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Transcript
1. Introduction and Bio-amplifier Requirements
1.1 The Ideal Amplifier
input
signal
AV
RE
output
signal
signal

source
Fig. 1 The Ideal Amplifier
Some of the properies of an ideal amplifier will be recalled as:
 Infinite Input Resistance, Ri  
No current (power) is demanded from the source feeding the amplifier. There is no
attenuation of the source signal reaching its input. This means that the internal
resistance of the source is not important and may be quite high without any
detrimental effect.
 Zero Ouput resistance, RO  0
There is no limiting factor on the output current available from the amplifier. The
amplifier can drive any load connected to it without any loss of signal or restriction
on the load.
 Infinite Bandwidth, BW  
The amplifier can accept signals with unlimited frequency content. There is no
limit on the rate of change of the signal. All signal profiles are reproduced without
distortion.
 Defined Gain, AV = VO / Vi
The voltage gain is determined by component values chosen by the design engineer.
The gain should not change with manufacturing variations in the amplifier. The
gain should not depend on the source or load conditions.
1
1.2 The Non-Ideal Amplifier:
The properties of a non-ideal amplifier address the same issues as those of a
ideal amplifier but are finte and limited in their extent.
power supply rail
non-ideal
amplifier
Ri  
ideal
amp
RO  0
RO
RS
signal
source
Vi

Ri
VO
VL
RL
load
Vs
VL ≠ VO
Vi ≠ Vs
Fig. 2 The Non-Ideal amplifier

Finite Input Resistance, Ri  
The input resistance is finite and limited. This means that the source must
deliver a current to the input of the amplifier. The input signal level present
at the input to the amplifier depends on the relative values of the source
resistance and amplifier input resistance. Consequently, there is an
attenuation of the signal generated by the source on reaching the input of the
amplifier.

Finite Ouput Resistance, RO  0
The ouput resistance of the amplifier is not zero but is finite. There is a
limiting factor on the output current available from the amplifier. The
current or power which can be delivered to the load is therefore also limited.

