Utah State University Utah State University
DigitalCommons@USU DigitalCommons@USU
Space Dynamics Lab Publications Space Dynamics Lab
1-1-1980
Computer-Aided Design of Optimal Infrared Detector Computer-Aided Design of Optimal Infrared Detector
Preampli7ers Preampli7ers
D. Gary Frodsham
Doran J. Baker
Follow this and additional works at: https://digitalcommons.usu.edu/sdl_pubs
Recommended Citation Recommended Citation
Frodsham, D. Gary and Baker, Doran J., "Computer-Aided Design of Optimal Infrared Detector
Preampli7ers" (1980).
Space Dynamics Lab Publications.
Paper 49.
https://digitalcommons.usu.edu/sdl_pubs/49
This Article is brought to you for free and open access by
the Space Dynamics Lab at DigitalCommons@USU. It has
been accepted for inclusion in Space Dynamics Lab
Publications by an authorized administrator of
DigitalCommons@USU. For more information, please
contact digitalcommons@usu.edu.
Computer -aided design of optimal infrared detector preamplifiers
D. Gary Frodsham, Doran J. Baker
Electro- Dynamics Laboratories, Department of Electrical Engineering
Utah State University, UMC 41, Logan, UT 84322
Abstract
A mathematical model is given for a frequency -compensated detector /preamplifier appro-
priate for cryogenically-cooled infrared sensors operating under low background conditions.
By use of a digital computer, this model is used to rapidly select the optimal combination
of design values.
These parameters include load resistance, compensation resistance, com-
pensation capacitance, chopping frequency and detector area to meet desired specifications
of noise equivalent power, frequency response, dynamic range, and level of output noise.
This computer -aided optimal design approach is demonstrated using a contemporary infrared
sensor application.
Introduction
The optimal design of infrared detector /preamplifier configurations is complicated by
nonlinear interdependencies among system characteristic factors including the frequency
response, the dynamic range, the output noise level, the detector size and the noise equiva-
lent power of the sensor. The calculation and plotting of the interactive effects due to
varying design parameters is arduous.
However, the advent of the desk -top computer - graphic
system has greatly facilitated the optimization procedure.
Once the software has been de-
veloped, the engineer can in a matter of a few minutes plot a family of curves of NEP as a
function of load resistance, frequency or detector size, for example.
The mathematical model given in this paper is an expansion of the work previously re-
ported by Frodsham and Baker.1 The algorithms are limited to detector /preamplifier configu-
rations operating under low infrared background (zilch) and white input noise conditions.
However, the algorithms have proven to be sufficiently accurate for the designer in charac-
terizing most contemporary cryogenically- cooled detectors combined with JFET input electro-
meter preamplifiers.
Detector /preamplifier configuration
The infrared detector and preamplifier combination with frequency compensation is illus-
trated in Figure 1. The negative feedback elements of the operational preamplifier of open
loop gain A are shown as RL and CL. The external shunt capacitance CL (typically 1 to 3 pf)
is added to swamp out the stray capacitance distributed along the body of RL.
The compensa-
tion elements Cc and Rs are then added to compensate for the frequency response roll -off due
to RL and CL.
The capacitor Cs is a modification to the configuration previously published
by Frodsham and Baker;1 it is added to compensate for the roll -up associated with Ct = Ci +
Cd, where Ci is the capacitance inherent within the preamplifier and Cd is that associated
with the detector.
Detector
Vbias
cs
Rd
Vna
Figure 1.
Configuration model for detector /preamplifier subsystem used in radiometer.
Mathematical model
The total in -band noise produced by the modeled detector /preamplifier under zilch infra-
red background conditions is Vnt = f(RL)f(w).
The function f(RL) is given by
f(RL)
= RL {[4kTGp +
Vna2Gp2I(f2
-
fl)
+
[Vna2TrCp]2(f23
- f13)/3}2
(1)
SPIE Vol. 246 Contemporary Infrared Sensors and Instruments (1980) / 39
Computer-aided
design
of
optimal
infrared
detector
preamplifiers
D.
