Download To Get a Perfect “A”…

To Get a Perfect “A”…
An Engr. 311 Project by Corrin Meyer
Project Statement

The tuner should generate a pure and perfect A.
The sine wave should oscillate to with in 5% of 440
Hz (which is a perfect tuning A).
 The sine wave should have as little distortion as
possible.



The tuner should be able to drive a speaker.
The tuner should be portable (in concept).
Design Process




Research sinusoidal oscillators.
Understand benefits and pitfalls of different
oscillator designs.
Choose an appropriate oscillator.
Improve basic circuit design.
Basic Theory of Oscillators



Oscillators are by definition
unstable.
The basic oscillator is depicted
to the right. (The response is
also shown)
For oscillations to occur


Negative Feedback: A*B = -1
Positive Feedback: A*B = 1


Vout
A  Vin  A    Vout
Vout
A  Vin  Vout 
A  Vin
Vout  A    Vout
A  Vin
Vout  1  A   
Vout
A
Vin
1  A
Meet the Wein Bridge

Basics



Uses an Op-Amp for amplification
Uses positive feedback through a
RC band-pass filter
R3

-
Few parts
Able to generate very accurate sine
waves (Used in audio equipment)

Not easily tuned to the desired
frequency
May introduce significant
distortions into the resulting wave
without proper amplitude control.
Vout
OUT
R1
+
C1
Disadvantages

R4
0
Advantages


Op-Amp amplifier
C2
R2
0
Positive RC band-pass feedback filter
Wein Bridge Continued…

Derivation of the Loop Gain
(A*B)





Positive feedback: A*B=1
B is a real number when w=1/RC
B=1/3 when w=1/RC
A=3 for the loop gain to equal 1
The oscillator will oscillate at
the frequency w, where
w=1/RC and has units rad/s
A
1
R4
R3
If R1 = R2 and C1 = C2...
R
RCs 1

R
1
Cs

1
R
3  RCs 
RCs  1
1
Gain loop
A
1
R3
R4
3  j  RC 

1


RC 
1
RCs
3  j  RC 



RC 
1
The Wein Bridge Problem




For oscillations to start, A must be slightly
greater than 3.
If A is greater than 3 , then the loop gain is
greater than 1.
If the loop gain is greater than 1, then the sine
wave amplitude will tend towards infinity.
Circuit does not infinite power, so the output
sine wave becomes severely distorted.
…Solution…


Design amplitude limiting
circuitry.
There are 3 general solutions.




Passive devices (diodes)
Resistive lamp
Automatic Gain Control
(AGC)
VCC
R1
3k
D1
D1N4148
R2
20.3k
VDD
R4
4
2
-
VOS1
10k
OUT
0
3
A diode limited Wein Bridge
is depicted to the right.
+ 7
OS2
V+
R3
1.2k
U1
LM741
1
6
Vout
5
VCC
C2
33n
0
C1
R5
33n
10.96k
R6
1.2k
R7
10.96k
0
D2
D1N4148
R8
3k
Amplitude Limiter
VDD
Not So Perfect…




The diode limited Wein Bridge does NOT
produce a perfect sine wave.
The amplifier gain is different when the diodes
conduct and when they do not conduct.
Result: Distorted sine wave.
Solution: AGC
The All Mighty AGC

AGC stands for Automatic Gain Control.


Controls the gain of the amplifier based on the
output sine wave amplitude.
The AGC requires two parts…
An AC rectifier with signal smoothing.
 A VCR (Voltage Controlled Resistor).

The Rectifier



Depicted below is the precision rectifier used in the final
oscillator circuit.
The rectifier is designed to invert the positive peaks of the sine
so that the wave is always negative.
Signal smoothing is not included here.
R1
R2
Vi n
D1
OUT
+
0
OUT
D2
R3
+
Vout
Rectifier Stimulus Response
3.0V
2.0V
Rectifier Input
1.0V
-0.0V
-1.0V
Rectifier Output
-2.0V
-3.0V
250ms
251ms
V(U4:OUT)
V(U1:OUT)
252ms
253ms
254ms
255ms
Time
256ms
257ms
258ms
259ms
260ms
The VCR
VCC





