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>==
  
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Because
+
1) if the output is high:
  
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  <math>R = R_1 = R_2 = 1\ k\Omega \ll R_3 = 10\ k\Omega</math>
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  <math>V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{cc}</math>
  
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we can use the approximate formula to calculate the threshold voltages (ch.10.19 the Schmitt Trigger "Introductory electronics for scientists and engineers"):
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2) if the output is low:
  
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1) if the output is high:
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<math>V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{cc}</math>
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 +
where
  
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  <math>V_2 \cong \frac{V_{ref}}{2} + \frac{R}{2R_3}V_{cc}</math>
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  <math>R_{123} = (R_1 || R_2 || R_3) = \frac{R_1 R_2 R_3}{R_1+R_2+R_3}</math>
  
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2) if the output is low:
 
  
−
<math>V_2^' \cong \frac{V_{ref}}{2} - \frac{R}{2R_3}V_{cc}</math>
 
  
 +
By substituting the actual values:
  
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By substituting the actual values and doing math and error propagation we find:
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<math>V_2 = \frac{R_{123}}{R_2}V_{ref} + \frac{R_{123}}{R_3}V_{cc}</math>
  
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  <math>V_2 \cong \frac{(15\pm 0.01)\ V}{2} + \frac{(1\pm 0.01) k\Omega}{2\cdot(10\pm 0.01) k\Omega}(15\pm 0.01)\ V = (8.25\pm 0.009)\ V</math>
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  <math>V_2^' = \frac{R_{123}}{R_2}V_{ref} - \frac{R_{123}}{R_3}V_{cc}</math>
  
−
<math>V_2^' \cong \frac{(15\pm 0.01)\ V}{2} - \frac{(1\pm 0.01) k\Omega}{2\cdot(10\pm 0.01) k\Omega}(15\pm 0.01)\ V = (6.75\pm 0.009)\ V </math>
+
and doing math and handling the error propagation:
  
 
==Compare the threshold values to what is expected.==
 
==Compare the threshold values to what is expected.==

Revision as of 15:08, 26 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. [math]R_1 = (1\pm)\ k\Omega[/math]
  2. [math]R_2 = (1\pm)\ k\Omega[/math]
  3. [math]R_3 = (10\pm)\ k\Omega[/math]
  4. [math]\mbox{OP}\ \mbox{AMP}\ 741[/math]
  5. [math]V_{ref} = (15\pm)\ V[/math]
  6. [math]V_{cc} = (15\pm)\ V[/math]
  7. [math]V_{ee} = (15\pm)\ V[/math]

Graph [math]V_{out}[/math] as a function of [math]V_{in}[/math]. Is there a hysteresis loop?

Identify the input voltage threshold levels at which a [math] V_{in}[/math] will produce [math]V_{out} \approx V_{cc}[/math]

1) if the output is high: 

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

2) if the output is low: 

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


By substituting the actual values: 

[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]

and doing math and handling the error propagation:

Compare the threshold values to what is expected.

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