Difference between revisions of "GradFinalLab RS"

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==Identify the input voltage threshold levels at which a <math> V_{in}</math> will produce <math>V_{out} \approx V_{cc}</math>==
 
==Identify the input voltage threshold levels at which a <math> V_{in}</math> will produce <math>V_{out} \approx V_{cc}</math>==
  
The theory does say:
+
The theory does say (ch. 10.19 The Schmitt Trigger R. Simpson "Introductory electronics for scientists and engineers"):
 +
 
 +
<math>V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{out}</math>
  
 
1) if the output is high:
 
1) if the output is high:
  
  <math>V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{cc}</math>
+
  <math>V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{out_1}</math>
  
 
2) if the output is low:
 
2) if the output is low:
  
  <math>V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{cc}</math>
+
  <math>V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{out_1}</math>
  
 
where
 
where
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Here a little trick to improve my predicted threshold voltages. Because in real circuit <math>V_{cc} \neq V_{out}</math> I am going to use the actual values of <math>V_{out}</math> in the formulas above instead of <math>V_{cc}</math>, which are:
+
 
 +
The actual measured values of high and low output voltages are (they do not really equal to <math>\pm V_{cc}</math>):
  
 
# <math>V_{out_1} =  (+11.06\pm0.01)\ V</math>
 
# <math>V_{out_1} =  (+11.06\pm0.01)\ V</math>
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By substituting the actual values:
+
Substituting all values in the formulas above:
  
  <math>R_{123} = (R_1 || R_2 || R_3) = \frac{R_1 R_2 R_3}{R_1+R_2+R_3}</math>
+
  <math>R_{123} = (1.01\pm 0.01)\ k\Omega || (1.01\pm 0.01)\ k\Omega || (5.10\pm 0.05)\ k\Omega = (0.459\pm 0.003)\ k\Omega</math>
  
  <math>V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{cc}</math>
+
  <math>V_2 = \frac{(0.459\pm 0.003)\ k\Omega}{(1.01\pm 0.01)\ k\Omega}(11.90\pm 0.01)\ V + \frac{(0.459\pm 0.003)\ k\Omega}{(5.10\pm 0.05)\ k\Omega}(11.06\ pm 0.01)\ V</math>
  
 
  <math>V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{cc}</math>
 
  <math>V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{cc}</math>

Revision as of 03:10, 27 April 2011

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Construct a Schmitt Trigger using the 741 Op Amp

Draw the Schmitt Trigger circuit you constructed. Identify the values of all components

Schmitt trigger 01.png

To construct the circuit above I am going to use the following components and voltages:

  1. R1=(1.01±0.01) kΩ
  2. R2=(1.01±0.01) kΩ
  3. R3=(5.10±0.01) kΩ
  4. OP AMP 741
  5. Vref=(+11.90±0.01) V
  6. Vcc=(+11.90±0.01) V
  7. Vee=(12.11±0.01) V

Graph Vout as a function of Vin. Is there a hysteresis loop?

Identify the input voltage threshold levels at which a Vin will produce VoutVcc

The theory does say (ch. 10.19 The Schmitt Trigger R. Simpson "Introductory electronics for scientists and engineers"):

[math]V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{out}[/math]

1) if the output is high:

[math]V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{out_1}[/math]

2) if the output is low:

[math]V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{out_1}[/math]

where

[math]R_{123} = (R_1 || R_2 || R_3) = \frac{R_1 R_2 R_3}{R_1+R_2+R_3}[/math]


The actual measured values of high and low output voltages are (they do not really equal to ±Vcc):

  1. Vout1=(+11.06±0.01) V
  2. Vout2=(10.54±0.01) V


Substituting all values in the formulas above:

[math]R_{123} = (1.01\pm 0.01)\ k\Omega || (1.01\pm 0.01)\ k\Omega || (5.10\pm 0.05)\ k\Omega = (0.459\pm 0.003)\ k\Omega[/math]
[math]V_2 = \frac{(0.459\pm 0.003)\ k\Omega}{(1.01\pm 0.01)\ k\Omega}(11.90\pm 0.01)\ V + \frac{(0.459\pm 0.003)\ k\Omega}{(5.10\pm 0.05)\ k\Omega}(11.06\ pm 0.01)\ V[/math]
[math]V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{cc}[/math]

and doing math and handling the error propagation we end up with the following threshold voltages:

[math]V_2 = [/math]
[math]V_2^' =[/math]

Compare the threshold values to what is expected.

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