Gary
Frodsham,
Doran
J.
Baker
Electro-Dynamics
Laboratories,
Department
of
Electrical
Engineering
Utah
State
University,
UMC
41,
Logan,
UT
84322
Abstract
A
mathematical
model
is
given
for
a
frequency-compensated
detector/preamplifier
appro-
priate
for
cryogenically-cooled
infrared
sensors
operating
under
low
background
conditions.
By
use
of
a
digital
computer,
this
model
is
used
to
rapidly
select
the
optimal
combination
of
design
values.
These
parameters
include
load
resistance,
compensation
resistance,
com-
pensation
capacitance,
chopping
frequency
and
detector
area
to
meet
desired
specifications
of
noise
equivalent
power,
frequency
response,
dynamic
range,
and
level
of
output
noise.
This
computer-aided
optimal
design approach
is
demonstrated
using
a
contemporary
infrared
sensor
application.
Introduction
The
optimal
design
of
infrared
detector/preamplifier
configurations
is
complicated
by
nonlinear
interdependencies
among
system
characteristic
factors
including
the
frequency
response,
the
dynamic
range,
the
output
noise
level,
the
detector
size
and
the
noise
equiva-
lent
power
of
the
sensor.
The
calculation
and
plotting
of the
interactive
effects
due
to
varying
design
parameters
is
arduous.
However,
the
advent
of
the
desk-top
computer-graphic
system
has
greatly
facilitated
the
optimization
procedure.
Once
the
software
has
been
de-
veloped,
the
engineer
can
in
a
matter
of
a
few
minutes plot
a
family
of
curves
of
NEP
as
a
function
of
load
resistance,
frequency
or
detector
size,
for
example.
The
mathematical
model
given
in
this
paper
is
an
expansion
of
the
work
previously
re-
ported
by
Frodsham
and
Baker.
1
The
algorithms
are
limited
to
detector/preamplifier
configu-
rations
operating
under
low
infrared
background
(zilch)
and
white
input
noise
conditions.
However,
the
algorithms
have
proven
to
be
sufficiently
accurate
for
the
designer
in
charac-
terizing
most
contemporary
cryogenically-cooled
detectors
combined
with
JFET
input
electro-
meter
preamplifiers.
Detector/preamplifier
configuration
The
infrared
detector
and
preamplifier
combination
with
frequency
compensation
is
illus-
trated
in
Figure
1.
The
negative
feedback
elements
of
the
operational
preamplifier
of
open
loop
gain
A
are
shown
as
RL
and
CL.
The
external
shunt
capacitance
CL
(typically
1
to
3
pf)
is
added
to
swamp
out the
stray
capacitance
distributed
along
the
body
of
RL.
The
compensa-
tion
elements
C
c
and
R
s
are
then
added
to
compensate
for
the
frequency
response
roll-off
due
to RL
and
CL»
The
capacitor
C
s
is
a
modification
to
the
configuration
previously
published
by
Frodsham
and
Baker;
1
it
is
added
to
compensate
for
the
roll-up
associated
with
C-£
=
Cj_
+
Cj,
where
C-[
is
the
capacitance
inherent
within
the
preamplifier
and
C^
is
that
associated
with
the
detector.
Detector
Vbias
Figure
1.
Configuration
model
for
detector/preamplifier
subsystem
used
in
radiometer.
Mathematical
model
The
total
in-band
noise
produced
by
the
modeled
detector/preamplifier
under
zilch
infra-
red
background
conditions
is
V
nt
=
ffRjJfCuO.
The
function
£(RL)
i
s
given
by
=
R
L
{[4kTG
p
+
V
na
2
G
p
2
](f
2
-
f
x
)
+
[V
na
2TrCp]
2
(f
2
3
-
£^3/3}*
(D
SPIE
Vol.
246
Contemporary
Infrared
Sensors
and
Instruments
(1980)
/
39
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/13/2014 Terms of Use: http://spiedl.org/terms
Frodsham, D. Gary, and Doran J. Baker. 1980. “Computer-Aided Design of Optimal Infrared Detector Preamplifiers.”
