Data processing: measuring – calibrating – or testing – Calibration or correction system – Circuit tuning
Reexamination Certificate
2000-06-30
2003-02-18
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Calibration or correction system
Circuit tuning
C378S091000
Reexamination Certificate
active
06522984
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to pole zero correction generally and, more particularly, to a novel instant pole-zero corrector for digital radiation spectrometers and the same with automatic attenuator calibration.
2. Background Art
The problem of pole-zero cancellation was recognized at the early development of charge sensitive preamplifiers for radiation spectroscopy. See, for example, C. H. Nowlin and J. L. Blankenship, “Elimination of Undesirable Undershoot in the Operation and Testing of Nuclear Pulse Amplifiers”,
Rev. Sci. Instr.,
Vol 36, 12, pp 1830-1839, 1965. The charge sensitive preamplifier produces a voltage step that is proportional to the collected charge from the radiation detector. The charge-to-voltage conversion is achieved by using a capacitor as a negative feedback element of a low noise amplifier. The capacitor accumulates the input charge, which leads to constant increase of the output voltage of the amplifier. Supply voltages limit the output dynamic range of the preamplifier. Therefore, the total charge accumulated across the feedback capacitor is also limited.
To maintain a linear operation of the preamplifier, it is necessary to discharge (reset) periodically the feedback capacitor or to bleed the capacitor charge continuously through a resistor connected in parallel with the feedback capacitor. The first type of preamplifier is known as a “reset” feedback charge sensitive preamplifier. The pole-zero cancellation is associated with the second type of preamplifier often referred to as a “resistive” feedback preamplifier. Hereafter in this description, this type of preamplifier will be simply called a “preamplifier”. A simplified diagram of the preamplifier is shown in FIG.
1
.
When radiation interact with the detector a short current pulse I(t) is produced. The response of the preamplifier to this current is Vp(t). A simple analysis of the circuit can be carried out in the frequency domain −I(s), Vp(s). The input impedance of the preamplifier is
Z
i
=
1
C
i
(
s
+
1
τ
i
)
,
The feedback impedance is
Z
f
=
1
C
f
(
s
+
1
τ
f
)
,
where &tgr;
f
=C
f
R
f
. For simplicity it is assumed that the gain A of the amplifier is frequency-independent.
The transfer function of the preamplifier can be found by solving the following system of equations:
I
(
s
)=
I
i
(
s
)+
I
f
(
s
) (1)
I
1
(
s
)
·
Z
1
(
s
)
=
-
V
p
(
s
)
A
(
2
)
I
i
(
s
)·
Z
i
(
s
)−
V
p
(
s
)=
I
f
(
s
)·
Z
f
(
s
) (3)
where, I
l
(s) and I
f
(s) are the currents flowing through the input impedance and the feedback impedance respectively.
After solving the system of equations (1) to (3) the transfer function is found to be:
H
p
(
s
)
=
V
p
(
s
)
I
(
s
)
=
1
1
A
·
Z
i
(
s
)
+
A
+
1
A
·
Z
f
(
s
)
(
4
)
After substituting the expressions for Z
I
(s) and Z
I
(s) into (4), H
p
(s) can be expressed as:
H
p
(
s
)
=
A
A
+
1
(
C
f
+
C
i
A
+
1
)
(
s
+
1
R
i
R
f
R
i
+
R
f
A
+
1
(
C
f
+
C
i
A
+
1
)
)
(
5
)
Let
C
p
=
(
C
f
+
C
i
A
+
1
)
(
6
)
R
p
=
R
i
R
f
R
i
+
R
f
A
+
1
(
7
)
τ
p
=
R
p
C
p
(
8
)
k
p
=
(
A
A
+
1
)
1
C
p
(
9
)
Using the new variables the preamplifier transfer function can be rewritten as:
H
p
(
s
)
=
k
p
s
+
1
τ
p
(
10
)
Equation (10) represents a single real pole transfer function similar to the transfer function of a low-pass filter. For large gain of the amplifier (A>>)
τ
p
≈
τ
f
=
R
f
C
f
and
k
p
≈
1
C
f
·
From equation (10) the impulse response of the preamplifier can be found. The inverse Laplace transform gives the well known exponential response:
h
p
(
t
)
=
k
p
ⅇ
-
t
τ
p
(
11
)
The response of the preamplifier to a detector current I(t) is given by the convolution integral:
v
p
(
t
)
=
∫
u
.
t
I
(
λ
)
h
p
(
t
-
λ
)
ⅆ
λ
=
∫
u
t
I
(
λ
)
k
p
ⅇ
-
t
-
λ
τ
p
ⅆ
λ
(
12
)
One important property of this response is that if the current has a finite duration, than the signal at the output of the preamplifier will decay exponentially after the current becomes zero. The decay time constant of the tail of the signal is the same as the decay time constant of the impulse response.
