Question 4.66: Thermometer Design Problem There is a need to design a therm......
Thermometer Design Problem
There is a need to design a thermometer that can read from 350º C to 1100º C to monitor the temperature of a rocket’s nose cone. The output will feed a 0- to 5-V ADC prior to transmission of the temperature data to the ground. The 350º C will deliver 0 V to the ADC, while 1100º C will deliver 5 V. Select from Figure P4-55 an appropriate thermocouple and design the instrumentation amplifier. Other criteria are: the transducers have a 15-Ω series resistance, the fewer OP AMPs the better, since power is limited, the maximum OP AMP gain is 1000, and the bias voltage, if needed, must be from the available 5-V supply.
The temperature range in Figure P4-55 does not extend to 1100° C, but we will assume the thermocouple is linear beyond 1000° C. Thermocouple K is a reasonable choice, since it is linear across the required temperature range. At 350° C, its output voltage is approximately 14 mV. At 1000° C, its output voltage is approximately 42 mV. If we extend the line to 1100° C, the output should be approximately 46 mV, as shown below.
Script File
clear all
format short eng
% Compute the expected thermocouple voltage at 1100 degrees
% assuming linear operation.
T1 = 350;
T2 = 1000;
T3 = 1100;
V1 = 14e-3;
V2 = 42e-3;
V_per_T = (V2-V1)/(T2-T1);
V3 = V2 + (T3-T2)*V_per_T
V3 =
46.3077e-003
Use MATLAB to calculate the required gain and bias for this interface.
syms K vBias
% 350 deg: 14 mV input maps to a 0 V output
% 1100 deg: 46 mV input maps to a 5 V output
Eqn1 = '0 - (K*14e-3 + vBias)';
Eqn2 = '5 - (K*46e-3 + vBias)';
Soln = solve(Eqn1,Eqn2,'K','vBias');
K = double(Soln.K)
vBias = double(Soln.vBias)
K =
156.2500e+000
vBias =
-2.1875e+000
The following circuit meets the interface specifications.
The first stage of the circuit is an inverting amplifier with a high input impedance and a gain of -5. The second stage is an inverting summer with gains of -31.25 and -0.4375 to produce the correct final gain and bias for the interface. Other correct designs are possible.
Answer:
Presented above.
