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Automatic Gain Control Circuit for
Quartz Crystal Microbalance (QCM)
By
Abhijat Goyal
&
Saliya Subasinghe
What is QCM
Quartz
Top Electrode
Bottom Electrode
Addition of mass on the surface of the resonator causes
changes in its resonance frequency.
Sauerbrey Equation
2 f 2

m
f   0


A


q
q


Objective of the Circuit

Maintain the amplitude of oscillation to be
constant.

Compensate for the change in motional
resistance (Rm) due to change of
ambience of the resonating crystal.

We need a circuit with feedback control
which can dynamically adjust to changing
Rm of the oscillator, in order to sustain
oscillations.
Proposed circuit
Mixer Simple Amplifier
½ Wave
Rectifier
Unity Gain
Stage
Integrator
Proposed circuit
Offset
Control
Mixer
Unity
Gain
Buffer
Output
Buffers
Integrator
Integrator
This resistor and capacitor
determine the time constant of
the integrator
These two resistor
bias the opamp at
2.5V
Average power of this
circuit = 1.9 mW
Maximum power of this
circuit = 1.9 mW
Determines the
amplitude of input
waveform.
Small high to low
transition at input
Large low to high
transition at input
Large high to low
transition at input
Minimum Attenuation of high
Frequency signal passing through
Input-Output curve
Idea was to make this part of the curve as less steep as
possible.
Multiplier
Vout = KRfVin2Vin1 – KRfVTVin1 + Vin1
where K = μoCoxW/L
VT and K are constant
If we set Rf =1/(KVT)
Vout = (Vin2Vin1)/VT
When Vin1 ≤ Vin2 - VT
G.A. Hadgis, P.R. Mukund, "A novel CMOS monolithic analog multiplier with wide input dynamic range," vlsid, p. 310,
8th International Conference on VLSI Design, 1995.
Unity Gain Buffer
Compensation
Voltage Buffer using Multiplier

How do we implement a buffer using the
circuit topology for the multiplier?

Vout = KRfVin2Vin1 – KRfVTVin1 + Vin1

K is on the order of magnitude 10-6

Make Rf small

Then Vout ~ Vin1
Questions?