FIG. 2
illustrates such response. The preamplifier response to a finite current signal can be easily derived from Equation (12). First, the detector current is defined as:
I
(
t
)
=
{
I
(
t
)
0
≤
t
<
T
c
0
t
<
0
,
t
≥
T
c
(
13
)
From Equations (12) and (13) the response of the preamplifier for t>T
c
can be written as:
v
p
(
t
)
=
∫
0
T
c
I
(
λ
)
k
p
ⅇ
-
t
-
λ
τ
p
ⅆ
λ
=
k
p
ⅇ
-
t
τ
p
∫
0
T
c
I
(
λ
)
k
p
ⅇ
λ
τ
p
ⅆ
λ
(
14
)
where, the integral
∫
0
T
c
I
(
λ
)
k
p
ⅇ
λ
τ
p
ⅆ
λ
is a constant. Therefore, for t>T
c
the preamplifier signal exponentially decays with the same time constant as given by the impulse response.
FIG. 2
shows the preamplifier response to a finite detector current.
Due to various constraints such as noise performance and stability requirements, the preamplifier time constant is usually large. In order to optimize signal to noise ratio and to meet certain throughput requirements it is necessary to “shorten” the preamplifier exponential pulse. Traditionally, this is done using a CR differentiation network (CR high-pass filter).
FIG. 3
shows a preamplifier-CR differentiator configuration.
The CR differentiation network plays an important role in analog pulse shapers. Digital pulse processors also benefit from digitizing short exponential pulses—better utilization of ADC resolution, reduced pile-up losses, and simple gain control. The pole-zero cancellation is an important procedure for both analog and digital pulse processing systems.
When exponential pulses pass through a CR differentiation, circuit the output signal is bipolar. The combined transfer function of the preamplifier-differentiator configuration can be written as:
H
(
s
)
=
k
p
s
+
1
τ
p
s
s
+
1
τ
d
=
k
p
·
s
1
s
+
1
τ
p
1
s
+
1
τ
d
(
15
)
where &tgr;
d
=C
d
R
d
. The impulse response can be obtained from the inverse Laplace transformation:
h
(
t
)
=
k
p
1
1
τ
d
-
1
τ
p
(
1
τ
d
ⅇ
-
t
τ
d
-
1
τ
p
ⅇ
-
t
τ
p
)
(
16
)
If the ratio between the time constants of the preamplifier and the differentiator is
w
=
τ
p
τ
d
,
then Equation (16) can be rewritten as:
h
(
t
)
=
k
p
w
w
-
1
(
ⅇ
-
t
τ
d
-
1
w
ⅇ
-
t
τ
p
)
=
k
p
w
w
-
1
ⅇ
-
t
τ
d
-
1
w
-
1
(
k
p
ⅇ
-
t
τ
p
)
(
17
)
Equation 17 indicates that the response of the preamplifier-differentiator can be expressed as difference of two responses. Both responses represent single real pole systems. The second term in equation (17) is the response of the preamplifier attenuated by a factor of
1
w
-
1
·
Thus, a single pole response with time constant &tgr;
d
can be achieved by simply adding a fraction
1
w
-
1
of the preamplifier signal to the output of the differentiation network.
FIG. 4
shows a basic pole-zero cancellation circuit. The preamplifier signal is applied to a high-pass filter network and a resistive attenuator (e.g. trimpot). The high-pass filter output and the attenuated preamplifier signal are added together and than passed to the pulse shaper. In early designs the analog adder was built using passive components—resistors. Although simple, the resistive adder has a major drawback—its impedance will ch
Canberra Industries, Inc.
Charioui Mohamed
Crozier John H.
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