A simple charge sensitive preamplifier for experiments with a small number of detector channels

Transcription

1 A siple charge sensitive preaplifier for experients with a sall nuber of detector channels laudio Arnaboldi and Gianluigi Pessina Istituto Nazionale di Fisica Nucleare (INFN) Università degli Studi di Milano Bicocca - Dipartiento di Fisica P.za della Scienza 3, 06 Milano, Italy gianluigi.pessina@ib.infn.it NSS07

2 ABSTAT We present a harge Sensitive Preaplifiers, SP, based on a very siple design. It is indicated for applications where a sall nuber of detector channels do not need a onolithic solution. The SP consists of an input transistor and an Operational Aplifier in the second stage. The circuits do not ake use of a cascode connection to load the input transistor, to iniize both the nuber of active devices needed and the supply voltage, with a consequence reduction of power dissipation. Thank to the circuit design, very siple atheatical rules are needed to optiized the dynaic perforances and stability. NSS07

3 The harge Sensitive Preaplifier, SP: the classical design I DG Q J Q A SP based on the use of transistors only as active devices is often used in both discrete and onolithic ipleentations. DET GS L F F A SP ipleented with discrete devices is very siple if use is ade of an Operational Aplifier, OA, as active device. One of the very iportant ites that concerns the design of these and any other stuff is the frequency stability. DET J F - This way the input transistor J is chosen for the optiization of the S/N, while the OA allows for obtaining a large open loop gain and drives the output load. F NSS07 3

4 SP with Operational Aplifier: classical DET DG V L V - OP7 When using discrete devices the design is siplified if an OA is exploited. The reark for this adoption is the stability. If we neglect for a while the output ipedance of the OA the inverse of the return path, β, (green/pink path in the figure) around the OA itself is: GS F GS F ( g ) F DET L DG β g L For large values of the product g L, that allows to aintain liited the input referred noise of the OA, we have: β g L >> DG F Soeties this value ay be sall, and the preaplifier ay breaks into oscillation. NSS07 4

5 SP dynaic perforances of the classical configuration Let s consider a situation, aybe unreal, but interesting for what concern the study of the stability: The coparison of the OA and /β and the phase of their product gives rise to a very sall phase argin:.5 Overshot: 68.9 %, rise tie: 0.06 µsec Aplitude (A.U.) 0 4 OA gain and /β (left), phase of the loop gain (rigth) / β = f= KHz Phase Margin: Freqeuncy (Hz) Phase ( ) F = 500 pf DET =30 pf L =400 Ω GS=350 pf DG=0 pf g =0.5 A/V Aplitude a.u Tie (µsec) As a consequence, the response to an input ipulse of the preaplifier has a very long settling tie. NSS07 5

6 SP copensation for the classical configuration V Adding cc and cc allows to obtain, at frequencies large enough, the gain lowered to about g cc, fro g L. DET DG L V - OP37 At large frequencies: ( g ) F DET cc GS β g F cc GS F g cc should be sall, of the order of or less, if we would like the closed loop gain to have enough phase argin. Since cc is uch saller than L at large frequencies the input noise of the OA is reflected at the input with a saller attenuating factor. NSS07 6

7 Effects of copensation on the classical configuration The effect of copensation iproves the return path gain at high frequencies. As a consequence, the phase argin iproves. 0 4 OA gain and /β (left), phase of the loop gain (rigth) In the exaple shown cc = 0 Ω, while cc = 00 nf. The input reflected noise of the OA at large frequencies is only.5 V/V in this exaple.. Overshot: 5.3 %, rise tie: µsec Aplitude (A.U.) / β = /β=.87 f= KHz 60 Phase Margin: Freqeuncy (Hz) 0 00 Phase ( ) Aplitude a.u The phase argin increase reflects in a ipulse response that has a uch shorter settling tie Tie (µsec) NSS07 7

8 DET DG GS A SP with Operational Aplifier: a further suggested ethod The ai of the suggested ethod was to ake independent the Miller effect due to DG and the gain, fro the detector requireents. To do this we have exploited both inputs of the OA and ade the gain of the transistor partially coon ode at the OA inputs: B V J F D - OP7 We added 3 resistors to accoodate the drain of J. The equivalent resistor that loads J is now: V So we have that Eq < Miller. Miller ( ) = At the OA input we obtain instead: V = = Miller onsidering the condition that at D V V - we obtain eqs that allows to set V DS and I DS. After having selected the other paraeters Miller and Eq 4 eqs are obtained to find the 4 resistors NSS07 A,.., D. 8 B B A A A A D g AD D D V i g = V i Eq g V i

9 SP with Operational Aplifier: a further suggested ethod, cont The roots of the 4 eqs that fors a linear syste gives the value of the 4 resistors as a function of the static and dynaic paraeters. NSS07 9

10 SP with Operational Aplifier: a further suggested ethod, cont V The inverse of the return path (green/red path) is: DG A B - OP37 ( g ) F DET GS Miller DG β g When g Miller >> /β reduces to: F Eq DET GS J F D β g Miller >> DG F Miller Eq JFET transistor and F can be chosen to satisfy the detector requireents. Miller and Eq are set to satisfy the stability condition of the network. The input reflected noise of the OA is inversely proportional to g Eq. Eq can be asked the further requireents to aintain liited the OA noise reflected to the input. The last consideration concerns the input parallel noise of OA.. NSS07 0

11 NSS07 NSS07 SP with Operational Aplifier: a further suggested ethod, cont SP with Operational Aplifier: a further suggested ethod, cont 3 The effect at the input of the OA parallel noise is given by: ( ) ( ) ( ) = = i g i i i g e No D A D Eq Eq D A D Eq ioa

12 SP with Operational Aplifier: a further suggested ethod, cont 4 Following the sae exaple above we have set Miller = kω and Eq =00 Ω. As a consequence /β resulted 4.3 and the phase argin 70 ( A =00 Ω, B =40 Ω, =300 Ω and D =4500 Ω, V =0 V, V DS =3 V and I DS =5 A). At all frequencies the input reflected series noise of OA has an attenuation of 5 V/V, and the noise reflected resistor No for parallel noise is about 7 Ω.. Overshot:. %, rise tie: 0.66 µsec Aplitude (A.U.) OA gain and /β (left), phase of the loop gain (rigth) / β = Phase Margin: f= 38.8 KHz Freqeuncy (Hz) Phase ( ) Aplitude a.u Tie (µsec) With a so large phase argin the overshot of the signal is alost negligible. Setting Eq to 00 Ω the phase argin lowers to 54 and the overshot rises to 5 %, with a rise tie of about 90 ns. This way the noise reflected to the input has an attenuation of 30 V/V and No is 5 Ω. NSS07

13 SP with Operational Aplifier: a further suggested ethod, cont 5 The actual response of the preaplifier is shown here. We can see that the overshot is slightly larger than 5 %. This effect coes about if we consider that the OA output ipedance is not negligible and lower the phase argin. The OP7, when loaded with about KΩ, has an output ipedance of about 50 Ω.. Overshot: 9. %, rise tie: 0.46 µsec Including the effect of the OA output ipedance in our odel we are able to take into account also for this effect. Aplitude a.u Tie (µsec) NSS07 3

14 onclusions A ethod is suggested for the frequency copensation of a charge sensitive preaplifier based on the use of an OA as second stage in the feedback loop. The ethod allows to have degrees of freedo in setting the return path gain by only selecting the value of 4 resistors. NSS07 4