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A logarithmic converter for nuclear pulses
NUCLEAR INSTRUMENTS AND METHODS 32 (1965) 141 -146 ; D, NORTH-HOLLAND PUBLISHING CO.
A LOGARITIUMC CONVERTE
FOR WCL" MLMS
T. MRAMOTO Physics Division, National Institute of Radiological Sciences, 250, Kurosuna-cho, Chiba, Japan Received 1 .4 July 1964 This paper describes a logarithmic converter which provides a means of adapting a regular linear amplifier to logarithmic operations . The converter basically consists of a current generator and a log-take element. To stabilize the static reference level
and to obtain a wide logarithmic range, the author proposes a particular method of polarizing the conversion diode. Operational characteristics, pulse response and the effect of variations in temperature are discussed.
1. Introdtwdon In scintillation beta- or gamma-spectrometry, the dynamic range of a conventional pulse-height analyzer combined with a linear amplifier is often too short when mixed radiation ofwidely different or unknown energies are analyzed. This is particularly true in low level application because repeating measurements by rearranging the linear amplifier gain is quite time consuming. In such cases, it is desirable to represent the energy axis in a logarithmic scale by using a logarithmic converter in the pules amplifier . The following logarithmic converter circuit was developed to identify radioactive nuclides at low levels using the coincidence type beta-ray scintillation spectrometer'- 2). There are two types of logarithmic pulse converters, the indirect and direct types. The converter developed by Crouch et al?) is based on amplitude-to-time conversion using a constant level discriminator for exponentially decaying pulsts .'This inethod is stable and a wide dynamic range may be obtained . However, this type of converter is not suitable for coincidence work. Gianelli et A') reported a direct conversion method for multiplying or dividing two or more pulses . They used the emitter-base junction of germanium drift transistors as the log-take elements. These junctions have a wide dynamic range with close logarithmic characteristics, but the circuit configuration is more or less limited by the fact that the base must be grounded and that transistors of this type are only of the prip type. A direct type logarithmic amplifier using a germanium diode was reported by Udo et al.). To improve duty cycle,, they proposed a stabilization ofthe lode voltage in a quiescent state, and obtained reasonable characteristics . The converter described in this paper is also the direct type using a silicon diode as the log-take element . The convener allows a linear amplifier to be modified to the logarithmic type 'Jy insertion of the converter tx:tw ,Ûen the appropriate amplifying stages . The complete converter circuit i., transistorized.
2. Log-take element The normal theory for rectification of a p-n junction diode leads to the expression V = (kTIe) In
+ 1]
(1)
where 1, is the thermally generated saturation current, I the diode current, e the electronic charge, k the Boltzmann constant, T the absolute temperature, and V the forward voltage of the diode. In the forward direction, the unity term can be neglected for V > 0.1 V at room temperature . Thus, eq. (1) may be approximated by V = (Ule) In 111,
(2)
the present application, a diode with close logarithmic characteristics of about three decades may be sufficient . The value of the diode current corresponding to these decades is restricted by a converter circuit in which this diode is employed . When a transistorized circuit is used, the preferable current range may be between 10' - 10' A, taking into consideration the transistor collector cutoff current and pulse response of the circuit, etc. In general, the actual d.c. characteristics of typical diodes exhibit a noticeable departure from eel. (1). For d.c. current, the ohmic drop across the entire diode and the conductivity modula-don must be taken into account at comparatively high current levels . The latter effect is due to the change in conductivity of semiconductor material caused by the change in the carrier density . In addition to the d .c. characteristics, diodes generally show reactive effects which become appreciable when used for high speed pulses. When a comparatively high current pulse is fed to the diode, the diode may initially exhibit an excessive voltage drop, which decays to its normal d.c. value, as if the diode possessed an apparent series inductance . This effect is also considered to be caused by conducliv~!y modulation. The diode capacitance also afl'u, ~,, tile pulse In
142
T. HIRAMOTO