Limited Bandwidth, BW  
Bandwidth is not infinite but limited. There is a maximum frequency which
is passed by the amplifier with full gain. Frequency components outside of
the bandwidth of the amplifier are attenuated and this can lead to distortion
2
of the signal if the amplifier has insufficient bandwidth to pass the full
frequency spectrum of the signal of interest.
AV
fMAX
Fig. 3 Finite Amplifier Bandwidth
 Gain Variation
In simple amplifers manufacturing variations in the semiconductor
fabrication process give rise to large fluctuations in the amplifying properties of the
devices used to construct the amplifier. This gives rise to varition in the amplifer
gain, A, which can only be overcome by more advanced design techniques such as
the use of negative feedback.
VDD
iD
RD
D
G
input signal
Vgs
VO = VDS
S
~
VGS = Vi
gate bias VGS
Fig. 4 Discrete MOS Transistor Amplifier
3
output voltage
1.3
Negative Feedback:
In modern semiconductor technology devices can readily be manufactured
having substantial gain and several can be combined in various circuit
configurations to form amplifiers with higher gain when required. The problem is
that there are large tolerances associated with the manufacturing process and
consequently the gain of each transistor can vary widely, often by as much as a
factor of 10:1. The variation is further exacerbated with changes in operating
temperature or supply voltage. This makes it impossible to design amplifiers with
any precision unless a means of overcoming the effects of these variations is found.
The technique is to manufacture integrated amplifiers with an extremely
high gain, much higher than is required in circuit applications, and then to use
negative feedback in the design of an amplifier with a stable lower gain for a
particular purpose.
AO subject to
large variation
+
input
signal
sourc
e
Vi
Σ
_
AO = VO / Ve
error
signal Ve
output
signal
β =Vf /VO
Vf
feedback
signal
Fig. 5 General Structure of a Negative Feedback Amplifier
4
VO
A block diagram of the general structure of a feedback amplifier is shown in
Fig. 5. This consists of an amplifier having a voltage gain, AO. The amplifier will be
taken as having a very high input resistance and a very low output resistance so
that the effects of these can be neglected.
In this structure the input signal is not applied directly to the input of the
amplifier but to a summing unit, as shown. The output signal of the amplifier is fed
into a feedback unit. This unit simply senses the output signal of the amplifier and
generates a feedback signal which is a fraction, β, of the output (β is taken as real
and ≤ 1), i.e. Vf = βVO. The feedback signal is then fed into a second input of the
summing unit where it is first inverted, so that it is actually subtracted from the
input signal in the summing unit. This is why the feedback is called negative. The
error signal, Ve , at the output of the summing unit is then the difference between
the input and feedback signals. This error signal is then fed into the amplifier
where it is amplified by the gain, AO, to generate the output signal, VO.
Consider changes in the amplifier properties such that the gain varies.:
If the input signal level is constant but the gain of the amplifier increases,
then the output signal level will tend to increase. This in turn means that the
feedback signal level will increase proportionately. The increased feedback signal
level is then subtracted in the summing unit from the constant input signal level to
give a reduced error signal. This reduced error signal appears at the input of the
amplifier and when passed through the amplifier will tend to reduce the output
signal level to counteract its original tendency to increase.
Alternatively, if the input signal level is constant but the gain of the amplifier
decreases, then the output signal level will tend to decrease. This in turn means that
the feedback signal level will decrease proportionately. The reduced feedback
signal level is then subtracted in the summing unit from the constant input signal
level to give an increased error signal. This increased error signal appears at the
input of the amplifier and when passed through the amplifier will tend to increase
the output signal level to counteract its original tendency to decrease.
Consequently, the change in output signal level caused by the variation in the
gain of the amplifier is much diminished compared to that which exists when no
negative feedback is present. Hence, it can be seen that negative feedback reduces
the effects of parameters variations in the amplifier.
The operation of the feedback amplifier can be analysed to find the overall
input-to-output gain or transfer function of the closed-loop system:
5
For the amplifier:
VO  AO Ve
But the error signal is:
Ve  Vi  Vf
Substituting:
VO  AO Vi  Vf 
But the feedback signal is:
Then:
so that:
Vf  VO
VO  AO Vi  VO 
VO  A O Vi  A O VO
VO 1  A O    A O Vi
Then the voltage gain of the feedback amplifier is:
AV 
VO
AO

Vi 1  A O  
If AOβ >> 1 then:
VO
AO
1
AV 


Vi
AO  
6
This means that when negative feedback is used, the overall voltage gain, AV,
of the feedback amplifier becomes independent of the voltage gain of the amplifier
itself, AO, and depends only on the feedback factor, β, which is determined by
external components. If external components which have low manufacturing
tolerances and temperature coefficients, such as good quality resistors, are used to
determine the feedback factor, β, then a precise amplifier gain can be
accomplished. Some important definitions are:
Open Loop Voltage Gain:
Closed Loop Voltage Gain:
The Feedback Factor:
V
AO  O
Ve
V
AV  O
Vi
The input-output voltage gain of the
complete amplifier with negative
feedback applied.
V
 f
VO
The fraction of the output signal of
the amplifier which is fed back to
the summing network.
AO 
This is the gain around the
feedback loop from the input
through the amplifier and back
through the feedback network.
Loop Gain:
1.5
The voltage gain of the amplifier in
isolation without feedback applied.
The Operational Amplifier:
The operational amplifier is an integrated amplifier which is manufactured
specifically for the purposes of designing negative feedback amplifiers as shown in
Fig. 2. It is a differential amplifier having two input terminals so that two separate
input voltages can be applied to it.
+
Ve
AO
_
V
+
VO = AOVe
V-
Fig. 6 An Operational Amplifier
7
The ‘positive’ terminal is a non-inverting input so that it influences the
output in the same sense, i.e. an increase in the voltage V+ causes an increase in the
output voltage. The ‘negative’ terminal is an inverting input so that it influences
the output in the opposite sense, i.e. an increase in the voltage V- causes a decrease
in the output voltage.
The output voltage is therefore the open-loop gain times the differential
voltage seen between the non-inverting and inverting inputs, i.e. VO = AO ( V+ - V- ).
This means that the subtracting operation of the negative feedback amplifier
can be performed by the operational amplifier if the feedback, βVO, is applied to
the inverting input of the op-amp, as shown in Fig. 7.
The open-loop gain, AO, is deliberately made extremely high so that the loopgain, AOβ, can be made much greater than unity even for small values of β.
error
signal Ve
input
signal
sourc
e
Vi
+
AO = VO / Ve
_
output
signal
β =Vf /VO
VO
Vf
feedback
signal
Fig. 7 A Negative Feedback Amplifier Composed of an Operational Amplifier
Precisely the same analysis of the closed loop voltage gain as carried out above can
be applied to the op-amp based circuit with exactly the same result:
VO
AO
1
AV 