Proceedings of SPIE 0246: 39–47. doi:10.1117/12.959354.
FRODSHAM, BAKER
where
k = 1.38 x 10-23 joule / °K
T = absolute temperature of RL and Rd
fl = upper cut -off frequency
Gp =
1 /RL +
1 /Rd
Cp = CL + Ci + Cd
The square of the frequency function is given by
[f(w)12 =
(TS
+ Tc + 1)/{[TS + TL + apT1/K + aTd/K + p/K)w +
(TLTSL -
+
[(1 + ap/K)
-
(TSTL + aT1Td/K + pTl/K +
Td/K)w2]}2
where p
= (RL + Rd) /Rd and the various time constants are given by
Ts = RSCs
TL = RLCL
T1 = RS(CL + Cs)
Td = RL(CL + Cd)
Tc = RsCc
TSL = RSCL
K = preamp open loop d.c. gain
a = preamp open loop frequency break point
AL» Rs
Cs + Cc» CL
(2)
Whereas the function f(w) describes the frequency response of the model for any values
of the capacitance Cs and Cc, the condition of interest is that of compensation, namely,2
Cc = RLCL/Rs -
CS
Under conditions of compensation, the function f(w) simplifies to
f(w)
= w112/[w2
(2 /wn2) + wn2]
where
wn = (K/RLC)
= RSCSw2/2
The value of frequency con is the upper cutoff frequency of the compensated detector /pre-
amplifier combination. Therefore,
f2(max) _
(1/27r) [K/RLCp]
i
(5)
Under critically- damped conditions, the ç damping factor is equal to unity. Thus, the value
of Cs for the non -oscillatory case is
Cs(crit) = (2/Rs)[RLCp/K]Z
(6)
To ascertain the noise equivalent power from the model, we use the defining relationship
where
NEP = Vn(rms) /responsivity(rms /watt) = Vntc /RXRLTrf(w)
c = chopping factor
T
r
= transmittance
RX = detector current responsivity
40 / SPIE Vol. 246 Contemporary Infrared Sensors and Instruments (1980)
(7)
FRODSHAM,
BAKER
where
k
=
1.38
x
10"
23
joule/°K
T
=
absolute
temperature
of
RL
and
R^
£
=
upper
cut-off
frequency
G
P
=
i/R
L
+
i/R
d
c
p
=
C
L
+
q
+
c
d
The
square
of
the
frequency
function
is
given
by
[f(u)]
2
=
(
TS
+
T
C
+
!)/{[T
S
+
T
L
+
apTj/K
+
aT
d
/K
+
p/K)
u
+
^
L
^
SL
-
t^)^]
2
+
[(1
+
ap/K)
-
(T
S
T
L
+
ai^d/K
+
p^/K
+
T
d
/K)u)
2
]}
2
(2)
where
p
=
(R^
+
R
d
)/R
d
and
the
various
time
constants
are
given
by
T
=
R
C
K
=
preamp
open
loop
d.c.
gain
T
T
=
RiCr
a
=
preamp
open
loop
frequency
break
point
T
X
=
R
S
(C
L
+
C
s
)
RL
>;>
R
s
t
d
=
R
L
(C
L
+
C
d
)
C
s
+
C C
»C
L
T
C
=
R
S
C C
T
SL
=
R
s
C
L
Whereas
the
function
f
(w)
describes
the
frequency
response
of
the
model
for
any
values
of
the
capacitance
C
s
and
C c
,
the
condition
of
interest
is
that
of
compensation,
namely,
2
C
c
=
R
L
C
L
/R
S
-
C
s
(3)
Under
conditions
of
compensation,
the
function
fO)
simplifies
to
£(*>)
=
a,
n
2
/[
u
2
+
(2c/ Un
2
)
+
u
n
2
]
(4)
where
u)
n
=
(K/R
L
C
p
)
?
=
R
s
C
s
co
2
/2
The
value
of
frequency
w
n
is
the
upper
cutoff
frequency
of
the
compensated
detector/pre-
amplifier
combination.
