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SOLID STATE DIVISION TECHNICAL INFORMATION SD-37 Characteristics and use of Charge amplifier Table of contents 1. General description ····································································································· 3 2. Principle of operation ···································································································· 3 3. Gain ······························································································································ 3 3-1 Amplifier ··················································································································· 3 3-2 Amplifier with detector ······························································································· 4 4. Characteristics ·············································································································· 4 4-1 Open-loop gain ········································································································· 4 4-2 Noise ······················································································································· 5 5. Applications ·················································································································· 7 5-1 Gamma ray measurement (Direct detection using a PIN photodiode) ···························· 7 5-2 Power and stability measurements from lasers ···························································· 7 6. Specifications ··············································································································· 8 7. Precautions for handling charge amplifier ····································································10 2 Characteristics and use of Charge amplifier ○○○○○○○○○○○ As a result, the signal charge pulses Qs are all integrated to 1. General description the feedback capacitance Cf and then output as voltage When a semiconductor detector such as Si is used for the pulses eout(t). At this point, since the feedback resistance Rf measurement of soft X-rays and low to high-energy gamma for direct current is connected in parallel to the feedback rays, the output signal is a weak charge pulse having a pulse capacitance Cf, the output becomes voltage pulses that slowly width of several tens of nanoseconds. As the detector element discharge with the time constant determined by τ=Cf · Rf. itself is a capacitive device, its impedance is very high. There- ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ If a detector provides a constant charge generation over a time fore, the performance of the preamplifier to be connected, interval t=0 to to, the output signal charge Qs is given by the must be taken into consideration when amplifying this output following equation using the Laplace transform. 1 e -Sto signal. Qs (S) = Qs - . (2-1) In such applications, operational amplifier mode integrators ()S S using feedback capacitance are commonly used. As these Similarly, the transmission coefficient T(S) is given by amplifiers have high input impedance, they integrate weak 1 1 τ T (S) = - · 1 ( = Cf · Rf) . (2-2) charge pulses and convert them into voltage pulses for ampli- Cf S + τ fication then provide a low-impedance output. Thus the output voltage V(S) is expressed using Eqs (2-1) and Because of this operation, this type of amplifier is called a (2-2) as follows: “charge amplifier”. The first stage of a charge amplifier is 1 e -Sto 1 1 V (S) = Qs (S) · T (S) = Qs - · · 1 usually a low-noise FET and its open-loop gain is set ()S S Cf S + τ sufficiently high so that the amplification is not influenced by Qs 1 1 e -Sto 1 = - ··1 - 1 the detector capacitance. The output stage is a low- Cf ()S S + τ S S + τ impedance buffer so as to drive an external stage which is . (2-3) connected using a long cable. As a result, the output voltage pulse eout(t) is given by τ Qs 1- e-t/ eout (t) = - · 0 ≤ t < to 2. Principle of operation Cf to/τ to/τ Qs (e -1) -t/τ Figure 2-1 Principle of operation = -· e to ≤ t . (2-4) Rf Cf to/τ Because generally to << τ, Eq (2-4) can be simplified as follows: Cf +- Q -t/τ eout (t) = - e . (2-5) Qs Cf to As can be seen from Eq (2-5), the signal charge pulses Qs are Qs - converted into voltage pulses with amplitude Vout = - , AOL eout (t) Cf + which is damped with time constant τ=Cf · Rf. Cj Cj : Semiconductor detector capacitance Cf : Feedback capacitance Rf : Feedback resistance AOL : Open-loop gain of amplifier 3. Gain KACCC0015EA The gain of charge amplifier is given in one of two ways: the When soft X-rays or gamma rays strike for example a Si gain for amplifier or the gain for a detector/amplifier semiconductor detector, signal charge pulses Qs are gener- combination. ated, with an amplitude according to the particle energy. Due to this charge generation, the input-end potential of the charge 3-1 Amplifier amplifier rises and at the same time, a potential with reverse The gain of amplifier Gc, referred to also as “charge gain”, is polarity appears at the output end. However because the given by the following equation: amplifier's open-loop gain is sufficiently large, the output-end Vout 1 potential works through the feedback loop so as to make the Gc ==[V/coulomb] or [V/pico coulomb] Qs ()Cf input-end potential zero instantaneously. (3-1) 3 Characteristics and use of Charge amplifier 3-2 Amplifier with detector ○○○○○○○○○○○○○○○○○○ 4-1 Open-loop gain In this case we usually use the term called “sensitivity” rather There are various semiconductor detectors used for the detec- than “gain”. Sensitivity is expressed in the output voltage (mV) tion of soft X-rays and gamma rays. Even among Si detectors per one MeV of particle energy irradiated onto a detector. for example, a variety of types are used to match the applica- The amplitude of the signal charge obtained with a semicon- tion, which have different active areas and depletion layer ductor detector is determined by the input particle energy such thicknesses. Furthermore, detectors also differ in regards to as soft X-rays and gamma rays and also by the material of the capacitance. However, when the same Si detector is used semiconductor. for the detection of soft X-rays and gamma rays, the amount of E · e- generated charge must be the same if the particle energy of Qs = (coulomb) or (pico coulomb) . (3-2) ε the soft X-rays and gamma rays is equivalent. Therefore, E : Particle energy (MeV) ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ charge amplifier must provide a constant gain regardless of e-: Elementary charge 1.6 × 10-19 (coulomb) the capacitance value. In fact as shown in Eq (2-5) in ε : Energy required to create one electron/hole pair. “Principle of operation”, the output from the detector is For example with silicon, Qs ranges from 3.62 eV independent of the junction capacitance Cj. This is because (at 300 K) to 3.71 eV (at 77 K). the open-loop gain of the charge amplifier is very high. Thus, from Eqs (3-1) and (3-2), sensitivity is given by Figure 4-1 Equivalent circuit Qs Cf Vout Cf Rs = = ε E Qs · e- - = e · 1 (mV/MeV) . (3-3) Cf ε AOL eout For example when using a Si detector and an H4083 charge Cj (Qs) Zin amplifier (Cf=2 pF), the sensitivity at room temperatures Rs becomes Cj : Semiconductor detector capacitance Cf : Feedback capacitance - AOL : Open-loop gain of amplifier Rs = e · 1 Cf ε KACCC0016EA -19 When a charge amplifier is connected with a Si detector, its = 1.6 × 10 · 1 2 × 10 -12 3.62 equivalent circuit is like that shown in Figure 4-1. = 2.2 × 10-8 (V/eV) In this equivalent circuit, when seen from the amplifier's input, the input impedance Zin is given by = 22 (mV/MeV) . (3-4) 1 ω Zin = j Cf . (4-1) 1 + AOL (jω) 4. Characteristics If signal charge Qs is generated in the Si detector, the voltage In general, the following characteristics are required of charge ein at the amplifier's input becomes amplifier used for the detection of soft X-rays and low to high- Qs energy gamma rays. ein = . (4-2) jωCj + {1 + AOL (jω)} · jωCf High gain Thus the output voltage eout is expressed using Eq (4-2), as Low noise follows: Excellent integration linearity ω High-speed rise time eout = AOL (j ) · ein Qs High temperature stability, etc. = AOL (jω) · jωCj + {1 + AOL (jω)} jωCf Qs The following sections discuss major characteristics of charge = . (4-3) ω jω amplifier. j Cf +AOL (jω) (Cf + Cj) 4 Characteristics and use of Charge amplifier ○○○○○○○○○○○○○○○○○○ Here, assuming that AOL >> 0, in other words, the open-loop ◆Thermal noise of first-stage FET gain of the amplifier is very large, then eout can be simplified Thermal noise of the first-stage FET, en1, is given by as follows: 8 KT en1 =V/Hz() . (4-5) Qs 3 gm eout = . (4-4) jωCf K : Boltzmann constant As discussed above, the output voltage eout of charge T : Absolute temperature amplifier is not dependent on the capacitance of Si detectors. gm: Mutual conductance of first-stage FET Figure 4-2 Open-loop gain (H4083) ◆Shot noise caused by gate current of first-stage 100 FET and dark current of detector ○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○ FET and dark current of detector The shot noise in is given by 80 in = 2q (IG + ID)A/Hz() . (4-6) 60 q : Elementary charge IG : Gate leakage current of first-stage FET 40 ID : Dark current of detector ◆Thermal noise caused by feedback resistance 20 OPEN-LOOP VOLTAGE GAIN (dB) The thermal noise en2 caused by the feedback resistance Rf is given by 0 100 1 k 10 k 100 k 1 M 10 M en2 = 4KTRf()
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    NIST Special Publication 1038 The International System of Units (SI) – Conversion Factors for General Use Kenneth Butcher Linda Crown Elizabeth J. Gentry Weights and Measures Division Technology Services NIST Special Publication 1038 The International System of Units (SI) - Conversion Factors for General Use Editors: Kenneth S. Butcher Linda D. Crown Elizabeth J. Gentry Weights and Measures Division Carol Hockert, Chief Weights and Measures Division Technology Services National Institute of Standards and Technology May 2006 U.S. Department of Commerce Carlo M. Gutierrez, Secretary Technology Administration Robert Cresanti, Under Secretary of Commerce for Technology National Institute of Standards and Technology William Jeffrey, Director Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose. National Institute of Standards and Technology Special Publications 1038 Natl. Inst. Stand. Technol. Spec. Pub. 1038, 24 pages (May 2006) Available through NIST Weights and Measures Division STOP 2600 Gaithersburg, MD 20899-2600 Phone: (301) 975-4004 — Fax: (301) 926-0647 Internet: www.nist.gov/owm or www.nist.gov/metric TABLE OF CONTENTS FOREWORD.................................................................................................................................................................v