T962 Readout Signal Path vs Signal Shape -------------------------------------------- Original Rev. 23-JAN-2008 Current Rev. 31-JAN-2008 This note is an attempt to gather together information about all of the steps in the electrical signal path that effect the shape of the LArTPC signals from the T962 detector. First there is the signal path getting from the charge in the LAr to the preamp input. TPC Detector Wires: ------------------- The wires are 6 mill Beryllium Copper Alloy #125. They are spaced 4 mm apart and have a normal length of 460 mm. There are 3 planes of wires in the T962 TPC: - Innermost: a "shield" plane Vertical wires 226 wires Not read out - Middle plane: an induction plane -60degree wires 240 wires - Outermost: a collection plane +60degree wires 240 wires The +/-60degree angle is measured from the horizontal. Two 6 mil wires spaced 4 mm apart have a capacitance of about 2.14 pFd/ft so with a wire on each side and 460 mm long this is about 6.46 pFd of capacitance per detector wire. I believe that Be-Cu alloy #125 has about 25% the conductance of Copper. A 6 mil Copper wire is about 0.3 Ohms/ft. So a 460 mm long Be-Cu detector wire should have about 1.9 Ohms. Bias Voltage Distribution Card: ------------------------------- The Bias Voltage is connected to the detector wire through a 100 Meg Ohm resistor. This resistor plays almost no part in the signal shape. The detector current is low enough so that there is little Voltage drop across this resistor. This resistor can not inject Johnson Noise into the signal path because the RC time constant puts any noise from this source below the frequency band of the real LArTPC signals. The DC blocking capacitor is a 10 nFd 1600 Volt capacitor in series with the signal. This capacitor is sized so that it also has almost no effect on the signal shape. The main signal frequency of the LArTPC signals is at about 150 kHz. At that frequency the 10 nFd capacitor has a reactance of about 100 Ohms. 10 nFd is much more than the detector capacitance so there is almost no charge division across this capacitor. Internal Readout Cables: ------------------------ From the BVDC cards, which are mounted right on the TPC wire frames, up to the cold side of the signal feedthrough the LArTPC signals travel through about 9 feet of 50 mil pitch polyolefin twist-and-flat cable. This cable has about 17 pFd/ft of capacitance and about 0.066 Ohms/ft of resistance. So for 9 feet this is: 153 pFd and 0.59 Ohms. This twist-and-flat cable has a Zo of about 110 Ohms and a velocity of 0.57 ft/nsec. So it takes about 15.8 nsec to travel the 9 feet. In 100 nsec the signal can bounce many times. For signal shape considerations slower than about 100 nsec the Zo of the cable is not important. For signal shape calculations interested in components faster than 100 nsec we would need to consider the Zo of this cable. Because the ADCs only sample once every 198 nsec I believe that we can ignore the "transmission line effects" of this cable on the signal shape (and only concern ourselves with the overall capacitance and resistance of this cable). Signal Feedthrough Card: ------------------------ The design of this card that I saw showed that it used 7 mil traces and 1 oz Copper. The longest traces are about 12.8" This implies about 1.8 Ohms of resistance in the signal path. The capacitance to ground will vary depending on what layer the trace was routed on. A typical number will be about 20 pFd. My understanding of this is limited because I do not know the laminate thickness that was finally selected to build the feedthrough card. The propagation time for the signal to get through the feedthrough card should be about 1.9 nsec. This is based on a 12.8" strip line trace in a circuit board laminate with dielectric constant of 3.0 External Readout Cables: ------------------------ From the warm side of the signal feedthrough card to the input of the preamplifier the LArTPC signals travel through 40 inches of standard twist-and-flat cable. This cable has about 16 pFd/ft of capacitance and about 0.066 Ohms/ft of resistance. So in the 40" (i.e. 2 sections) there is about 53 pFd of capacitance to ground and about 0.22 Ohms of series resistance. The signal propagation time along this cable is about 5.4 nsec. Summary of getting the LArTPC signal from the detector wire to the preamp: ------------------------------------- Signal Signal Path Series Capacitance Propagation Section Resistance to Ground Time -------------- ---------- ----------- ----------- Detector Wire 1 Ohm 6 pFd - Internal Cable 0.6 Ohm 153 pFd 15.8 nsec Feedthrough 1.8 Ohm 20 pFd 1.9 nsec External Cable 0.2 Ohm 53 pFd 5.4 nsec --------- --------- ----------- Totals 3.6 Ohm 232 pFd 23.1 nsec Note that this 3.6 Ohms is the DC resistance at room temperature. For "typical" copper the DC resistance goes down by a factor of perhaps 5 when moving from room temperature to LN2 temperature. The change in resistance when moving from DC to 150 kHz is complicated to calculate and depends on a number of factors. To set the scale you can consider just solid round straight copper wires. The increase from DC resistance to 150 kHz resistance for a #28 wire (as in the twist-and-flat cable) is about 1.013. The increase in resistance for a #12 wire is about 3.27 Preamplifier Characteristics: ----------------------------- The charge integrating preamplifier has an effective feedback capacitor of 2.0 pFd and a feedback resistor of 100 Meg Ohms. The open loop gain of the preamplifier is high enough so that in the frequency range of interest for LArTPC signals the effective resistance looking into the preamplifier input is about 30 Ohms. Thus for charge that appears in the detector this preamplifier can pull it out of the total detector capacitance with a time constant of about 30 Ohms x 232 pFd = 7 nsec. A worst case calculation of the time constant for the preamplifier pulling charge out of the detector is to include the resistance of all the elements in the signal path between the preamp and the detector wire and assume that all of the detector capacitance is at the far end of this resistance. In that case the time constant is about (30 Ohms + 3.6 Ohms) x 232 pFd = 7.8 nsec. In either case this time constant is many times faster than the 198 nsec sampling time so for the T962 setup it basically does not effect the signal shape. 