reqwnse and is mainly due to the capacitance of the junction transition layer. The rise time ofthe converted I increases with this capacitance. Diodes having desirable d.c. and pulse characteristics &scr~ " = rarely available although the types ing either d.c. or pulse characteristics are readily available commercially. As an "ample, the voltage-current characteristics of some typical silicon diodes are shown in fig. 1, in which the dotted lines
time required to reach the final d.c. values, about 5 psec, is independent of the diode current . The forward characteristics ofcertain types of silicon voyage regulator diodes are also shown in fig. 1 . The regulating voltages are about 15 V, 13 V and 5 V for the IS142, RIB13A and RD5A, respectively. The 1557 is supplied for meter protection when the forward direction is used, however, this diode has the same structure as the voltage regulators. These voltage regulators have good logarithmic characteristics with a negligible conductivity modulation effect . The best results were obtained with diodes having regulating voltages around 10 V. It is considered that these good characteristics are due to the diffused junction made of highly doped materials, It should be noted that the transition layer capacitance of these diodes are fairly large compared with usual diodes due to the highly doped materials . This capacity amounts to several hundreds pF at the applied voltage of about 0.5, V . The effect of the junction capacitance is, however, not a serious problem because this effect can be reduced to some extent by the use of capacitive feed-back, which will be described later. One I S57 is used in the present converter . 3. Some problems In SPOICation of the conversion diodes 3.1 . POLARIZING THE CONVERSION DIODES
vars Fig. 1 . 6 4 characteristics of some silicon diodes .
represent the peak voltage of initial drop due to the conductivity modulation .The measurements were made with test pulses of 0.25 psec rise. As shown in this figure, fast diodes such as the bonded type do not have and logarithmic characteristics although they do not exhibit conductivity modulation effects. On the other haud, slow diodes of alloy or diffvse topes have good logarithmic characteristics . In these diodes, then is a tendency that diodes of higher maximum allowable inverse voltage begin to show conductivity modulation at a lower diode current . I .he diodes I S 180 and SD102, have good logarithmic characteristics in the region less than 2 and. But in these diodes ., the rise time has a slow component, although its rrtechan.ism is not understandable . The
In a practical conve! tar circuit, it is necessary that the conversion diode be polarized by a constant current . The main roles of polarization are to stabilize the d.c. condition of the diode by avoiding temperature effect of 1. in eq. (1), to improve the response to fast input signals by preventing excessive voltage excursion in the !ow current range and to obtain fast recovery from transient by reducing the dynamic resistance of the diode in a quiescent state. The last role is especially important when the diode is coupled to the other circuit through a capacitor .
Fig. 2. Method of pr,!arizir% the conversion diode . 1 : signal current, 10 : polariziug current, D1 . conversion diode, D2 . compensating diude.
143
A LOGARITHMIC CONVERTER FOR NUCLEAR PULSES
A simple method of polarization is to supply a constant current through the high resistance R, as shown in fig. 2(a). In this case, the converted voltage V,, is given by V, = (kTIe) In (I + 10 + IJI(Io + IS)
(3)
where 10 is the polarizing current and I the signal
current . Therefore, if 10 ~ 1, the temperature dependence of 1, can be avoided. However, the use of large I0 values results in the shortening of the dynamic range, because ideal logarithmic characteristics are expected only when I > 10.
3.2. PULSE RESPONSE
A large capacitance of the conversion diode affects pulse response of the converter. The transition layer capacitance varies inversely as the square or cubic root of the difference between the barrier voltage and the applied voltage, according to the type of the junction . The variation of this capacitance is about 20*/,, per decade of diode current changes in the current region of interest. The waveform of the converted signal is quite different from that of the usual pulse in a linear circuit and is dependent on the amplitude of the input signal . For sty signal current, the. time t required for the converted pulse to reach a fraction a of its final value is calculated as follows : t = ~qRd loglo I/i o - I D [(I/IO) I
l-"I - I I
Fig . 3. Signal current-converted voltage characteristics. (a) without compensation, (b) with compensation .
where C is the diode capacitance, Rd the final value of the diode resistance at diode current of I and D is the ratio 1110 in terms of decades. In the above calculation, the diode capacitance was azsumed to be constant, since its variation is negligible compared with that of diode resistance.