Therefore,
f
2
(ma>0
-
(l/20[K/R
L
C
p
]
(5)
Under
critically-damped
conditions,
the
c
damping
factor
is
equal
to
unity.
Thus,
the
value
of
C
s
for
the
non-oscillatory
case
is
C
s(crit)
=
(2/R
s
)[R
L
Cp/
K
^
^
To
ascertain
the
noise
equivalent
power
from
the
model,
we use
the
defining
relationship
NEP
=
V
n(rms)
/responsivity(rms/watt)
=
V^c/R^^f
(a,)
(7)
where
c
=
chopping
factor
transmittance
detector
current
responsivity
T
=
transmittance
40
/
SPIE
Vol.
246
Contemporary
Infrared
Sensors
and
Instruments
(1980)
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/13/2014 Terms of Use: http://spiedl.org/terms
COMPUTER -AIDED DESIGN OF OPTIMAL INFRARED DETECTOR PREAMPLIFIERS
Finally, substitution of the algorithm (Eqs. 1 and 2) for Vnt into Equation (7) gives
NEP = C /RATr[(4kTGp + Vna2Gp2)(f2
- fl) +
(Vna27Cp)2(f23 - f13) /30
(8)
Two additional characterizing functions, which can be derived from Equations (1) and (2),
are preamplifier dynamic range Dr and preamplifier output noise density Vna(f). The dynamic
range is defined as the maximum possible rms signal output voltage divided by the zero
signal rms noise.
Thus, a working value for Dr is simply
Dr = 4/f(RL)
(9)
The noise density function Vnt(f) expressed in volts / Hz is derived from Vnt by substi-
tuting f = fl = f2 -
1 and w /2rr into Equations (1) and (2) to obtain
Vnt (f)
= RL [4kTGp
+
Vna2
+ (Vna2
rCp) 2 (f2 f + 1/3) ]
1/2
f (w)
Application to radiometer
To demonstrate the utility of the computer -aided design approach, an actual application
used in the design of a cryogenically -cooled, dual- channel radiometer is summarized. This
radiometer was subsequently flown on a space vehicle.
(10)
Equations (1) through (10) characterize the Frodsham -Baker detector /preamplifier model
for any given detector assuming the detector resistance Rd and capacitance Cc are known.
In Table 1 below, these detector parameters are characterized as a function of sensitive
area for three types of detectors:
(1) intrinsic silicon at 77 °K, (2) extrinsic silicon at
10 °K, and (3) indium antimonide at 77 °K.
Table 1. Detector characteristics
Rd(ext. Si) = 1.35 x 1012/Ad (ohms)
Cd(ext. Si)
=
2 x 10-13[Ad] (farads)
Rd(int. Si)
= 1 x 1015
(ohms)
Cd(int. Si) = 1 x
10 11[Ad]2
(farads)
Rd(InSb) =
2
x 106/Ad
(ohms)
Cd(InSb)
= 5 X 10-8 Ad (farads)
where Ad = detector active area
The system design parameters for the dual- channel radiometer, which is liquid- nitrogen
cooled and is designated by the Model No. NR -7, are listed in Table 2
(computer listing).
Table 2.
The system input parameters are:
Signal Coupling (AC or DC) -(F$)= AC
Electrical Bandwidth (F3)= 3.00E +001(HZ)
Chopper Frequency
(F4)= 1.00E +002(HZ)
Preamp Input Capacitance
(A1)= 8.00E- 012(FARAD)
Preamp Input Noise (A2)= 2.00E -008(V / HZ)
Feedback Resistance
(A3)= 1.00E +009(OHMS)
Feedback Capacitance
(A4)= 1.00E- 012(FARADS)
Component Temperature
(A5)= 7.70E +001(KELVIN)
Detector Area (D1)= 7.85E- 003(SQ.CM)
Detector Responsivity
Det. Type(In:Sb,As:Si,Sil)
Collector Area
Field of View(Half Angle)
Optical Transmission
(D2)= 1.00E+000(A/W)
(D$)s In:Sb
(ol)= 1.82E+000(SQ.CM)
(02)= 2.00E+000(DEG)
(03)= 3.50E-001
The parameter values shown for the chopper frequency, the resistance and capacitance,
and the detector area are initial estimates for the working values.
