Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Quantization (signal processing) wikipedia , lookup

Spectral density wikipedia , lookup

Heterodyne wikipedia , lookup

Islanding wikipedia , lookup

Mains electricity wikipedia , lookup

Rectifier wikipedia , lookup

Voltage optimisation wikipedia , lookup

Dynamic range compression wikipedia , lookup

Control system wikipedia , lookup

Flip-flop (electronics) wikipedia , lookup

Voltage regulator wikipedia , lookup

Power electronics wikipedia , lookup

Oscilloscope history wikipedia , lookup

Resistive opto-isolator wikipedia , lookup

Pulse-width modulation wikipedia , lookup

Switched-mode power supply wikipedia , lookup

Buck converter wikipedia , lookup

Analog-to-digital converter wikipedia , lookup

Schmitt trigger wikipedia , lookup

Opto-isolator wikipedia , lookup

Transcript
```5/15/2017
841021612
1/3
An Application of the
Inverting Integrator
Note the time average of a signal v (t) over some arbitrary time
T is mathematically stated as:
1
average of v (t ) v (t ) 
T
T
v (t ) dt
0
Note that this is exactly the form of the output of an op-amp
integrator!
We can use the inverting integrator to determine the timeaveraged value of some input signal v (t) over some arbitrary
time T.
For example, say we wish to determine the time-averaged value
of the input signal:
vin(t)
5
0
-5
1
2
3
4
t
5/15/2017
841021612
2/3
I.E.,
 5

vin (t )  5
 0

0 t  2
2 t  3
t 3
The time average of this function over a period from 0 < t < T=3
is therefore:
3
1
5
vi (t )  vi (t ) dt 
30
3
We could likewise determine this average using an inverting
integrator. We select a resistor R and a capacitor C such that
the product RC = 3 seconds.
The output of this integrator would be:
 5t
 3

t
1
 5t  20


vout (t ) 
v
(
t
)
dt


in
3 0
 3
 5
 3

0 t  2
2 t  3
t 3
5/15/2017
841021612
v o (t )
0


1
3
2
3/3
4
t
5
3
10
3
Note that the value of the output voltage at t =3 is:
3
1
5


vout (t  3) 
v
(
t
)
dt


in
3 0
3
The time-averaged value (times –1)! Thus, we can use the
inverting integrator, along with a voltage sampler (e.g., A to D
converter) to determine the time-averaged value of a function
over some time period T.
vin (t)
vo (t)
t =T=RC
vout (t T )  vout (t )
```
Related documents