In fig. 3, the curve (a) is a calculated coriversion characteristic neglecting I., and the dashed line is the ideal one expressed by VC = (kTIe) In 1/10. According to the calculation, the lowest signal current is limited to 22 10 to keep the departure within 0.02 decades . This departure is greatly ; educed by the use of a compensating diode as shown in fig. 2 (b). When the signal current flows, the voltage drop across D, decreases, hence the polarizing current decreases accordingly. In this case, the converted voltage Vr is given by Vc = (4) (Ule) In [(1121 0) {I + V1 + (10/2J)2) ]
-
provided diodes of the same characteristics are used in the conversion and compensation. The calculated relation is shown as the curve (b) in fig. 3 . The lower limit of the current range is decreased to 4.7 10 keeping the error within 0.02 decades, If two or more diodes cascaded in series are used as the conversion diodes in combination with one compensating diode, closer logarithmic characteristics will be obtained .
Fig . 4. Waveform of the converted signal .
The calculated waveforms fcr different values of D are shown in fig. 4. The waveform of pulses integrated by the constant CR is also shown in the figure. The values of i are expressed as a function of t,'CRd . The hiss time of the converted pulse becomes very large for the small input signal since Rd increases with the decrease of the signal current . It will also be seen that a faster pulse response is expected in the higher current range than in the lower range for the given I/10 ratio . 3 .3. TEMPERATURE EFFECT
The temperature dependence of the core c' $ 4,~on diodes
T. HIRAMOTO must
kept within
± 3° C, at room temperature, in
keep the error within ± 0.02 decades at the current of 101 x 10. Therefore, it would be
order to signal
necessary to immerse the conversion
91.0
diode in a constant
temperature bath or to control the gain of the output
amplifier by a temperature sensitive element such as a thermistor . 1
1 O
1 10
1 1 1 1 20 ZO 4n 50 TEMPERATM fl
Fig. 5. Temperature dependence of the a serious problem in
1
4. Converter
conversion diode.
their practical use,
SIi41e of the conversion characteristic is
because the
a function of
temperature. The slope expressed in terms of voltage decade is calculated from eq. (1) as follows: VD =
where the effect of IS
(kTfe)
In 10
(6)
is ignored since the effect is
avoided by polarizing the diode.
circuit
The current generator dri-ing the conversion diode must have an internal resistance much larger than the diode resistance and the output curreat in the quiescent state must be sufficiently smaller than the polarizing current.' Several circuits of the converter were designed and tested . Block diagrams of th circuits are shown in fig. 6. Each is composed of an amplifier and a driving transistor. The driving transistor is slightly cutoff in the quiescent state. Types (a) and (c) acoept positive pulses and type (b)
tcl cal tel Fig . 6. Block diagrams of converter circuits . Vs : input voltage signal, Vc : Converted signal. The slope was measured experimentally using the 1 S57. The results are plotted in fig. 5. The solid line in
the figure is the theoretical change of the slope. These data are normalized to unity at 24"C. As shown by the results, the temperature variation
accepts negative pulses, respectively . Provided the gain of the amplifier is very large, the current fed to the conversion diode is equal to VdR(I + I/ß) in types (b) and (c) and V,(1 + I/P)/R in (a), where P is the current gain ofthe driving transistor . Type (a:) is less stable than
145
A LOGARITHMIC CONVERTER FOR NUCLEAR PULSES
The converter oftype (c) was chosen for the following work, because its input impedance is higher than the others. The whole circuit is shown in fig. 7. 'transistors Tf and T2 compose the amplifier and T3 is the driving transistor. The RC high pass network on the collector circuit of T7 is provided to prevent oscillation . The gain and the rise time of the amplifier are 120 and 1 .3
Fig . 8. Conversion characteristics of the converter.
