity
Single-balance diode mixer
Induce switching and one level of symmetry
LO-IF isolation: short at RF = reproduced at IF
RF-IF isolation: lack of symmetry no isolation
Double-balance diode mixer
2nd level of symmetry
LO positive => D3 & D4 conduct => ground of T1 is
Reproduced at D => vRF = vIF, LO neg => vRF = -vIF
LO must be higher than RF to keep diodes work
Higher breakdown => put 2 or more diodes in series
but requires more LO power
max 5 GHz