Practice Problems (KEY)#
An inertial navigation system’s (INS) accelerometers put out \(-70\ \text{mV}\) when \(-5g\) is detected and \(20\ \text{mV}\) when \(5g\) is detected. An aircraft’s navigation system reads voltages between \(-7\ \text{V}\) and \(2\ \text{V}\) when the detected signal is between \(-5g\) and \(5g\). Design a signal conditioning circuit to adjust the INS to the nav system.
Linear Model: \(V_{\text{out}} = K V_{\text{in}} + B\)
At \(-5g\): \((-70\ \text{mV})K + B = -7\ \text{V}\)
At \(5g\): \((20\ \text{mV})K + B = 2\ \text{V}\)
Subtracting: \((90\ \text{mV})K = 9\ \text{V}\) → \(K = 100\)
Solving for \(B\): \((-70\ \text{mV})(100) + B = -7\ \text{V}\) → \(B = 0\)
Final System: Amplifier only with \(K = 100\).
An elevator for a UAS requires \(1\ \text{V}\) to move the elevator fully down and \(-9\ \text{V}\) to move the elevator fully up. The pilot’s control column (joystick) produces \(-1\ \text{mV}\) when fully down and \(4\ \text{mV}\) when fully up. Design the interface between the control unit and the actuator.
Linear Model: \(V_{\text{out}} = K V_{\text{in}} + B\)
\((-1\ \text{mV})K + B = 1\ \text{V}\)
\((4\ \text{mV})K + B = -9\ \text{V}\)
Subtracting: \((5\ \text{mV})K = -10\ \text{V}\) → \(K = -2000\)
\((-1\ \text{mV})(-2000) + B = 1\ \text{V}\) → \(B = -1\ \text{V}\)
Final System: Amplifier and summer required.
For each of the following devices, determine whether it is an input transducer, an output transducer, both, or neither.
a. Computer mouse — Input transducer.
b. Electric motor — Output transducer.
c. Stereo speakers — Output transducer.
d. Op amp — Neither.
e. Light bulb — Output transducer.
f. Electronic thermometer — Input transducer.
g. Transformer — Neither.
h. iPhone touch screen — Both.
i. Control stick of a fly-by-wire aircraft — Input transducer.
j. Aircraft HUD (Head Up Display) — Output transducer.
Why don’t we use transformers to amplify information signals?
Transformers conserve power. If voltage increases, current decreases proportionally. True amplification requires increasing power, not simply trading voltage for current.
Transformers require AC signals. Information signals that change slowly or contain DC components will not pass properly through a transformer.
A device that is used to add two or more signals is a
a. Input transducer
b. Output transducer
c. Summer
d. Instrumentation System
Correct Answer: c. Summer
A microphone converts an incoming voice signal to a range of \(\pm 2.5\ \text{mV}\). Design an instrumentation system to amplify this signal to drive a speaker which requires \(\pm 4\ \text{V}\).
Since both ranges are symmetric about zero: \(B = 0\)
Final System: Amplifier with gain \(1600\).
Using the instrumentation system you designed in Problem 6 above, what would the output voltage be if the signal from the microphone was \(1\ \text{mV}\)?
The rudder control unit for a fly-by-wire aircraft produces a \(-2.5\ \text{mV}\) signal when fully left is desired and \(2.5\ \text{mV}\) for fully right. The rudder actuator requires \(-5\ \text{V}\) for fully left and \(+10\ \text{V}\) for fully right.
Linear Model: \(V_{\text{out}} = K V_{\text{in}} + B\)
\((2.5\ \text{mV})K + B = 10\ \text{V}\)
\((-2.5\ \text{mV})K + B = -5\ \text{V}\)
\((5\ \text{mV})K = 15\ \text{V}\) → \(K = 3000\)
\((2.5\ \text{mV})(3000) + B = 10\ \text{V}\) → \(B = 2.5\ \text{V}\)
Final System: Amplifier and summer required.
The flight control computer generates a \(4\ \text{mV}\) signal when the ailerons need to be deflected \(15^\circ\) and a \(-16\ \text{mV}\) signal when \(-20^\circ\) deflection is needed. The aileron actuators require \(15\ \text{V}\) and \(-10\ \text{V}\) respectively.
Linear Model: \(V_{\text{out}} = K V_{\text{in}} + B\)
\((4\ \text{mV})K + B = 15\ \text{V}\)
\((-16\ \text{mV})K + B = -10\ \text{V}\)
\((20\ \text{mV})K = 25\ \text{V}\) → \(K = 1250\)
\((4\ \text{mV})(1250) + B = 15\ \text{V}\) → \(B = 10\ \text{V}\)
Final System: Amplifier and summer required.