the other types due to the fact that the loop gain in type (a) varies considerably with the signal level, since the diode resistance in the emitter circuit of the driving transistor varies with the diodL current . These circuit may be replaced by cr)mplementary types, but pnp transistors ate not suitable as driving transistors because: the very small collector cutoff current is not available; with the pnp type. 20
x
psec without feedback, respectively. A silicon transistor 2SC18 was chosen as the driving transister by virtue of its very small collector cutoff current . The diode D1 is the conversion diode. The value of the polarizing current chosen was 13 pA to compromise the wide logarithmic range and the fast pulse response. The conversion diode was immersed in a small constant temperature bath containing a heater of about 200 mW, which kept the diode temperature at 45 ± l 'C. A fast diode was used as the compensating diode D,, since close logarithmic characteristics were not required for this diode. The output signal is amplified by T4, T5 and T6. The input impedance of the output amplifier was about 330 W, which is sufficiently higher than the maximum dynamic resistance of the conversion diode over the operating range. The positive capacitive feedback from the output to the conversion diode was employed to improve the rise time of the converted pulse for the small input signal. The value of this feedback capacitance is adjusted to obtain the fastest rise time without oscillation . By this feedback, the rise time is decreased to about 0.5 psec from 2 ,sec for a signal current of40 pA.
ENERGY Ik®V) 100 200
500
1000
2000
"apb(74%) 239 k®V
s a J 1 .0 w
2"Th (71%) ®4 kOV
v r ua a 0 cx
" ,,, TI (88%) 583kev ~T 112574)
511 keW j i,
0.5
729kev ~ eoaT101%) !880keV a F 50
1 150
1 200
Fig. 9. Pulse height distribution of gamma-rays from Th"g .
2o0 T((100-h) 26t5kev iÎ 1\ 250
146
T. HIRAMOTO
of the co verter erfo The conversioncharaAeristics ofthis converter tested with a pulse generator z,xe shown in fig. 8. The rise and decay time ofthe test pulses were 0.25 psec and 10 psec, respectively . The deviation from the ideal relation was less than 0.02 decades over 2.5 decades. For small input signais less than 0.07 V, which corresponds to 100,äA of the conversion diode current, outputs were slightly smaller than expected from eq. (4). This is attributed to the reduction in j3 ofthe driving transistor . Forfaster d .sying pulses, the amplitudes of the converted pulses were somewhat reduced because of the slow rise . To examine its performance for random pulses, the converter was combined with a linear amplifier, and the pulse height distribution for gamma-rays from Tb2 as was observed with a scintillation detector usùrg a 2'o x 2' N; 1T1) crystal. The converter was inserted between the two cascaded sections ofa slightly modified AL-1 amplifier and the output pulses were analyzed by a.
256-channel pulse height analyzer . The distribution obtained is shown in fig. 9. There was no deterioration in energy resolution due to the conversion. The mea. surement were tried at different counting rates, but no energy shift was observed up to 35(0 cps. The author would like to thank Dr. E. Tanaka for his excellent direction and advice for this work. The author also wishes to thank Mr. G. Ito, chief of the
pl .ysics division, for his constant encouragement and guidance. References 1) E.