VCR stands for Voltage
Controlled Resistor.
A JFET transistor is used as
the basis for the VCR.
Feedback is utilized to
linearize the voltage to
resistance conversion.
Response equations are given
at right.
For better AC response, a
capacitor is added between
R1 and R2
Rd
R2
i2
iD
R1
J1
Vi n
i1
W
1
id
k
2 n L
1
Need to remove the
2
v in  v GS
v GS  v DS
R1
R2
R2
R1
vin  vGS
2
v DS
v GS  1 
v  v DS
R1 in
2
v in 
term to linearize iD

R2 

R1 
Setting R2 = R1, we get a
1
0
v GS  v D
R2
v GS
2
 v GS  Vt v DS  2 v DS 


1
1
v
2 DS
1
v
2 DS
Placing this result in the equation removes the
1
2
2
v DS
VCR Response
2.0K
1.6K
1.2K
0.8K
0.4K
0
-0.4K
-10V
-9V
V(J1:d)/ I(J1:d)
-8V
-7V
-6V
-5V
V_V1
-4V
-3V
-2V
-1V
-0V
Frequency Selection




An output frequency of 440
Hz is desired.
Capacitors have 5% to 20%
tolerances so keep capacitor
values low.
Use 1% tolerance resistors.
The 10.96k resistors can be
rounded up to 11k (use a 10k
and 1k in resistor in series).
R3
R4
4.7k
10k
0
Vout
OUT
R1
+
10.96k
0
C1
C2
R2
0.033u
0.033u
10.96k
Putting It All Together…
R1
R2
D1
10k
6
D1N4148
-
OUT
5
OS2
VCC
+
VCC
4.7k
R14
470k
R9
4.7k
4.7k
0
10k
R10
10k
C2
0.033u
VDD
4
R13
R8
R5
J1
2N5486/PLP
2
-
C3
10u
3
0
OS1
OUT
R15
+
7
R12
1k
3
V-
+
U2
LM741
2
4
OS1
D2
3
V-
1
OUT
OS2
VDD
10.96k
OS2
U4
LM741
1
6
5
V+
5
-
10k
D1N4148
U1
LM741
2
7
6
OS1
7
1
V-
4
VDD
V+

The final oscillator
circuit is depicted at
right.
In addition to the
discussed sections, R12,
R14, and C3 were added
to smooth the rectified
output.
V+

VCC
0
0
C4
C5
R16
0.033u
0.033u
10.96k
Additional Improvements



Run on batteries.
Volume control could be added.
The 741 Op-Amp can only source about 50mA
of current so an output stage to drive a speaker
could be implemented.
Final Circuit – With Improvements
Precision Rectifier
R2
R1
D1
10k
4
1
OS1
D2
OS2
R5
VCC
4.7k
0
4
2
J1
2N5486/PLP
-
OUT
3
0
+
7
R15
C3
10u
OS1
10.96k
OS2
U4
LM741
1
-
OS1
+
OS2
0
1
VDD
6
Speaker
VCC
5
Q3
VCC
Q4
Q2N2907
Q2N2222
R11
10k
6
5
VDD
V+
R14
470k
3
Q1
Q2N2222
VDD
OUT
10k
VDD
C2
0.033u
V-
R13
U3
LM741
2
47k
R10
4.7k
4.7k
R6
0
10k
R9
R8
R12
1k
SET = 1
3
V+
VCC
+
4
5
R3
10k
Q2
Q2N2907
OUT
V-
D1N4148
-
VCC
VCC
R4
100k
7
+
6
3
Output Stage
Volume Control
U2
LM741
2
V+
OUT
OS2
VDD
V-
-
V+
5
OS1
10k
D1N4148
U1
LM741
2
7
6
7
1
V-
4
VDD
VDD
VCC
AGC
C4
C5
R16
0.033u
0.033u
10.96k
0
Wein Bridge Oscillator
OSC
Final Circuit Continued
Rectifier
Volume Control
VCR
Output Stage
Wein Bridge
Operation of Circuit in Real Life

The output sine wave is much smaller than predicted.






Predicted amplitude: 3V
Actual amplitude: 25mV
This is due to extreme dependence on Wein Bridge amplifier
gain setting resistors.
Volume control can make up for the smaller amplitude
without introducing distortion.
The output sine wave is very clean and precise.
The output frequency is surprisingly close to the ideal
frequency that was designed for. (plus or minus 5Hz)
Final Comments

Accomplishments



Generates a near perfect sine wave (when taken directly from
the oscillator circuit) at around 440Hz.
Runs of batteries.
Areas needing further development/improvement.



Output stage introduces some distortion.
Make the oscillator easier to tune. (plus or minus 10Hz)
Improve the AGC amplitude detection.