Download Amplifier Frequency

Survey
yes no Was this document useful for you?
   Thank you for your participation!

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

Document related concepts

Spectrum analyzer wikipedia , lookup

Schmitt trigger wikipedia , lookup

Power electronics wikipedia , lookup

Analog television wikipedia , lookup

Klystron wikipedia , lookup

405-line television system wikipedia , lookup

Transistor–transistor logic wikipedia , lookup

Oscilloscope wikipedia , lookup

Analog-to-digital converter wikipedia , lookup

HD-MAC wikipedia , lookup

Oscilloscope types wikipedia , lookup

Phase-locked loop wikipedia , lookup

Rectiverter wikipedia , lookup

Loudspeaker wikipedia , lookup

Equalization (audio) wikipedia , lookup

Naim Audio amplification wikipedia , lookup

Tektronix analog oscilloscopes wikipedia , lookup

Oscilloscope history wikipedia , lookup

Mathematics of radio engineering wikipedia , lookup

Instrument amplifier wikipedia , lookup

Distortion (music) wikipedia , lookup

Naim NAIT wikipedia , lookup

Audio crossover wikipedia , lookup

Superheterodyne receiver wikipedia , lookup

Resistive opto-isolator wikipedia , lookup

Cellular repeater wikipedia , lookup

Index of electronics articles wikipedia , lookup

PS Audio wikipedia , lookup

Bode plot wikipedia , lookup

Regenerative circuit wikipedia , lookup

Negative feedback wikipedia , lookup

Operational amplifier wikipedia , lookup

Public address system wikipedia , lookup

Audio power wikipedia , lookup

Opto-isolator wikipedia , lookup

Radio transmitter design wikipedia , lookup

Wien bridge oscillator wikipedia , lookup

Amplifier wikipedia , lookup

Valve RF amplifier wikipedia , lookup

Transcript
5/10/2017
840996991
1/7
Amplifier Frequency
Response
An ideal amplifier takes an input signal and reproduces it
exactly at its output, only with a larger magnitude!
vin(t )
vout(t )  Avo vin(t )
Av
where Avo is the open-circuit voltage gain of the amplifier.
Now, let’s express this result using our linear circuit theory !
Recall, the output vout(t ) of a linear device can be determined
by convolving its input vin(t ) with the device impulse response
g (t ) :
vout (t ) 
t
 g (t t )v

in
(t )dt 
5/10/2017
840996991
2/7
The impulse response for the ideal amplifier would therefore
be:
g (t )  Avo  (t )
so that:
vout (t ) 
t
 g (t t )v
in
(t )dt 


t
 A  (t t )v
vo
in
(t )dt 

 Avo vin (t )
We can alternatively represent the ideal amplifier response in
the frequency domain, by taking the Fourier Transform of the
impulse response:
T ( ) 

 g (t )e
 j t
dt



 j t
A

(
t
)
e
dt
vo


 Avo  j 0
This result, although simple, has an interesting interpretation.
It means that the amplifier exhibits gain of Avo for sinusoidal
signals of any and all frequencies!
T  
Avo

5/10/2017
840996991
3/7
Moreover, the ideal amplifier does not alter the relative phase
of the sinusoidal signal (i.e., no phase shift).
In other words, if:
vin (t )  cos (t )
then at the output of the ideal amplifier we shall see:
vout (t )  T   cos (t  T  )
 Avo cos (t )
BUT, there is one big problem with an ideal amplifier:
They are impossible to build !!
Q: Why is that ??
A: Two reasons:
a)
An ideal amplifier has infinite bandwidth.
b)
An ideal amplifier has zero delay.
Not gonna happen !
Let’s look at this first problem first. The ideal amplifier
impulse response g (t )  Avo  (t ) means that the signal at the
5/10/2017
840996991
4/7
output occurs instantaneously with the signal at the input. This
of course cannot happen, as it takes some small, but non-zero
amount of time for the signal to propagate through the
amplifier. A more realizable amplifier impulse response is:
g (t )  Avo  (t   )
resulting in an amplifier output of:
vout (t ) 
t
 g (t t ) v
in
(t )dt 


t
A
vo
 (t   t ) vin (t )dt 

 Avo vin (t   )
In other words, the output is both an amplified and delayed
version of the input.
*
Note the delay does not distort the signal, as the output
has the same form as the input.
*
Moreover, the delay for electronic devices such as
amplifiers is very small in comparison to human time scales (i.e.,
 1 second ).
*
Therefore, propagation delay 
problem for most amplifier applications.
is not considered a
5/10/2017
840996991
5/7
Let’s examine what this delay means in the frequency domain.
Evaluating the Fourier Transform of this modified impulse
response gives:
T ( ) 


g (t ) e  j t dt



A
vo
 (t   ) e  j t dt

 Avo cos ( )  j Avo sin ( )
 Avo e j 
We see that, as with the ideal amplifier, the magnitude
T ( )  Avo . However, the relative phase is now:
T    
As a result, if vin t   cos (t ) , the output signal will be:
vout (t )  T   cos (t  T  )
 Av cos (t   )
In other words, the output signal of a real amplifier is phase
shifted with respect to the input.
In general, the amplifier phase shift T   will not be a
perfectly linear function (i.e., T     ), but instead will be a
more general function of frequency 
5/10/2017
840996991
6/7
Now, let’s examine the second problem with the ideal amplifier.
This problem is best discussed in the frequency domain.
We discovered that the ideal amplifier has a frequency
response of T    Avo . Note this means that the amplifier gain
is Avo for all frequencies 0     (D.C. to daylight !).
The bandwidth of the ideal amplifier is therefore infinite !
*
Since every electronic device will exhibit some amount of
inductance, capacitance, and resistance, every device will have a
finite bandwidth.
*
In other words, there will be frequencies  where the
device does not work !
*
From the standpoint of an amplifier, “not working” means
T   Avo (i.e., low gain).
*
Amplifiers will therefore have finite bandwidths.
There is a range of frequencies  between L and H where
the gain will (approximately) be Avo. For frequencies outside
this range, the gain will typically be small (i.e. T   Avo ):

T w   

 Avo L    H
Avo   L ,  H
5/10/2017
840996991
7/7
The width of this frequency range is called the amplifier
bandwidth:
Bandwidth H  L (radians/sec)
fL  fH
T  
(cycles/sec)
Avo

L
H
One result of having a finite bandwidth is that the amplifier
impulse response is not an impulse function !

g (t )  T ( ) e  j t dt  Avo  (t   )

The ideal amplifier is not really possible!