Tanaka, Nucl. Instr. and Meth., 13 (1961) 43. E. Tanaka and T. Hiramoto, Nucl . Instr. and Meth., 22 (1963) 292. 3) M. F. Crouch and T. Matano et al., INSJ-8 (1958). 4) G. Gianelli and L. Stanchi, Nucl. Instr. and Meth., 8 (1960) 79. s) E. Udo, R. E. Rumphorst and L. A. Ch. Koerts, Proc. Conf. on Nucl. Electroni .-s, Belgrade 1961 . Vol . II, p. 413 . 2)
A LOGARITIUMC CONVERTE
FOR WCL" MLMS
T. MRAMOTO Physics Division, National Institute of Radiological Sciences, 250, Kurosuna-cho, Chiba, Japan Received 1 .4 July 1964 This paper describes a logarithmic converter which provides a means of adapting a regular linear amplifier to logarithmic operations . The converter basically consists of a current generator and a log-take element. To stabilize the static reference level
and to obtain a wide logarithmic range, the author proposes a particular method of polarizing the conversion diode. Operational characteristics, pulse response and the effect of variations in temperature are discussed.
1. Introdtwdon In scintillation beta- or gamma-spectrometry, the dynamic range of a conventional pulse-height analyzer combined with a linear amplifier is often too short when mixed radiation ofwidely different or unknown energies are analyzed. This is particularly true in low level application because repeating measurements by rearranging the linear amplifier gain is quite time consuming. In such cases, it is desirable to represent the energy axis in a logarithmic scale by using a logarithmic converter in the pules amplifier . The following logarithmic converter circuit was developed to identify radioactive nuclides at low levels using the coincidence type beta-ray scintillation spectrometer'- 2). There are two types of logarithmic pulse converters, the indirect and direct types. The converter developed by Crouch et al?) is based on amplitude-to-time conversion using a constant level discriminator for exponentially decaying pulsts .'This inethod is stable and a wide dynamic range may be obtained . However, this type of converter is not suitable for coincidence work. Gianelli et A') reported a direct conversion method for multiplying or dividing two or more pulses . They used the emitter-base junction of germanium drift transistors as the log-take elements. These junctions have a wide dynamic range with close logarithmic characteristics, but the circuit configuration is more or less limited by the fact that the base must be grounded and that transistors of this type are only of the prip type. A direct type logarithmic amplifier using a germanium diode was reported by Udo et al.). To improve duty cycle,, they proposed a stabilization ofthe lode voltage in a quiescent state, and obtained reasonable characteristics . The converter described in this paper is also the direct type using a silicon diode as the log-take element . The convener allows a linear amplifier to be modified to the logarithmic type 'Jy insertion of the converter tx:tw ,Ûen the appropriate amplifying stages . The complete converter circuit i., transistorized.
2. Log-take element The normal theory for rectification of a p-n junction diode leads to the expression V = (kTIe) In
+ 1]
(1)
where 1, is the thermally generated saturation current, I the diode current, e the electronic charge, k the Boltzmann constant, T the absolute temperature, and V the forward voltage of the diode. In the forward direction, the unity term can be neglected for V > 0.1 V at room temperature . Thus, eq. (1) may be approximated by V = (Ule) In 111,
(2)
the present application, a diode with close logarithmic characteristics of about three decades may be sufficient . The value of the diode current corresponding to these decades is restricted by a converter circuit in which this diode is employed . When a transistorized circuit is used, the preferable current range may be between 10' - 10' A, taking into consideration the transistor collector cutoff current and pulse response of the circuit, etc. In general, the actual d.c. characteristics of typical diodes exhibit a noticeable departure from eel. (1). For d.c. current, the ohmic drop across the entire diode and the conductivity modula-don must be taken into account at comparatively high current levels . The latter effect is due to the change in conductivity of semiconductor material caused by the change in the carrier density . In addition to the d .c. characteristics, diodes generally show reactive effects which become appreciable when used for high speed pulses. When a comparatively high current pulse is fed to the diode, the diode may initially exhibit an excessive voltage drop, which decays to its normal d.c. value, as if the diode possessed an apparent series inductance . This effect is also considered to be caused by conducliv~!y modulation. The diode capacitance also afl'u, ~,, tile pulse In
142
T. HIRAMOTO
