Difference between revisions of "Lab 3 RS"

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:<math>f_{exp} = 10^{0.982} = 9.59\ kHz </math>
 
:<math>f_{exp} = 10^{0.982} = 9.59\ kHz </math>
  
The error is:
+
:The error is:
  
 
  <math>Error = \left| \frac{f_{exp} - f_{theor}}{f_{theor}} \right| = \left| \frac{9.59 - 12.1}{12.1} \right|= 20.7\ %</math>
 
  <math>Error = \left| \frac{f_{exp} - f_{theor}}{f_{theor}} \right| = \left| \frac{9.59 - 12.1}{12.1} \right|= 20.7\ %</math>

Revision as of 21:00, 25 January 2011

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RC Low-pass filter

1-50 kHz filter (20 pnts)

1. Design a low-pass RC filter with a break point between 1-50 kHz. The break point is the frequency at which the filter starts to attenuate the AC signal. For a Low pass filter, AC signals with a frequency above 1-50 kHz will start to be attenuated (not passed).

To design low-pass RC filter I had:
[math]R=10.5\ \Omega[/math]  
[math]R=1.250\ \mu F[/math]
[math]\omega_b = \frac{1}{RC} = 76.2\ \mbox{kHz}[/math]
[math]f_b = \frac{\omega_b}{2\pi} = 12.1\ \mbox{kHz}[/math]


2. Now construct the circuit using a non-polar capacitor.

TF EIM Lab3.png

3. Use a sinusoidal variable frequency oscillator to provide an input voltage to your filter.

4. Measure the input (Vin) and output (Vout) voltages for at least 8 different frequencies(ν) which span the frequency range from 1 Hz to 1 MHz.

ν [kHz] Vin [V] Vout [V] VoutVin δt [μs] ϕ=ωδt [rad]
0.1 5.0 5.0 1.0
1.0 4.2 4.2 1.0 15.0 0.094
2.0 3.2 3.1 0.97 15.0 0.188
5.0 1.8 1.6 0.89 15.0 0.471
10.0 1.14 0.88 0.77 10.0 0.628
16.7 0.90 0.54 0.60 10.0 1.049
20.0 0.88 0.48 0.54 8.0 1.005
25.0 0.82 0.38 0.46 7.0 1.099
33.3 0.78 0.28 0.36 6.0 1.255
50.0 0.76 0.18 0.24 4.5 1.413
100.0 0.75 0.09 0.12 2.0 1.256
125.0 0.74 0.07 0.095 1.8 1.413
200.0 0.75 0.04 0.053 0.8 1.005
333.3 0.76 0.03 0.039 0.25 0.523
200.0 0.76 0.03 0.039 -0.25 -0.785
1000.0 0.78 0.06 0.077 -0.25 -1.570

5. Graph the log(VoutVin) -vs- log(ν)


RS lab3 voltage gain.png

phase shift (10 pnts)

  1. measure the phase shift between Vin and Vout as a function of frequency ν. Hint: you could use Vin as an external trigger and measure the time until Vout reaches a max on the scope (sin(ωt+ϕ)=sin(ω[t+ϕω])=sin(ω[t+δt])).
See table above, columns #5 and #6.

Questions

  1. Compare the theoretical and experimentally measured break frequencies. (5 pnts)
Theoretical break frequency: 12.1 kHz
Experimentally measured break frequency: 9.59 kHz
 Q: The above was read off the graph?  Why not use fit results?
 A: The fit was made by using GIMP Image Editor. I do not have so much experience with ROOT. But I will try to do it. Thank you for comment.
 A1: The fit was done by ROOT
The fit line equation from the plot above is  y=0.89890.915x.
From intersection point of line with x-axis we find:
log(fexp)=0.89890.915=0.982
fexp=100.982=9.59 kHz
The error is:
[math]Error = \left| \frac{f_{exp} - f_{theor}}{f_{theor}} \right| = \left| \frac{9.59 - 12.1}{12.1} \right|= 20.7\ %[/math]


  1. Calculate and expression for VoutVin as a function of ν, R, and C. The Gain is defined as the ratio of Vout to Vin.(5 pnts)

We have:

1) Vin=I(R+RC)=I(R+1iωC)
2) Vout=I(1iωC)


Dividing second equation into first one we get the voltage gain:

 VoutVin=I(1iωC)I(R+1iωC)=(1iωC)(R+1iωC)=11+iωRC


And we are need the real part:

|VoutVin|=(VoutVin)(VoutVin)=(11+iωRC)(11iωRC)=1(1+(ωRC)2=1(1+(2πνRC)2


  1. Sketch the phasor diagram for Vin,Vout, VR, and VC. Put the current I along the real voltage axis. (30 pnts)

Phase diagram m.png


  1. Compare the theoretical and experimental value for the phase shift θ. (5 pnts)
  2. what is the phase shift θ for a DC input and a very-high frequency input?(5 pnts)
  3. calculate and expression for the phase shift θ as a function of ν, R, C and graph θ -vs ν. (20 pnts)


Forest_Electronic_Instrumentation_and_Measurement

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