Quartz Crystal Microbalance Digital Controller

24 Theory, Operation and Calibration Chapter 23. A source resistance, R s , of 100 . This source resistance consists of two series 50 resistors, one of which is inside the amplifier A 1 . This source impedance is reducedby a factor of 4 x, to 25 , by the 2:1 transformer which follows.4. An isolation transformer with a 2:1 turns ratio, hence an attenuation of A t = 0.5. Thistransformer allows galvanic isolation of the crystal from the oscillator circuit whichis important in electrochemistry applications. In addition to reducing the sourceimpedance by 4 x, the transformer also increases the load impedance seen at the inputof the transformer by 4 x, so that when R m = 0 , the load will be 200 .5. R m , the motional resistance of the crystal at series resonance. R m can vary from about10-40 for a dry crystal, to about 375 for a crystal in water, to about 5 k for acrystal in 90% (w/w) glycerol/water solution.6. A second isolation transformer with a turns ratio of 1:1. This transformer allowsgalvanic isolation of the crystal from the oscillator circuit.7. A load resistance, R L , of 50 . The network of R s , R m , and R L provide a networkattenuation, A n , which depends on the crystal’s motional resistance.ARLn = Rs4 + Rm+ R(eqn. 2)L8. An RF amplifier with an adjustable gain, A 2 , of about 4.43 x. The gain of thisamplifier, A 2 , is set during calibration to compensate for gain variations of all theother circuit elements.9. A low pass filter. This filter is a 5 th order Bessel low pass filter with f c = 3.7 MHz,adjusted so as to provide 180º of phase shift at 5 MHz. The phase shift of this filter,together with the 180º phase shift of the inverting amplifier A 1 , provides the 360º ofphase shift necessary for oscillation. The low pass filter is required to suppressspurious oscillations which would occur due to the high bandwidth of the loopamplifiers. The low pass filter attenuates a signal at 5 MHz by about A f = -7.8 dB (or0.407x).The motional resistance of the crystal at series resonance can now be computed. Theproduct of the gain (or attenuation) of all of the elements around the loop is exactly onewhen the circuit is oscillating at constant amplitude. Hence,A A A A A A 1(eqn. 3)a 1 t n 2 f =Rearranging and substituting the equation for A n and solving for R m ,1AnR4 + R+ RA( A A A A )s m L= = a 1 t 2 f(eqn. 4)RLRmRs= RL Aa( A1 At A2 Af)- RL-(eqn. 5)4From the characteristics of the voltage variable attenuator described above, A a = 10 -Vc/5 ,where V c is the voltage at the Conductance output BNC on the QCM200. A 2 is adjustedQCM200 Quartz Crystal Microbalance