reqwnse and is mainly due to the capacitance of the junction transition layer. The rise time ofthe converted I increases with this capacitance. Diodes having desirable d.c. and pulse characteristics &scr~ " = rarely available although the types ing either d.c. or pulse characteristics are readily available commercially. As an "ample, the voltage-current characteristics of some typical silicon diodes are shown in fig. 1, in which the dotted lines
time required to reach the final d.c. values, about 5 psec, is independent of the diode current . The forward characteristics ofcertain types of silicon voyage regulator diodes are also shown in fig. 1 . The regulating voltages are about 15 V, 13 V and 5 V for the IS142, RIB13A and RD5A, respectively. The 1557 is supplied for meter protection when the forward direction is used, however, this diode has the same structure as the voltage regulators. These voltage regulators have good logarithmic characteristics with a negligible conductivity modulation effect . The best results were obtained with diodes having regulating voltages around 10 V. It is considered that these good characteristics are due to the diffused junction made of highly doped materials, It should be noted that the transition layer capacitance of these diodes are fairly large compared with usual diodes due to the highly doped materials . This capacity amounts to several hundreds pF at the applied voltage of about 0.5, V . The effect of the junction capacitance is, however, not a serious problem because this effect can be reduced to some extent by the use of capacitive feed-back, which will be described later. One I S57 is used in the present converter . 3. Some problems In SPOICation of the conversion diodes 3.1 . POLARIZING THE CONVERSION DIODES
vars Fig. 1 . 6 4 characteristics of some silicon diodes .
represent the peak voltage of initial drop due to the conductivity modulation .The measurements were made with test pulses of 0.25 psec rise. As shown in this figure, fast diodes such as the bonded type do not have and logarithmic characteristics although they do not exhibit conductivity modulation effects. On the other haud, slow diodes of alloy or diffvse topes have good logarithmic characteristics . In these diodes, then is a tendency that diodes of higher maximum allowable inverse voltage begin to show conductivity modulation at a lower diode current . I .he diodes I S 180 and SD102, have good logarithmic characteristics in the region less than 2 and. But in these diodes ., the rise time has a slow component, although its rrtechan.ism is not understandable . The
In a practical conve! tar circuit, it is necessary that the conversion diode be polarized by a constant current . The main roles of polarization are to stabilize the d.c. condition of the diode by avoiding temperature effect of 1. in eq. (1), to improve the response to fast input signals by preventing excessive voltage excursion in the !ow current range and to obtain fast recovery from transient by reducing the dynamic resistance of the diode in a quiescent state. The last role is especially important when the diode is coupled to the other circuit through a capacitor .
Fig. 2. Method of pr,!arizir% the conversion diode . 1 : signal current, 10 : polariziug current, D1 . conversion diode, D2 . compensating diude.
143
A LOGARITHMIC CONVERTER FOR NUCLEAR PULSES
A simple method of polarization is to supply a constant current through the high resistance R, as shown in fig. 2(a). In this case, the converted voltage V,, is given by V, = (kTIe) In (I + 10 + IJI(Io + IS)
(3)
where 10 is the polarizing current and I the signal
current . Therefore, if 10 ~ 1, the temperature dependence of 1, can be avoided. However, the use of large I0 values results in the shortening of the dynamic range, because ideal logarithmic characteristics are expected only when I > 10.
3.2. PULSE RESPONSE
A large capacitance of the conversion diode affects pulse response of the converter. The transition layer capacitance varies inversely as the square or cubic root of the difference between the barrier voltage and the applied voltage, according to the type of the junction . The variation of this capacitance is about 20*/,, per decade of diode current changes in the current region of interest. The waveform of the converted signal is quite different from that of the usual pulse in a linear circuit and is dependent on the amplitude of the input signal . For sty signal current, the. time t required for the converted pulse to reach a fraction a of its final value is calculated as follows : t = ~qRd loglo I/i o - I D [(I/IO) I
l-"I - I I
Fig . 3. Signal current-converted voltage characteristics. (a) without compensation, (b) with compensation .
where C is the diode capacitance, Rd the final value of the diode resistance at diode current of I and D is the ratio 1110 in terms of decades. In the above calculation, the diode capacitance was azsumed to be constant, since its variation is negligible compared with that of diode resistance.
