REV. E
–8–
AD743
Figures 4 and 5 show two ways to buffer and amplify the output of
a charge output transducer. Both require using an amplifier that
has a very high input impedance, such as the AD743. Figure 4
shows a model of a charge amplifier circuit. Here, amplifica-
tion depends on the principle of conservation of charge at the
input of amplifier A1, which requires that the charge on capaci-
tor CS be transferred to capacitor CF, thus yielding an output
voltage of
Q/C
F. The amplifier’s input voltage noise will appear at
the output amplified by the noise gain (1 + (CS/CF)) of the circuit.
A1
*OPTIONAL, SEE TEXT
CS
CF
CB*
RB*
R1
=
CS
CF
R1
R2
RB*
Figure 4. Charge Amplifier Circuit
A2
*OPTIONAL, SEE TEXT
CS
CB*
RB*
R1
R2
RB
Figure 5. Model for a High Z Follower with Gain
The circuit in Figure 5 is simply a high impedance follower with
gain. Here the noise gain (1 + (R1/R2)) is the same as the gain
from the transducer to the output. In both circuits, resistor RB is
required as a dc bias current return.
There are three important sources of noise in these circuits.
Amplifiers A1 and A2 contribute both voltage and current noise,
while resistor RB contributes a current noise of
Nk
T
R
f
B
= 4
where
k = Boltzman’s Constant = 1.381
× 10–23 joules/kelvin
T = Absolute Temperature, kelvin (0
°C = 273.2 kelvin)
f = Bandwidth—in Hz (assuming an ideal “brick wall” filter)
This must be root-sum-squared with the amplifier’s own
current noise.
Figure 6 shows that these circuits in Figures 4 and 5 have an
identical frequency response and noise performance (provided
that CS/CF = R1/ R2). One feature of the first circuit is that a “T”
network is used to increase the effective resistance of RB and to
improve the low frequency cutoff point by the same factor.
–100
–110
–120
–130
–140
–150
–160
–170
–180
–190
–200
–210
–220
0.01
0.1
110
100
1k
10k
100k
FREQUENCY (Hz)
DECIBELS
REFERENCED
TO
1V
/
Hz
TOTAL
OUTPUT
NOISE
DUE TO
RB ALONE
NOISE
DUE TO
IB ALONE
Figure 6. Noise at the Outputs of the Circuits of
Figures 4 and 5. Gain = +10, CS = 3000 pF, RB = 22 M
However, this does not change the noise contribution of RB which,
in this example, dominates at low frequencies. The graph of
Figure 7 shows how to select an RB large enough to minimize
this resistor’s contribution to overall circuit noise. When the
equivalent current noise of RB ((
√4kT)/R equals the noise of I
B
(
√2qIB), there is diminishing return in making R
B larger.
1pA
10pA
100pA
1nA
10nA
5.2
1010
5.2
109
5.2
107
5.2
106
5.2
108
INPUT BIAS CURRENT
RESISTANCE
(
)
Figure 7. Graph of Resistance vs. Input Bias Current
Where the Equivalent Noise
√4kT/R, Equals the Noise
of the Bias Current
√2qIB
To maximize dc performance over temperature, the source
resistances should be balanced on each input of the amplifier.
This is represented by the optional resistor RB in Figures 4 and 5.
As previously mentioned, for best noise performance, care should
be taken to also balance the source capacitance designated by CB.
The value for CB in Figure 4 would be equal to CS in Figure 5.
At values of CB over 300 pF, there is a diminishing impact on
noise; capacitor CB can then be simply a large bypass of 0.01
F
or greater.