A pressure sensor outputs a voltage varying as 100 mV/psi and has a 2.5- output impedance. Develop signal conditioning to provide 0 to 2.5 V as the pressure varies from 50 to 150 p... A pressure sensor outputs a voltage varying as 100 mV/psi and has a 2.5- output impedance. Develop signal conditioning to provide 0 to 2.5 V as the pressure varies from 50 to 150 psi.
Understand the Problem
The question is asking us to design a signal conditioning circuit for a pressure sensor that outputs a specific voltage range corresponding to pressure variations. Specifically, it requires transforming the output voltage from a certain range into another specified range as the pressure changes.
Answer
The output voltage from the pressure sensor must be scaled down by a factor of $-\frac{1}{6}$ and offset by $-\frac{5}{6} \, \text{V}$.
Answer for screen readers
To convert the output voltage from a pressure sensor from $[5 , \text{V}, 15 , \text{V}]$ to $[0 , \text{V}, 2.5 , \text{V}]$, you need a gain of $-\frac{1}{6}$ and an offset of $-\frac{5}{6} , \text{V}$ applied using an op-amp circuit.
Steps to Solve
- Understand the sensor's output characteristics
The pressure sensor outputs a voltage of $100 , \text{mV/psi}$. Therefore, the voltage output ($V_{out}$) at a given pressure ($P$) can be calculated as: $$ V_{out} = 100 , \text{mV/psi} \times P , (\text{in psi}) $$
- Calculate the voltage range for specified pressures
We need to calculate the voltage output for the minimum and maximum pressures:
-
At $P = 50 , \text{psi}$: $$ V_{out(min)} = 100 , \text{mV/psi} \times 50 , \text{psi} = 5000 , \text{mV} = 5 , \text{V} $$
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At $P = 150 , \text{psi}$: $$ V_{out(max)} = 100 , \text{mV/psi} \times 150 , \text{psi} = 15000 , \text{mV} = 15 , \text{V} $$
- Determine necessary adjustment for output
The output voltage needs to be converted from the range $[5 , \text{V}, 15 , \text{V}]$ to $[0 , \text{V}, 2.5 , \text{V}]$.
- Find the scaling factor
To convert from $5 , \text{V}$ to $2.5 , \text{V}$:
- The voltage needs to be scaled down by a factor of $k$. We calculate: $$ k = \frac{2.5 , \text{V}}{15 , \text{V}} = \frac{1}{6} $$
- Find the offset required
To adjust the range, we also need to adjust the output by adding an offset. The new output range is:
- With the scaling defined, calculate offset: Let the offset be $O$ such that:
$$ k \cdot V_{out(min)} + O = 0 $$ $$ \frac{1}{6} \cdot 5 + O = 0 $$ Solving gives: $$ O = -\frac{5}{6} , \text{V} $$
- Construct the signal conditioning circuit
Using an operational amplifier (op-amp) circuit configuration:
- Apply a scaling of $\frac{1}{6}$ and add an offset of $-\frac{5}{6} , \text{V}$.
- Final signal conditioning circuit design
The final circuit would consist of:
- An inverting amplifier with a gain of $-\frac{1}{6}$ and an offset adjustment using resistors to achieve the desired output range.
To convert the output voltage from a pressure sensor from $[5 , \text{V}, 15 , \text{V}]$ to $[0 , \text{V}, 2.5 , \text{V}]$, you need a gain of $-\frac{1}{6}$ and an offset of $-\frac{5}{6} , \text{V}$ applied using an op-amp circuit.
More Information
This design efficiently converts the high output from the sensor into a lower usable range for further processing, ensuring that the full range of pressure is represented appropriately in the voltage output.
Tips
- Not calculating the full range of output voltages from minimal and maximal pressures.
- Misunderstanding the relationship between gain and offset in scaling operations; ensure the correct design of the op-amp circuit with both scaling and offset adjustments.
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