In fig. 3, the curve (a) is a calculated coriversion characteristic neglecting I., and the dashed line is the ideal one expressed by VC = (kTIe) In 1/10. According to the calculation, the lowest signal current is limited to 22 10 to keep the departure within 0.02 decades . This departure is greatly ; educed by the use of a compensating diode as shown in fig. 2 (b). When the signal current flows, the voltage drop across D, decreases, hence the polarizing current decreases accordingly. In this case, the converted voltage Vr is given by Vc = (4) (Ule) In [(1121 0) {I + V1 + (10/2J)2) ]
-
provided diodes of the same characteristics are used in the conversion and compensation. The calculated relation is shown as the curve (b) in fig. 3 . The lower limit of the current range is decreased to 4.7 10 keeping the error within 0.02 decades, If two or more diodes cascaded in series are used as the conversion diodes in combination with one compensating diode, closer logarithmic characteristics will be obtained .
Fig . 4. Waveform of the converted signal .
The calculated waveforms fcr different values of D are shown in fig. 4. The waveform of pulses integrated by the constant CR is also shown in the figure. The values of i are expressed as a function of t,'CRd . The hiss time of the converted pulse becomes very large for the small input signal since Rd increases with the decrease of the signal current . It will also be seen that a faster pulse response is expected in the higher current range than in the lower range for the given I/10 ratio . 3 .3. TEMPERATURE EFFECT
The temperature dependence of the core c' $ 4,~on diodes
T. HIRAMOTO must
kept within
± 3° C, at room temperature, in
keep the error within ± 0.02 decades at the current of 101 x 10. Therefore, it would be
order to signal
necessary to immerse the conversion
91.0
diode in a constant
temperature bath or to control the gain of the output
amplifier by a temperature sensitive element such as a thermistor . 1
1 O
1 10
1 1 1 1 20 ZO 4n 50 TEMPERATM fl
Fig. 5. Temperature dependence of the a serious problem in
1
4. Converter
conversion diode.
their practical use,
SIi41e of the conversion characteristic is
because the
a function of
temperature. The slope expressed in terms of voltage decade is calculated from eq. (1) as follows: VD =
where the effect of IS
(kTfe)
In 10
(6)
is ignored since the effect is
avoided by polarizing the diode.
circuit
The current generator dri-ing the conversion diode must have an internal resistance much larger than the diode resistance and the output curreat in the quiescent state must be sufficiently smaller than the polarizing current.' Several circuits of the converter were designed and tested . Block diagrams of th circuits are shown in fig. 6. Each is composed of an amplifier and a driving transistor. The driving transistor is slightly cutoff in the quiescent state. Types (a) and (c) acoept positive pulses and type (b)
tcl cal tel Fig . 6. Block diagrams of converter circuits . Vs : input voltage signal, Vc : Converted signal. The slope was measured experimentally using the 1 S57. The results are plotted in fig. 5. The solid line in
the figure is the theoretical change of the slope. These data are normalized to unity at 24"C. As shown by the results, the temperature variation
accepts negative pulses, respectively . Provided the gain of the amplifier is very large, the current fed to the conversion diode is equal to VdR(I + I/ß) in types (b) and (c) and V,(1 + I/P)/R in (a), where P is the current gain ofthe driving transistor . Type (a:) is less stable than
145
A LOGARITHMIC CONVERTER FOR NUCLEAR PULSES
The converter oftype (c) was chosen for the following work, because its input impedance is higher than the others. The whole circuit is shown in fig. 7. 'transistors Tf and T2 compose the amplifier and T3 is the driving transistor. The RC high pass network on the collector circuit of T7 is provided to prevent oscillation . The gain and the rise time of the amplifier are 120 and 1 .3
Fig . 8. Conversion characteristics of the converter.
