Difference between revisions of "Lab 23 RS"

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;<math>V_{out}= -\frac{R_2}{R_1} V_1 + \left ( 1 + \frac{R_2}{R_1}\right)V_{io}  + R_2 I_B</math>
 
;<math>V_{out}= -\frac{R_2}{R_1} V_1 + \left ( 1 + \frac{R_2}{R_1}\right)V_{io}  + R_2 I_B</math>
  
Use the above equation and two measurements of <math>V_{out}</math>, <math>R_1</math>, and <math>R_2</math>  to extract <math>V_{io}</math> and <math>I_B</math>.
+
Use the above equation and two measurements of <math>V_{out}</math>, <math>R_1</math>, and <math>R_2</math>  to extract <math>V_{io}</math> and <math>I_B</math>. I will use two different values of <math>R_2</math> to make two different measurements. <math> V_{in}</math>=0 (grounded). I can now construct 2 equations with 2 unknowns <math>V_{io}</math> and <math>I_B</math>.
 
 
#measure <math>V_{out}</math> for <math>R_1</math> = 1 k<math>\Omega</math>, <math>R_2</math> = 100 k<math>\Omega</math>, and<math> V_{in}</math>=0 (grounded).
 
#measure <math>V_{out}</math> for <math>R_1</math> = 10 k<math>\Omega</math>, <math>R_2</math> = 1 M<math>\Omega</math>, and<math> V_{in}</math>=0 (grounded).
 
#You can now construct 2 equations with 2 unknowns <math>V_{io}</math> and <math>I_B</math>.
 
  
  

Revision as of 21:14, 16 April 2011

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Inverting OP Amp

1. Construct the inverting amplifier according to the wiring diagram below.

TF EIM Lab23.png

Here is the data sheet for the 741 Op Amp

File:LM741CN OpAmp.pdf


Use R1=1kΩ and R2=10kΩ as starting values.

2. Insert a 0.1 μF capacitor between ground and both Op Amp power supply input pins. The Power supply connections for the Op amp are not shown in the above circuit diagram, check the data sheet.

Gain measurements

1.) Measure the gain as a function of frequency between 100 Hz and 2 MHz for three values of R2 = 10 kΩ, 100 kΩ, 1MΩ. Keep R1 at 1kΩ.


I have used the following values of R1 and R2 (as was suggested by Dr Forrest at the lecture)

[math]R_1 = (10.02 \pm 0.02)\ k\Omega[/math]
a) [math]R_2 = (99.0 \pm 0.2)\ k\Omega[/math]
b) [math]R_2 = (198.5 \pm 0.2)\ k\Omega[/math]
c) [math]R_2 = (800.0 \pm 2.0)\ k\Omega[/math]

So my theoretical gain of OP Amp would be:

a) Gain1[math]= \frac{R_2}{R_1} = \frac{99.0 \pm 0.2}{10.02 \pm 0.02} = (9.88 \pm 0.03)[/math]
b) Gain2[math]= \frac{R_2}{R_1} = \frac{198.5 \pm 0.2}{10.02 \pm 0.02} = (19.81 \pm 0.04)[/math]
c) Gain3[math]= \frac{R_2}{R_1} = \frac{800.0 \pm 2.0}{10.02 \pm 0.02} = (79.84 \pm 0.26)[/math]


Below is my measurements and gain calculation for the case a) R1=(10.02±0.02) kΩ and R2=(99.0±0.2) kΩ

Gain011.png

Below is my measurements and gain calculation for the case b) R1=(10.02±0.02) kΩ and R2=(198.5±0.2) kΩ

Gain021.png


Below is my measurements and gain calculation for the case c) R1=(10.02±0.02) kΩ and R2=(800.0±2.0) kΩ

Gain032.png


2.) Graph the above measurements with the Gain in units of decibels (dB) and with a logarithmic scale for the frequency axis.


Below my plot of gain as function of frequency. Here

[math]G_{dB} \left(\frac{V_{out}}{V_{in}}\right) = 20\cdot \log_{10} {\frac{V_{out}}{V_{in}}}[/math]

Here the error calculation as usual and for this specific case is:

[math]dG_{dB}(x) = \frac{\partial G_{dB}(x)}{\partial x}\cdot dx = \frac{20}{x\ \ln 10}\cdot dx[/math]

where x and dx are corresponding gain and error of gain from the tables above


Gain p03.png

Impedance

Input Impedance

  1. Measure Rin for the 10 fold and 100 fold amplifier at ~100 Hz and 10 kHz frequency.


I am going to measure the input and output impedance of my amplifier using the following equivalent circuit:

Draw01.png

where the shaded region is my actual amplifier constructed before:

Draw02.png

From equivalent circuit the input impedance is:

[math]R_{inp} = \frac{V_{inp}}{I_{inp}}[/math]

and from my real circuit inside the shaded region:

[math]I_{inp} = \frac{V_{inp}-V_1}{R_1}[/math]

so finally my input impedance becomes:

[math]R_{inp} = \frac{V_{inp}}{V_{inp}-V_1}\ R_1[/math]


Below is the table with my measurements and input impedance calculations for four asked different cases

Inp01.png


As we can see the input impedance equals the resistor value R1 for low frequency f=100 Hz and increase up to 33 kΩ for high frequency f=10 kHz.

Output Impedance

  1. Measure Rout for the 10 fold and 100 fold amplifier at ~100 Hz and 10 kHz frequency. Be sure to keep the output (Vout) undistorted


Again the equivalent circuit I am going to use is:

Draw011.png

And my output impedance is:

[math]V_{out} = V - I_{out}\cdot R_{out}[/math]

But now I am going to use the load resistor RL to measure the output circuit:

[math]I_{out} = \frac{V_{out}}{R_L}[/math]

By graphing the current on the x-axis and the measured voltage Vout on the y-axis for several values of the load resistance RL we can find the output internal impedance of our amplifier as the slope of the line Vout=VAIoutRout


Below is my measurements and current calculation for the case f = 100 Hz, 10 kHz and gain = 10 (here nothing change with frequency)

Out01.png

Below is my measurements and current calculation for the case f = 100 Hz, 10 kHz and gain = 80 (here nothing change with frequency)

Out02.png


As we can see from the tables above my output voltage Vout doesn't change as the current Iout change. It is follow that the slope of the line is zero for all cases and the output impedance is also zero at least for load resistor varying from 100 kΩ up to 300 kΩ:

[math]R_{out} = 0[/math]

Vio and IB

Vout=R1R2V1+(1+R1R2)Vio+R2IB (need to be checked)


Vout=R2R1V1+(1+R2R1)Vio+R2IB

Use the above equation and two measurements of Vout, R1, and R2 to extract Vio and IB. I will use two different values of R2 to make two different measurements. Vin=0 (grounded). I can now construct 2 equations with 2 unknowns Vio and IB.


Below is my measurements for two different values of R2.

1) [math]f=1 kHz[/math] [math]R_1 = (99.0 \pm 0.2)\ k\Omega[/math], [math]R_2 = (99.0 \pm 0.2)\ k\Omega[/math]:  [math]V_{in}=(0 \pm 2)\ mV[/math] [math]V_{out}=(8 \pm 1)\ mV[/math]
2) [math]f=1 kHz[/math] [math]R_1 = (99.0 \pm 0.2)\ k\Omega[/math], [math]R_2 = (800.0 \pm 2.0)\ k\Omega[/math]:  [math]V_{in}=(0 \pm 2)\ mV[/math] [math]V_{out}=(60 \pm 2)\ mV[/math]

Iio

Now we will put in a pull up resistor R3=R1R2R1+R2 as shown below.

TF EIM Lab23a.png

Instead of the current IB we have the current Iio

Vout=R1R2V1+(1+R1R2)Vio+R2Iio

Use the same technique and resistors from the previous section to construct 2 equations and 2 unknowns and extract Iio, keep Vin=0.

The offset Null Circuit

TF EIM Lab23 b.png

  1. Construct the offset null circuit above.
  2. Adjust the potentiometer to minimize Vout with Vin=0.
  3. Use a scope to measure the output noise.

Capacitors

Revert back to the pull up resistor

Capacitor in parallel with R2

TF EIM Lab23 c.png

  1. Select a capacitor such that1ωC2R2 when ω= 10 kHz.
  2. Add the capacitor in parallel to R2 so you have the circuit shown above.
  3. Use a pulse generator to input a sinusoidal voltage Vin
  4. Measure the Gain as a function of the Vin frequency and plot it.

Capacitor in series with R_1

TF EIM Lab23 d.png

  1. Select a capacitor such that1ωC2R1 when ω= 1 kHz.
  2. Add the capacitor in series to R1 so you have the circuit shown above.
  3. Use a pulse generator to input a sinusoidal voltage Vin
  4. Measure the Gain as a function of the Vin frequency and plot it.

Slew rate

Measure the slew and compare it to the factory spec.

Power Supply Rejection Ratio

  1. Set V_{in} = 0.
  2. Measure Vout while changing Vcc

Output voltage RMS noise ΔVRMSout

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