Pitt MEMS 1082 - Mechatronics (27 pages)

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Mechatronics



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Mechatronics

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Pages:
27
School:
University of Pittsburgh
Course:
Mems 1082 - ELECTROMECHANICAL SENSORS AND ACTUATORS
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MEMS1082 Mechatronics Chapter 5 4 Operational amplifier Instrumentation amplifier Very high input impedance Large common mode rejection ratio CMRR Capability to amplify low level signals Consistent bandwidth Integrator Lossless capacitor 1 RC VO yt 1 RC t o x t dt t o vin dt t k x t dt o Differentiation and integration VO 1 RC t o vin dt Improved Integrator Lossy capacitor Rs is shunt resistor Rs 10R1 The use of shunt resistor is to limit the low frequency gain of the circuit Otherwise a small DC offset at the input would be integrated over time eventually saturating the op amp DC offset due to the input bias current can be minimized by R2 Choose R2 R1 Rs R1 Rs Integrator Example vs 15e vo 0 2t ut V 10 V Find vo t for t 0 Summing Integrator ic t vc t vc t i1 t 1 C 1 C i2 t t o t 0 v1 t R1 v2 t R2 x1 t R1 ic t dt v1 t R1 v2 t dt R2 yt yt x2 t R2 t 0 t 0 x1 t R1C k1 x1 t x2 t dt R2C k2 x2 t dt Differentiator Differentiator The input signal to the differentiator is applied to the capacitor The capacitor blocks any DC content so there is no current flow to the amplifier summing point resulting in zero output voltage The capacitor only allows AC type input voltage changes to pass through and whose frequency is dependant on the rate of change of the input signal At low frequencies the reactance of the capacitor is High resulting in a low gain Rf Xc and low output voltage from the op amp At higher frequencies the reactance of the capacitor is much lower resulting in a higher gain and higher output voltage from the differentiator amplifier Differentiator Improved Differentiator Amplifier Example Integrator and Switch An integrator and a voltage controlled switch An integrator is a circuit that can perform the mathematical operation of integration The output voltage vo t is related the input of the integrator vs t v0 t K t2 t1 vs t dt vo t1 Integrators have many applications One is to measure a time interval t2 t1 v 0 t2 K t 2 t1 Vs vo t1 Example Integrator and Switch Voltage controlled switch Switch can be controlled electronically The node voltage vc t is called the control voltage Example Integrator and Switch To design an integrator circuit v o t2 v o t2 K Vs K t 2 t1 Vs vo t1 10V t2 t1 200ms 10V 200ms K 10 1 s Example vo 1 RC 1 RC K t2 t1 vs dt C 1 F R 1 10 V s 1 F 100k vo t 50 t t1 Op Amp Open Loop Gain In Op amp practically the gain is so high that the output will be driven to Vcc or Vcc for any appreciable difference between V1 and V2 This is useful in the comparator For practical applications other than the comparator negative feedback is used to control the device gain Comparator The extremely large openloop gain of an op amp makes it an extremely sensitive device for comparing its input with zero For practical purposes if V2 V1 the output is driven to the positive supply voltage If V2 V1 it is driven to the negative supply voltage The switching time for to is limited by the slew rate of the op amp Comparator The basic comparator will swing its output to at the slightest difference between its inputs But there are many variations where the output is designed to switch between two other voltage values VH and VL Also the input may be tailored to make a comparison to an input voltage VT other than zero Comparator application Often it is desirable that switching occurs at prescribed voltage Comparator can be used for this purpose vo t VH if v v VL if v v VH and VL are the only two values that vo t can have Comparator Example For the following circuit suppose VA VT vc 0 VT is a threshold voltage and the input voltages for the comparator are vo t VH if vc t VT VL if vc t VT VA vc 0 v vc t v VT The output voltage The capacitor voltage vc t At t1 the comparator voltage switches from VL to VH VT VA vc 0 VA e t1 RC t1 RC ln vc 0 VA VT VA VA e t RC Comparator Example For the shown circuit the initial value of the capacitor voltage is vc 0 1 667V What value of the resistance R is required if the comparator is to switch from VL to VH at time t1 1ms Comparator Example For the shown circuit the comparator is used to compare the resistor voltage vR t with a threshold voltage VT Suppose VA VT RiL 0 At time t1 the comparator output voltage switches from VL to VH iL t VT VA R RiL t iL 0 VA VA e R RiL 0 R t L VA e R t1 L t1 L RiL 0 VA ln R VT VA Comparator Example For the shown circuit the initial value of the inductor is iL 0 1mA What value of the inductance L is required if the comparator is to switch from VL to VH at time t1 10ms The Sample and Hold circuit When The Sample and Hold circuit uses two buffers to keep a voltage level stored in a capacitor Pressing Ssample will charge the capacitor to the present signal level while the input buffer ensures the signal won t be changed by the charging process From there the output buffer will make sure that the voltage level across the storage cap won t decrease over time Pressing Sclear will short out the storage cap discharging it and setting the output to 0V We can build the Sample and Hold circuit with mechanical pushbutton switches to see it in action In actual practice the switches used are various forms of transistor switch which provides cleaner switching and also allows another circuit to control the sample and clearing operations Uses of Linear Op Amp Circuits Amplifiers Making signals bigger Summing Amp Mixing e g audio applications Analogue arithmetic Integrator Analogue computing Active filter design Difference Amp Balanced line receivers Ideal Op Amp Linear Circuit Analysis 1 I 0 and I 2 V V 3 VOUT 0 anything When negative feedback is applied the use of these assumptions makes design analysis much easier although not necessarily simple Of course they aren t really true


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