Online proceedings - EDA Publishing Association

11-13 May 2011, Aix-en-Provence, France
R1
V in
+
V +
VerilogA
OUT
-
V −
V
Transconductance
amplifier output
R2
Rf
Resonator
input
C1
Fig. 6. Integrator block
From now, these blocks stand as the MEMS oscillator model,
which consists of the association of the resonantor and the
oscillator circuit. Then transient simulations can be performed
and compared to experimental measurements to validate the
model.
Fig. 7. Starting oscillator
This accelerometer being modelled by equation (1), the
theoretical resonance frequency f 0 is given by (6) and (7)), and
should be 59,5kHz using values from Table 1:
k x
2
ω
0 = with ω
0
= 2π
f0
(6), (7)
m
III.
MODEL SIMULATIONS
One finds the same value from direct measurement on the VIA
and from temporal simulations.
A. Transient simulation
The Cadence transient simulation allows solving the current
and voltage in each node of the MEMS oscillator model. To
run the simulations, it becomes necessary to input a Dirac
spike on the transconductance amplifier. Indeed, this type of
self-sustained oscillator starts from the white noise flowing in
the loop. As the loop gain is greater than one at the resonator
eigenfrequency f 0 , it is the only frequency amplified.
17µs
Transconductance
amplifier output
In order to validate the model, simulations are performed
taking into account the parameters of the VIA Vibrating Beam
Accelerometer developed at ONERA [4] shown in table 1.
TABLE I
VIA accelerometer parameters
m (kg) ρ x (kg/s) k x (kg/s²)
1.10 -8 3,1.10 -7 1,4.10 3
These parameters have been extracted from measurements on
existing VIA devices.
The starting oscillator is shown in figure 7:
Resonator
input
Fig. 7. Transient simulation
Indeed, the transient simulation shows about a 17µs period i.e.
59kHz frequency. Moreover, the transconductance amplifier
has multiplied the amplitude by 10 and is limited by the
Automatic Gain Control.
B. Phase noise simulations
Once the resonance frequency is found, the Virtuoso
SpectreRF Simulator can simulate the loop phase noise.
The interesting point of this model resides in the control
possibility of the system parameters on each block. Thus, it is
possible to obtain the evolution of the phase noise as a
function of the resonator physical parameters. Phase noise
simulation is performed using the PSS module (Periodic
Steaty-State).
The module advantage is the simulation time. Indeed, it avoids
the long time temporal simulation.
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