the other types due to the fact that the loop gain in type (a) varies considerably with the signal level, since the diode resistance in the emitter circuit of the driving transistor varies with the diodL current . These circuit may be replaced by cr)mplementary types, but pnp transistors ate not suitable as driving transistors because: the very small collector cutoff current is not available; with the pnp type. 20
x
psec without feedback, respectively. A silicon transistor 2SC18 was chosen as the driving transister by virtue of its very small collector cutoff current . The diode D1 is the conversion diode. The value of the polarizing current chosen was 13 pA to compromise the wide logarithmic range and the fast pulse response. The conversion diode was immersed in a small constant temperature bath containing a heater of about 200 mW, which kept the diode temperature at 45 ± l 'C. A fast diode was used as the compensating diode D,, since close logarithmic characteristics were not required for this diode. The output signal is amplified by T4, T5 and T6. The input impedance of the output amplifier was about 330 W, which is sufficiently higher than the maximum dynamic resistance of the conversion diode over the operating range. The positive capacitive feedback from the output to the conversion diode was employed to improve the rise time of the converted pulse for the small input signal. The value of this feedback capacitance is adjusted to obtain the fastest rise time without oscillation . By this feedback, the rise time is decreased to about 0.5 psec from 2 ,sec for a signal current of40 pA.
ENERGY Ik®V) 100 200
500
1000
2000
"apb(74%) 239 k®V
s a J 1 .0 w
2"Th (71%) ®4 kOV
v r ua a 0 cx
" ,,, TI (88%) 583kev ~T 112574)
511 keW j i,
0.5
729kev ~ eoaT101%) !880keV a F 50
1 150
1 200
Fig. 9. Pulse height distribution of gamma-rays from Th"g .
2o0 T((100-h) 26t5kev iÎ 1\ 250
146
T. HIRAMOTO
of the co verter erfo The conversioncharaAeristics ofthis converter tested with a pulse generator z,xe shown in fig. 8. The rise and decay time ofthe test pulses were 0.25 psec and 10 psec, respectively . The deviation from the ideal relation was less than 0.02 decades over 2.5 decades. For small input signais less than 0.07 V, which corresponds to 100,äA of the conversion diode current, outputs were slightly smaller than expected from eq. (4). This is attributed to the reduction in j3 ofthe driving transistor . Forfaster d .sying pulses, the amplitudes of the converted pulses were somewhat reduced because of the slow rise . To examine its performance for random pulses, the converter was combined with a linear amplifier, and the pulse height distribution for gamma-rays from Tb2 as was observed with a scintillation detector usùrg a 2'o x 2' N; 1T1) crystal. The converter was inserted between the two cascaded sections ofa slightly modified AL-1 amplifier and the output pulses were analyzed by a.
256-channel pulse height analyzer . The distribution obtained is shown in fig. 9. There was no deterioration in energy resolution due to the conversion. The mea. surement were tried at different counting rates, but no energy shift was observed up to 35(0 cps. The author would like to thank Dr. E. Tanaka for his excellent direction and advice for this work. The author also wishes to thank Mr. G. Ito, chief of the
pl .ysics division, for his constant encouragement and guidance. References 1) E.
Tanaka, Nucl. Instr. and Meth., 13 (1961) 43. E. Tanaka and T. Hiramoto, Nucl . Instr. and Meth., 22 (1963) 292. 3) M. F. Crouch and T. Matano et al., INSJ-8 (1958). 4) G. Gianelli and L. Stanchi, Nucl. Instr. and Meth., 8 (1960) 79. s) E. Udo, R. E. Rumphorst and L. A. Ch. Koerts, Proc. Conf. on Nucl. Electroni .-s, Belgrade 1961 . Vol . II, p. 413 . 2)