參數(shù)資料
型號: AND8054
廠商: ON SEMICONDUCTOR
英文描述: Designing RC Oscillator Circuits with Low Voltage Operational Amplifiers and Comparators for Precision Sensor Applications
中文描述: RC振蕩器電路設計低電壓運算放大器和精密傳感器應用比較
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代理商: AND8054
AND8054/D
http://onsemi.com
16
Differentiator
+
V
IN
V
OUT
C
R
Figure 14. Ideal Differentiator
Listed below are the equations for the ideal differentiator
circuit shown in Figure 14.
VOUT(t)
VOUT(s)
VIN(s)
RCddt
sRC
However, the ideal differentiator does not consider the
effect of the amplifier’s voltage offset and current bias
errors, as shown below [3].
RCVdt
If the output offset and bias errors are referenced to the
input, as shown below,
dVIN(t)
dt
error
VOUT(t)
VIO
IBR
VIO
RC
IB
C
the following observations can be made:
1. Use small R, large C.
2. V
IO
1 / RC and I
B
1 / C .
A practical differentiator circuit is shown in Figure 15. For
simplicity, this circuit will neglect the effect of resistor R
5
.
There will be an error due to the operational amplifier’s
finite open loop gain as shown below:
VOUT(s)
VIN(s)
s
Ao
1
Ao
1
R3C4
s2
s
1
R4C4
1
R3C3
1
R3R4C3C4
If A
o
>> 1, the transfer equation can be simplified to:
VOUT(s)
VIN(s)
s
1
R3C4
s
1
R3C3
s
1
R4C4
sR4C3
1 sR4C4
sR3C3
1
+
V
IN
V
OUT
C3
R4
C4
R3
R5
Figure 15. Practical Differentiator (Neglect R5)
The error due to the operational amplifier’s finite open
loop gain and bandwidth is shown graphically in Figure 16.
The oscillator’s amplifier error and bandwidth error terms
are reduced if a higher gain and increased operational
amplifier is selected. The oscillation error can be minimized
by selecting an oscillation frequency that is as low as
practical (i.e. f
oscillation
10 KHz).
The Slew Rate (SR) error of a differentiator is identical to
the equation listed for an integrator.
dVOUT(t)
dt
|max
2 fpEo
SR
Figure 16. Graphical Error Analysis of Ideal Differentiator
Frequency (Hz)
Gain (dB)
0
20xlogC3
C4
20xlog
R4
R3
R5
Fp2
1
2 R3C3
Fz1
1
2 R4C3
FP1
1
2 R4C4
Gain Error
Bandwidth
Error
A
O
T
o
Open Loop Gain
Closed Loop Gain
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