The final design
values, along with those for the compensation elements, were determined by the computer -
aided design approach as follows.
SPIE Vol. 246 Contemporary Infrared Sensors and Instruments (1980) /
41
COMPUTER-AIDED
DESIGN
OF
OPTIMAL
INFRARED
DETECTOR
PREAMPLIFIERS
Finally,
substitution
of
the
algorithm
(Eqs
.
1
and
2)
for
V
nt
into
Equation
(7)
gives
NEP
=
C/R
x
T r
[(4kTG
p
-
f
(f
-
£
(8)
Two
additional
characterizing
functions, which
can
be
derived
from
Equations
(1)
and
(2),
are
preamplifier
dynamic
range
D
r
and
preamplifier
output
noise
density
V
na
(f).
The
dynamic
range
is
defined
as
the
maximum
possible
rms
signal
output
voltage
divided
by
the
zero
signal
rms
noise.
Thus,
a
working
value
for
D
r
is
simply
D
r
=
4/f(R
L
)
(9)
The
noise
density
function
V
n
^-(f)
expressed
in
volts//Hz
is
derived
from
V
nt
by
substi-
tuting
f
=
f
1
=
£
2
-
1
and
u/2n
into
Equations
(1)
arid
(2)
to
obtain
nt
(£)
=
R
L
[4kTG
p
-
f
1/3)
(10)
Application
to
radiometer
To
demonstrate
the
utility
of
the
computer-aided
design
approach,
an
actual
application
used
in
the
design
of
a
cryogenically-cooled
,
dual-channel
radiometer
is
summarized.
This
radiometer
was
subsequently
flown
on
a
space
vehicle.
Equations
(1)
through
(10)
characterize
the
Frodsham-Baker
detector/preamplifier
model
for
any
given
detector
assuming
the
detector
resistance
R<-j
and
capacitance
CQ
are
known.
In
Table
1
below, these
detector
parameters
are
characterized
as
a
function
of
sensitive
area
for
three
types
of
detectors:
(1)
intrinsic
silicon
at
77°K,
(2)
extrinsic
silicon
at
10°K,
and
(3)
indium
antimonide
at
77°K.
Table
1.
Detector
characteristics
R
d
(ext.
Si)
*
C
d
(ext.
Si)
*
R
d
(int.
Si)
*
C
d
(int.
Si)
-
R
d
(InSb)
-
2
>
C
d
(InSb)
-
5
>
1.35
x
10
12
/A
d
(ohms)
2
x
10-
13
[A
d
]
(farads)
1
x
10
15
(ohms)
1
x
10"
l l
[A,]
3
*
(farads)
Q
<
10
6
/A
d
(ohms)
<
10"
8
A
d
(farads)
where
A_,
=
detector
active
area
The
system
design
parameters
for the
dual-channel
radiometer,
which
is
liquid-nitrogen
cooled
and
is
designated
by
the
Model
No.
NR-
7
,
are
listed
in
Table
2
(computer
listing).
Table
2.
The
system
input
parameters
are:
_____
Signal
Coupling
(AC
or
DC)-(F$)=
AC
Electrical
Bandwidth--
-----
(F3)=
3
.
00E+001
(HZ)
Chopper
Frequency-
---------
(F4)=
1
.
00E+002
(HZ)
Preamp
Input
Capacitance-
--
(Al)
=
8
.
00E-012
(FARAD)
Preamp
Input
Noise-
--------
(A2)
=
2
Feedback
Resistance-
-------
(A3)
=
1
Feedback
Capacitance
-------
(A4)=
1
Component
Temperature
------
(A5)
=
7
Detector
Area-
-------------
(Dl)
=
7
.
85E-003
(SQ.
CM)
Detector
Responsivity--
----
(D2)
Det.
Type(In:Sb,As:Si,Sil)
(D$)
Collector
Area-
------------
(01)
=
1
.
