Datasheet
REV. D
AD745
–8–
Figures 5 and 6 show two ways to buffer and amplify the output
of a charge output transducer. Both require the use of an ampli-
fier that has a very high input impedance, such as the AD745.
Figure 5 shows a model of a charge amplifier circuit. Here,
amplification depends on the principle of conservation of charge
at the input of amplifier A1, which requires that the charge on
capacitor C
S
be transferred to capacitor C
F
, thus yielding an
output voltage of ∆Q/C
F
. The amplifiers input voltage noise will
appear at the output amplified by the noise gain (1 + (C
S
/C
F
))
of the circuit.
A1
C
B
* R
B
*
C
S
R2
R1
R
S
C
F
R1
R2
C
S
C
F
=
Figure 5. A Charge Amplifier Circuit
R
B
C
S
A2
C
B
*
R1
R2
R
B
*
*OPTIONAL, SEE TEXT.
Figure 6. Model for A High Z Follower with Gain
The second circuit, Figure 6, is simply a high impedance fol-
lower with gain. Here the noise gain (1 + (R1/R2)) is the same
as the gain from the transducer to the output. Resistor R
B
, in
both circuits, 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 R
B
contributes a current noise of:
~
N
k
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 5 shows that these two circuits have an identical frequency
response and the same noise performance (provided that
C
S
/C
F
= R1/ R2). One feature of the first circuit is that a “T”
network is used to increase the effective resistance of R
B
and
improve the low frequency cutoff point by the same factor.
FREQUENCY – Hz
–100
0.01
DECIBELS REFERENCED TO 1V/ Hz
–110
–120
–130
–140
–150
–160
–170
–180
–190
–200
–210
–220
0.1 1 10 100 1k 10k 100k
TOTAL
OUTPUT
NOISE
NOISE DUE TO
R
B
ALONE
NOISE DUE TO
I
B
ALONE
Figure 7. Noise at the Outputs of the Circuits of Figures 5
and 6. Gain = 10, C
S
= 3000 pF, R
B
= 22 M
Ω
However, this does not change the noise contribution of R
B
which, in this example, dominates at low frequencies. The graph
of Figure 8 shows how to select an R
B
large enough to minimize
this resistor’s contribution to overall circuit noise. When the
equivalent current noise of R
B
((冑4 kT)/R) equals the noise of
I
B
2qI
B
()
, there is diminishing return in making R
B
larger.
INPUT BIAS CURRENT
5.2 10
10
1pA 10nA10pA
RESISTANCE IN
100pA 1nA
5.2 10
9
5.2 10
8
5.2 10
7
5.2 10
6
Figure 8. Graph of Resistance vs. Input Bias Current
Where the Equivalent Noise
兹4 kT/R
, Equals the Noise
of the Bias Current
I
B
2qI
B
()
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 R
B
in Figures 5 and 6.
As previously mentioned, for best noise performance care should
be taken to also balance the source capacitance designated by
C
B
The value for C
B
in Figure 5 would be equal to C
S
in
Figure 6. At values of C
B
over 300 pF, there is a diminishing
impact on noise; capacitor C
B
can then be simply a large mylar
bypass capacitor of 0.01 µF or greater.