TFE 06

1
TFE 06 ASICs for MEMs

• 3rd order intermodulation in Micromechanical
  resonators

2
Outline

1. Introduction
2. Background
3. 1st Order Formulation for IIP3
4. Complete Formulation for IIP3
5. Experimental results
6. Conclusion

3
I. Introduction

• Nowadays cellular and cordless phone
  applications MUST satisfy strict specifications
  for LINEARITY
• µmechanical resonator technology to RF
  communication circuits have been delayed so far
  due to this linearity
• µmechanical signal processors possess sufficient
  linearity for such applications?
• Need to find a complete analytical formulation
  for the IIP3
• Paper deals with a method which is computing IIP3
  of capacitively driven CC-beam µmechanical
  resonators

4
II. Background

• 1) Third Intermodulation distortion (IM3)
• IM3 for a frequency filter occurs when system
  nonlinearities allow out-of-band signal
  components (tones) to generate an in-band
  component SIM3 back at w0 (in-band frequency)
• Quantitatively (in out)
• Finally the transfer function

5
II. Background

• Common case interferers located at frequencies
  ?w and 2?w from the fundamental the quantity
  (2w1-w2) will be equal to w0
• Possibly masking fundamental w0
• Even if Interfering tones outside the filter
  passband
• Still generate an in-band response highly
  undesirable
• The 3rd-order nonlinear term MUST be constrained
  below a minimum acceptable value.
• Most useful metrics to gauge the ability of a
  system to suppress IM3 distortion 3rd-order
  input intercept point IIP3

6
III. 1st Order Formulation for IIP3

• Principle
• Electrode and beam 2 plates of the transducer
  capacitor C(x)
• DC-bias Vp AC vi drive the beam into
  vibration.
• not mechanical nonlinearity that governs the
  degree of IM3 nonlinearity in the capacitive
  transducer.
• Why? vibrate with amplitudes much smaller than
  their lengths (e.g., 100 Angstrom amplitude for a
  40pm-long beam)

7
III. 1st Order Formulation for IIP3

• Total force acting on the suspended mass under an
  applied input Vp-vi
• And with
• You finally get
  

8
III. 1st Order Formulation for IIP3

• And finally, with the fundamental force, we can
  find the input voltage magnitude at the IIP3
• To be noticed IIP3 can be increased by reducing
  Vp and A0 and by increasing d0 and kreff
• Actually all modifications that will increase the
  series motional resistance Rx of the resonator
• Trade off between linearity and resistor size can
  be found (which for matching purposes often must
  be small)

9
IV. Complete formulation for IIP3

• Final equation is fairly close from the reality,
  but actually not exact
• Neglect of the beam bending due to Vp gt Gap
  spacing is a function of y
• kreff should be distributed rather than lumped
• Fully modelisation of effects d(y) and kreff(y)
  must be used to attain FIM3 and Ffund

10
V. Experimental results

• Characteristics of resonator
• IIP3 measurement using the previous test set-up
  with ?w2p (200kHz).

11
V. Experimental results
12
V. Experimental results

• Strong dependence of IIP3 on the initial gap
  spacing d0 it must be accurately known gt
  sufficiently accurate theoretical prediction for
  comparison with measurement.
• Plot of frequency f, versus DC-bias Vp is
  measured, from which the value of d0 is measured
  using results from others papers curve fitting
  with a theorical curve

13
V. Experimental results

• Verify accuracy of results very close agreement
  between measurement and theory
• There is an optimum Vp at which the PIIp3 is
  maximized 3 dBm)
• Vp increases, Rx decreases, hence RQ decreases,
  leading to an increase in PIIp3 . BUT as Vp
  becomes even larger, the IM3 force also steadily
  increases, due to both the direct increase in Vp
  and due to a decrease in d0 caused by Vp-induced
  beam bending. This latter effect begins to
  dominate after some threshold voltage Vp, beyond
  which the PIIp3 decreases with increasing Vp

14
V. Experimental results

• Quantify the dependence of IIP3 on the loaded Q
• Obtained Q of the resonator was controlled by
  adding an RQ resistor in series with the
  resonator.

15
V. Experimental results
16
VI. Conclusion

• Analytical expression for the IIP3 has been
  presented and verified experimentally
• This paper shows us IIP3s as high as -3 dBm for
  a 10 MHz CC-beam terminated via an impedance 3X
  its own series motional resistance.
• This measured value at 10 MHz easily satisfies
  GSM receive path requirements, it is still short
  of the 7.6 dBm needed for RF channel-selection
  in CDMA handsets

17
Questions ?