82E+000
(SQ
.
CM)
Field
of
View(Hal£
Angle)
--
(02)
=
2
.
00E+000
(DEC)
Optical
Transmission-------
(03)=
3.50E-001
00E-008
(V//HZ)
00E+009
(OHMS)
00E-012
(FARADS)
70E+001
(KELVIN)
1
.
00E+000
(A/W)
In:Sb
The
parameter
values
shown
for
the
chopper
frequency,
the
resistance
and
capacitance,
and
the
detector
area
are
initial
estimates
for the
working
values.
The
final
design
values, along
with
those
for
the
compensation
elements, were
determined
by
the
computer-
aided
design
approach
as
follows.
SP/E
Vol.
246
Contemporary
Infrared
Sensors
and
Instruments
(1980)
/
41
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/13/2014 Terms of Use: http://spiedl.org/terms
FRODSHAM, BAKER
The feedback load resistance RL was determined from the computer - generated curve shown
as Figure 2. The value was selected as 109 ohms since this gave an NEP which was less than
half of a decibel more than would occur for an infinite value for RL (indicated as zero db
on the ordinate scale) without impacting the dynamic range specification of 105 nor the
upper frequency cutoff requirement of 130 Hz.
Next, the detector area was examined with the aid of the generated curves shown in
Figure 3.
Since the optimum value of the load resistance (recomputed for each value of
detector area) decreases as Ad increases, the resultant NEP value worsens as the area
increases.
Consequently, the dynamic range capability also increases with increased
detector size.
It can be seen from the curves that the NER is approaching a constant and
is less than 3 db above the asymptotic value at the preselected value of 7.85 x 10 73cm2
for area.
From the curve shown in Figure 4, the effect of changing the chopping frequency can be
analyzed.
The practical application of the Nyquist rate dictates that the chopper frequency
be at least the 100 Hz initially selected. Any increase above the selected value of 100 Hz
would cause a degredation of both the dynamic range and the NEP.
Figure 5 gives the computed frequency curve for the detector /preamplifier combination
for Channel A of the radiometer using the actual and /or initially estimated parameter
values as shown. Curve 1 is the desired frequency response.
Using the initially selected
values of 27 and 56 pf for Cs and Cc, respectively, the frequency response curve was then
experimentally measured.
The unsatisfactory result is shown as Curve 1 in Figure 6.
Using
this curve, the computer model parameters were adjusted to reproduce the unsatisfactory
response curve; the values of Cs and Cc given by the computer were 24 and 42 pf, respec-
tively. The next step was to ratio the two sets of values, giving a value set of 30 and
75 pf.
The final step was to experimentally measure the response curve again using these
new values.
The result is Curve 2 of Figure 6 which shows excellent agreement with the
frequency response desired.
Figures 7 and 8 show the similar computer -aided analyses applied to Channel B of the
radiometer.
In this case a slightly larger value of CL was selected initially; the result
was the computer curve of Figure 7. The measured response curve, given in Figure 8, shows
excellent agreement without changing the compensation element values.
Finally, the de-
tector /preamplifier noise density functions (volts / /Hz) were computed for both Channels A
and B. The results are shown in Figures 9 and 10, respectively.
These data were generated
to verify preamplifier performance by comparing with measured data, and in this case good
agreement was found.
NR7-1
18E 8
7
6
s
4
3
2
0
OHMS
10E9
10E10
+
+
+
o
7
VARIABLE -FULL SCALE -DB=O REF. -UNITS
+ DR
70 DB
8.76E+802
- NEP
7 DB
2.66E-013(UATTS)
o F2(MAX)70 DB 1.38E+001(HZ)
+
+
+
..111
+
+
+
+
70
60
50
40
DB
30
20
10
0
Figure 2.
Relative dynamic range, NEP and upper frequency cutoff as a function of RL.
42
/ SPIE Vol. 246 Contemporary Infrared Sensors and Instruments (1980)
FRODSHAM,
BAKER
The
feedback
load
resistance
RL
was
determined
from
the
computer-generated
curve
shown
as
Figure
2.