Vi
AO  
8
Consider another analysis on the circuit of Fig. 7:
Ve  V   V Then substituting:
Ve  Vi  Vf
With:
Vf  VO
Ve  Vi  VO
But taking:
VO 
AO
Vi
1  A O  
Then:
AO
Ve  Vi  
Vi
1  AO  

AO 
Ve  Vi 1  



1

A

O


If AOβ >> 1
 AO  
Ve  Vi 1 
  Vi 1  1  0
 AO  
This means that if the loop gain is very high the differential error signal present
between the terminals of the op-amp, Ve= V+ - V- → 0. Essentially, a negative
feedback system is always trying to make the signal fed back to the inverting input
of the amplifier the same as the external input signal applied to the non-inverting
input, i.e. V+ = V-. This principle can be used in later analysis of op-amp circuits.
9
1.6
Bio-amplifier Requirements
The requirements for bio-potential amplifiers can often be more demanding
than for a lot of electronic equipment as might be used in the entertainment or
telecommunications sectors. When measuring electrical signals, such as the ECG,
from the surface of the body typical requirements could be:
 Very High Input Impedance:
Because the source impedance of electrodes can be quite high, this
necessitates very high input impedance in the amplifier. As seen previously, this
could reach to GΩ under extreme conditions. Getting very high input impedance is
not that difficult with op-amp type circuits but for differential amplifiers, as would
be used in ECG monitoring, it can be quite difficult to balance the impedance on
both inputs.
 Moderate Bandwidth:
The bandwidth requirements for most bioamplifiers are not extreme but
generally need to be higher than the highest frequency component in the signal
spectrum. This is in order to prevent phase distortion of the components at the
higher end of the spectrum. These components are often associated with minute
detail at low amplitude in biological signals and may contain diagnostically
important information to be used in a clinical environment. Any band-limiting
carried out by low-pass filtering must use a linear phase approach such as a BesselThompson filter design.
 Sufficient Gain-Bandwidth Product:
It must be possible to obtain sufficient gain over the bandwidth of interest.
Operational amplifiers can have very high open-loop gain at dc but this rapidly
falls off with frequency. A measure of the closed-loop gain which can be realised is
given by the Gain-Bandwidth Product parameter for the op-amps which must be
sufficiently high to meet requirements.
 High Common-Mode-Rejection:
Most biomedical amplifiers will have to operate in a differential manner,
measuring the potential difference between two inputs. The body picks up signals,
in particular mains supply interference, which are unwanted and present at both
inputs. Transducers which use bridge arrangements in their construction also have
large common-mode bias voltages at both outputs. Bioamplifiers in general must
have a high ability to reject common-mode signals in favour of the wanted
differential input signal so that only the latter contributes to the output.
10