Post on 23-Dec-2015
ENTC 4350BIOMEDICAL INSTRUMENTATION I
BASIC DIFFERENTIAL AMPLIFIER
Introduction
The differential amplifier can measure as well as amplify small signals that are buried in much larger signals.
There are two input terminals, labeled () input, and (+) input.
Superposition
If E1 is replaced by a short circuit, E2 sees an inverting amplifier with a gain of m.
• Therefore, the output voltage due to E2 is mE2.
mE2
Now let E2 be short-circuited:
• E1 divides between R and mR to apply a voltage of E1m/ (1+ m) at the op amp’s (+) input.
This divided voltage sees a noninverting amplifier with a gain of (m + 1).
• The output voltage due to E1 is the divided voltage:
• E1m/(1 + m) times the noninverting amplifier gain, (1 + m), which yields mE1.
mE1
Therefore, E1 is amplified at the output by the multiplier m to mE1.
• When both E1 and E2 are present at the (+) and () inputs, respectively.
• Vo is mE1 mE2.
The output voltage of the differential amplifier, Vo, is proportional to the difference in voltage applied to the (+) and () inputs.
Multiplier m is called the differential gain and is set by the resistor ratios.
When E1 = E2 the output voltage is 0.
• To put it another way, when a common (same) voltage is applied to the input terminals, Vo = 0.
Lab 6_Differential Amplifier
The gain of the amplifier below can be determined using the Superposition Principle.
'
'
─
+
2.2 k
4.7 k
22 k
RS
Ri
Rf
VOUT
RD
Inverting Amplifier
Forcing V2 to 0 develops an inverting amplifier with an output, VOUT of:
'
'
─
+
2.2 k
4.7 k
22 k
RS
Ri
Rf
VOUT
RD
V1
1111 1022
22V
k
kV
R
RVV
i
fOUT
.
i
fOUT R
RVV 11
Non-inverting Amplifier
Forcing V1 to 0 develops a non-inverting amplifier.
'
'
─
+
2.2 k
4.7 k
22 k
RS
Ri
Rf
VOUT
RD
V2
Applying Thevenin’s Theorem:
'
'
─
+
2.2 k
4.7 k
22 k
RS
Ri
Rf
VOUT
RD
V2
22 VRR
RVV
DS
Dopen
DS
DSTH RR
RRR
The output of the non-inverting amplifier is:
'
'
─
+
2.2 k
22 k
RTh
Ri
Rf
VOUT
DS
D
RR
RV
2
i
fOUT R
RVV 122
i
fOUT R
RVV 122
The total output is the sum:
To balance the circuit, we set the coefficients to add to zero.
i
f
i
fOUTOUT R
RV
R
RVVV 1212
i
f
i
f
R
R
R
R
fi
f
fi
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i
f
i
f
i
fi
i
f
i
f
i
i
i
f
i
f
RR
R
RR
R
R
R
R
R
R
RR
R
R
R
R
R
R
R
R
R
R
1212
12
1
2
2
12
VVR
RV
RR
RRV
R
R
VRR
R
RR
RV
R
R
R
RV
RRR
R
RRR
RRV
R
RV
R
R
RR
R
RR
RVV
i
f
fi
fi
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f
fi
f
fi
i
i
f
i
f
fii
f
fii
fi
i
f
i
f
fi
f
fi
fOUT
So the balanced condition yields
• and the differential gain Ad is
12 VVR
RV
i
fOUT
i
fD R
RA
Common-mode rejection of 60 cycle power line interference in medical instrumentation which measures difference potentials on the body is a fundamental problem. • Power-line interference may exceed the level
of the signal being measured. • This bad news is often cancelled by the fact that
the interfacing signal appears equally intense at both input terminals of the diff amp, and is therefore called a common-mode signal.
If the diff amp is not perfectly balanced, as is always the case in the real world, then the common-mode signal input will cause an output signal that then constitutes interference with the desired amplified signal. • Since one of the functions of the diff amp is to reject
the common-mode signal, we define a figure of merit, the common-mode rejection ratio (CMRR), which measures how well the rejection occurs.
The common-mode rejection ratio CMRR is defined as the magnitude of the ratio of the differential voltage gain Ad to the common-mode voltage gain Ac.
Ad equals VOUT divided by V1 when node 2 is grounded, and V1 is applied to node 1.
• Also, AC equals VOUT divided by V1 when node 1 is connected to node 2, and V1 is applied again.
V Vwhen
grounded is Vwhen
12
2
OUT
OUT
V
VCMRR
In practice the CMRR is measured in the following steps:
1.Ground V2, and apply a voltage V1 to the upper terminal.
2.Measure the resulting VOUT.
3.Lift V2 from ground and short the two input leads, then apply the same value of V1.
4.Measure the resulting VOUT.5.To compute CMRR, divide the results of step 2 by the
result of step 4, and take the magnitude.
The CMRR is a voltage ratio, and therefore in decibel units we may define CMRRdb as
CMRRCMRRdb log20
Common-Mode Voltage
The simplest way to apply equal voltages is to wire inputs together and connect them to the voltage source.
For such a connection, the input voltage is called the common-mode input voltage, ECM.
Now Vo will be 0 if the resistor ratios are equal (mR to R for the inverting amplifier gain equals mR to R of the voltage-divider network.)
Practically, the resistor ratios are equalized by installing a potentiometer in series with one resistor.
The potentiometer is trimmed until Vo is reduced to a negligible value. • This causes the common-mode voltage gain,
Vo/ECM to approach 0.
• It is this characteristic of a differential amplifier that allows a small signal voltage to be picked out of a larger noise voltage.
It may be possible to arrange the circuit so that the larger undesired signal is the common-mode input voltage and the small signal is the differential input voltage. • Then the differential amplifier’s output voltage
will contain only an amplified version of the differential input voltage.