The
value
was
selected
as 10
9
ohms
since
this
gave
an
NEP
which
was
less
than
half
of
a
decibel
more
than
would
occur
for
an
infinite
value
for
R
L
(indicated
as
zero
db
on
the
ordinate
scale)
without
impacting
the
dynamic
range
specification
of
10
5
nor
the
upper
frequency
cutoff
requirement
of
130 Hz.
Next,
the
detector
area
was
examined
with
the
aid
of the
generated
curves
shown
in
Figure
3.
Since
the
optimum
value
of
the
load
resistance
(recomputed
for
each
value
of
detector
area)
decreases
as
Aj
increases,
the
resultant
NEP
value
worsens
as
the
area
increases.
Consequently,
the
dynamic
range
capability
also
increases
with increased
detector
size.
It
can
be
seen
from
the
curves
that
the
NER
is
approaching
a
constant
and
is
less
than
3
db
above
the
asymptotic
value
at
the
preselected
value
of
7.85
x
10~
3
cm
2
for
area.
From
the
curve
shown
in
Figure
4,
the
effect
of
changing
the
chopping
frequency
can
be
analyzed.
The
practical
application
of
the
Nyquist
rate
dictates
that
the
chopper
frequency
be
at
least
the
100
Hz
initially
selected.
Any
increase
above
the
selected
value
of
100
Hz
would
cause
a
degredation
of
both
the
dynamic
range
and
the
NEP.
Figure
5
gives
the
computed
frequency
curve
for
the
detector/preamplifier
combination
for
Channel
A
of
the
radiometer
using
the
actual
and/or
initially
estimated
parameter
values
as
shown.
Curve
1
is
the
desired
frequency
response.
Using
the
initially
selected
values
of
27
and
56
pf
for
C
s
and
GC
,
respectively,
the
frequency
response
curve
was
then
experimentally
measured.
The
unsatisfactory
result
is
shown
as
Curve
1
in
Figure
6.
Using
this
curve,
the
computer
model
parameters
were
adjusted
to
reproduce
the
unsatisfactory
response
curve;
the
values
of
C
s
and
C c
given
by
the
computer
were
24
and
42
pf,
respec-
tively.
The
next
step
was
to
ratio
the
two sets of
values,
giving
a
value
set
of
30
and
75
pf.
The
final
step
was
to
experimentally
measure
the
response
curve
again using
these
new
values.
The
result
is
Curve
2
of
Figure
6
which
shows
excellent
agreement
with
the
frequency
response
desired.
Figures
7
and
8
show
the
similar
computer-aided
analyses
applied
to
Channel
B
of
the
radiometer.
In
this
case
a
slightly
larger
value
of
CL
was
selected
initially;
the
result
was
the
computer
curve
of
Figure
7.
The
measured
response
curve,
given
in
Figure
8,
shows
excellent
agreement
without
changing
the
compensation
element
values.
Finally,
the
de-
tector/preamplifier
noise
density
functions
(volts//Hz)
were
computed
for
both
Channels
A
and
B.
The
results
are
shown
in
Figures
9
and
10,
respectively.
These
data
were
generated
to
verify
preamplifier
performance
by
comparing
with
measured
data,
and
in
this
case
good
agreement
was
found.
NR7-1
10E
8
OHMS
5
-
10E
9
—1———
10E18
10E1I
VARIABLE-FULL
SCALE~Dfr=0
REF.-UNITS
+
DR
70
DB
8.78E+002
-
NEP
7
DB
2.86E-013CWATTS5
a
F2CMAX:>70
DB
1.38E+00KHZ3
"
D
-fc
[
.
|
.
I
.
1
.
t
T
T*.
I
.1
60
50
40
DB
30
20
10
Figure
2.
Relative
dynamic
range,
NEP
and
upper
frequency
cutoff
as
a
function
of
42
/
SPIE
Vol.
246
Contemporary
Infrared
Sensors
and
Instruments
(1980)
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 10/13/2014 Terms of Use: http://spiedl.org/terms
