AD743
–100
–110
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/CF. The amplifier’s input voltage noise will appear at
the output amplified by the noise gain (1 + (CS/CF)) of the circuit.
–120
–130
–140
TOTAL
OUTPUT
NOISE
–150
–160
–170
–180
–190
NOISE
DUE TO
R
ALONE
B
C
F
NOISE
–200
DUE TO
ALONE
R
*
R1
R2
I
B
B
–210
–220
0.01
1k
1
10
100
10k
100k
0.1
FREQUENCY (Hz)
C
A1
S
Figure 6. Noise at the Outputs of the Circuits of
Figures 4 and 5. Gain = +10, CS = 3000 pF, RB = 22 MΩ
C
C
R1
R2
S
C
*
R
*
=
B
B
F
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 IB
(√2qIB), there is diminishing return in making RB larger.
*OPTIONAL, SEE TEXT
Figure 4. Charge Amplifier Circuit
R1
C
*
B
10
R
*
B
A2
R2
C
R
S
B
9
*OPTIONAL, SEE TEXT
Figure 5. Model for a High Z Follower with Gain
8
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.
7
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
6
1pA
10pA
100pA
1nA
10nA
INPUT BIAS CURRENT
T
RB
Figure 7. Graph of Resistance vs. Input Bias Current
Where the Equivalent Noise √4kT/R, Equals the Noise
of the Bias Current √2qIB
˜
N = 4k
∆f
where
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 µF
or greater.
k = Boltzman’s Constant = 1.381 × 10–23 joules/kelvin
T = Absolute Temperature, kelvin (0°C = 273.2 kelvin)
ꢂf = 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.
–8–
REV. E