 # The circuits in Figures 1a and 1b are signal conditioning circuits ...

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The circuits in Figures 1a and 1b are signal conditioning circuits for measuring temperature within 0⁰C to 150⁰C in an industrial process using a resistance temperature detector (RTD). The Pt100 parameters are 𝛼 = 0.00385 𝐾 −1 and 𝑅𝜃 = 12.5 °𝐶/𝑊. a) Find the maximum current through the pt100 for a self-heating error less than 0.2⁰C. b) Design the bridge circuit so it complies with a non-linearity error less than 1.5%. The excitation voltage could be within the range of 0 to 30V for circuit in Figure 1a and the current source excitation could be selected between 0 to 10mA for circuit in Figure 1b. c) Propose a circuit that can amplify the voltage across the bridge sensing terminals. The circuit should output 0V at 0⁰C and 2V at 150⁰C. d) The output voltage of the circuit in part c (0V-0⁰C and 2V-150⁰C) is digitalised using an ADC. If the reference voltages of the ADC are Vref-=0 and Vref+=10V, find the temperature resolution after the signal conditioning circuit discuss in the previous section when the total number of bits during the ADC conversion process is 14 bits. e) The output voltage of the circuit explained in part c is displayed in an analogue temperature scale using a moving coil meter. The sensitivity of the moving coil meter is 100⁰C/mA and its maximum current is 3mA. A suitable circuit for displaying the right temperature in the moving coil meter is a voltage controlled current source. Explain a circuit that could be used for this purpose. Figure 1A. pt100 signal conditioning circuit Figure 1b. pt100 signal conditioning circuit RELEVANT FORMULAE   2 a t  = − =  t t t R I R C  t t I R R  = Voltage excitation 1 B s R V V R R = + 1 x A s x R V V R R = + 1 1 x AB s x R R V V R R R R   = −     + + 1 1 1 , 1 1 1 1 1 1 1 x x x x R R AB s s AB lin s s x x R R R R R R R R R R V V V V V V R R R R R R R R R R R R R   − − − = − = ⎯⎯⎯→ = =     + + + + + + If the bridge is designed according to the following resistor values: ( ) ( ) ( ) ( ) 1 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 0 , 1 2 1 1 1 1 1 x R rR R R x x R R t AB s s AB s x x AB s AB lin AB s r t R R R rR R R R t R V V V V V R R R R R R R R rR R rR R t r t r t V V V V V r r t r        = = = + +   − + − = − = ⎯⎯⎯⎯⎯→ =     + + + + + + +  = → = = + + + + The linearity error is defined:   , % 100% 100% 1 AB AB linear LV AB V V t V r   − = = − + Current excitation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 2 1 || || 1 1 1 1 1 1 1 1 || || x x x R R R R I I R R R R R R I I R R x x AB A B x AB x x R R R R R R R R V V V I R I R V I R R R R R R + + = + + + = +   + + + + = − = − ⎯⎯⎯⎯⎯⎯⎯→ = −     + +   ( )( ) ( ) ( )( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 x x x x x AB x x x x x x AB x R R R R R R R R R R R R R R R R R R V I R R I R R R R R R R R R R R R R R R V I R R R   + + + +   + + + +   + + = − = −       + + + + + +         − =   + +   ( ) 0 1 x R R t = + 1 0 R rR = ( ) ( ( ) ) ( ) ( ) 1 0 0 0 0 0 1 0 0 0 1 2 2 1 2 2 2 1 x AB x R R R rR R t R R r t r t V I I I IR R R R rR R R t r t r t         −   + −     = = = =               + + + + + + + + +       ( ) ( ) , 0 , 0 2 1 2 1 r t AB ideal AB lin r t r t V IR V IR r t r          = ⎯⎯⎯→ =         + + +     ( ) , , , 0.77 1 1 39.5 2 1 2 0.02 AB ideal AB lin r AB ideal r V V t t e r V r e −  − − = = − →  − = − = + The schematic in Figure 2a and 2b are astrain gauge signal conditioning circuits. These circuits are used to monitor strain in a beam. The range of strains considered in this application is between 0 µε and 5000 µε. The strain gauge has a nominal resistance of 200Ω and a gauge factor of 2. a. Find the voltage drop across the Wheatstone bridge sensing terminals if the bridge excitation voltage Vs is 10V. b. Find the voltage drop across the Wheatstone bridge sensing terminals if the bridge excitation current is 10mA. Assume that R1 =R in your calculations. c. Find the voltage gain required for an output voltage of 10V when the gauge is under a strain of 5000 µε (0V-0 µε and 10V-5000 µε). Explain a suitable signal conditioning circuit required for this application. d. The output voltage of the circuit in part b is digitalised using an ADC. If the reference voltages of the ADC are Vref-=0 and Vref+=10V, find the strain resolution after the signal conditioning circuit discuss in the previous section when the total number of bits during the ADC conversion process is 12 bits. e. The output voltage of the circuit explained in part c is displayed in an analogue temperature scale using a moving coil meter. The sensitivity of the moving coil meter is 1000 µε/mA and its maximum current is 10mA. The circuit for displaying the temperature in the moving coil meter is a voltage controlled current source as shown in Figure Q3. Provide the resistor value required to display the right temperature values. Justify your answer. Figure 2a. Wheatstone bridge using voltage excitation Figure 2b. Wheatstone bridge using current excitation Figure 3. Moving coil meter circuit RELEVANT FORMULAE Current excitation ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 1 1 1 1 1 2 1 || || 1 1 1 1 1 1 1 1 || || x x x R R R R I I R R R R R R I I R R x x AB A B x AB x x R R R R R R R R V V V I R I R V I R R R R R R + + = + + + = +   + + + + = − = − ⎯⎯⎯⎯⎯⎯⎯→ = −     + +   ( )( ) ( ) ( )( ) ( ) ( ) ( ) 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 x x x x x AB x x x x x R R R R R R R R R R R R R R R R R R V I R R I R R R R R R R R R R R R   + + + +   + + + +   + + = − = −       + + + + + +       x R R R = +  1 R R = ( ) 2 2 4 4 4 AB R R R R V I R R R I R R R R R R R   +   = +  − =     +  +  +  4 , , 4 4 4 4 R R AB ideal AB lin R R R KR V I R I V I I R R R R      = = ⎯⎯⎯⎯→ = = +   + The linearity error is defined as ( ) , , ( ) , , , , 4 4 4 4 4 4 4 4 4 4 4 4 4 4 AB ideal AB lin r AB ideal AB ideal AB lin r AB ideal RR R R R R R R R I R I R V V R R R R R R e V R R R I R R R R R R R R R V V R R R K e V RR R   −  +      − − − +  +  +  = = = =    +  +  +  − −   = = = =  A suitable signal conditioning circuit

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