2.0 pFd feedback implies 0.5 mVolt out of the preamp per femto Coulomb of input charge. Summary of Steps so far along the Signal Path: ---------------------------------------------- Because the propagation time from the detector wire to the preamp input and because the speed with which the preamp can pull charge out of the total detector capacitance are both significantly shorter than the time scale over which charge from a track is induced onto or collected by a detector wire and are significantly shorter than the ADC sampling time - I believe that none of the details about the detector wire to preamp input parts of the signal path will have a significant effect on the T962 signal shape. Thus for simulating the T962 signal shape the only important information presented so far in this notes is that the preamps integrate charge with a gain that produces 0.5 mV of output per femto Coulomb of input and that he preamp outputs return to zero with a time constant of 100 Meg Ohms x 2 pFd = 200 usec. Buffer Stage: ------------- Following the Preamplifier the next stage in the PFC-16 card is the "Buffer". The functions of the buffer stage are: - Convert the single ended preamplifier output to a differential analog signal. The ADF-2 cards that will digitize and circular buffer the LArTPC signals have a differential analog input (to help with the ground loop and ground current problems). All stages on the PFC-16 card after the preamp are implemented with differential analog signals. - Provide low noise amplification with a Voltage gain of 8.25. The PFC-16 card may be made to adjust this Voltage gain to match the various species of ADF-2 cards. - Provide one pole of high frequency and one pole of low frequency filtering. The intent is to set the break points of these filters some what outside the subsequent high and low pass filter cutoffs so that filtering done in the buffer stage would not need to track any changes made in the subsequent high and low pass filters. A schematic of the PFC-16 buffer stage is on the web at: www.pa.msu.edu/~edmunds/LArTPC/T962/Preamp_Filter_Card/ pfc_16_preamp_buffer_sch.pdf The PFC-16 buffer stage low frequency cutoff was set at 1.7 kHz and the high frequency cutoff was set at 800 kHz. In the piece wise model the Voltage gain is 8.25 from 1.7 kHz to 800 kHz. Below 1.7 kHz and above 800 kHz the gain falls off at 6dB per octave. First Stage Filter: ------------------- Following the Buffer the next stage in the PFC-16 card is the First Stage Filter. A schematic of the First Stage Filter is on the web at: www.pa.msu.edu/~edmunds/LArTPC/T962/Preamp_Filter_Card/ pfc_16_filter_one_schematic.pdf This filter is a complex pole pair setup as a Butterworth low pass filter with a cutoff frequency of 200 kHz. This stage also provides a voltage gain of 5.0 The input to this stage is AC coupled using capacitors that provide a time constant of 73 usec. Second Stage Filter: -------------------- Following the First Stage Filter the next stage in the PFC-16 card is the Second Stage Filter. A schematic of the First Stage Filter is on the web at: www.pa.msu.edu/~edmunds/LArTPC/T962/Preamp_Filter_Card/ pfc_16_filter_two_schematic.pdf This filter is a complex pole pair setup as a Butterworth high pass filter with a cutoff frequency of 10 kHz. This stage also provides a Voltage gain of 4.7 Without termination the differential output Voltage from the Second Stage Filter is 97 mV per femto Coulomb input to the Preamp. Coupling to the ADF-2 cards: ---------------------------- The differential analog output from the PFC-16 cards is connected to the ADF-2 cards using 25 foot long Pleated Foil Cables. There is very little signal loss along these PFC cables but there are two important points to consider about this connection: - These signals are "back terminated" (aka series terminated) on the PFC-16 cards and parallel terminated on the ADF-2 cards. Thus the ADF-2 card sees only 1/2 of the unterminated output signal from the last stage on the PFC-16 cards. - These signals are AC coupled. There is a 470 nFd coupling capacitor at each end of the PFC cable. The series terminator resistors and the Zo of the PFC cable gives a time constant for this connection of about: 155 Ohms x 470 nFd = 73 usec. The series terminator resistors and the 470 nFd capacitors at the output of the PFC-16 card can be seen in the Second Stage Filter schematic. Analog Signal Processing on the ADF-2 Cards: -------------------------------------------- After passing through the AC coupling capacitors and parallel termination resistors the differential analog input signal is received on the ADF-2 card by a differential line receiver with that has good common mode rejection. A schematic of the analog input section of the ADF-2 card is on the web at: www.pa.msu.edu/hep/d0/ftp/run2b/l1cal/hardware/adf_2/drawings/ adf_2_differential_amp.pdf Note that besides the AC input coupling with a time constant of 73 usec there are also two real poles of high frequency filtering (i.e. low pass filters). These have a time constant of about 10 nsec each, i.e. well above any frequency of interest in the LArTPC signals. The 10 bit ADC on the ADF-2 card is shown in the following drawing on the web: www.pa.msu.edu/hep/d0/ftp/run2b/l1cal/hardware/adf_2/drawings/ adf_2_adc_10_bit.pdf The ADF-2 cards are setup so that the digital output from the ADC's is an unsigned 10 bit binary number, i.e. 0:1023 decimal. When the ADF-2 cards are used to record LArTPC signals, the pedestal control DAC's, shown in the first ADF-2 card schematic, are typically adjusted so that with zero input signal the output of the ADC's is 400 counts decimal. A complicating factor is that there are 4 "species" of ADF-2 cards and to have enough cards to run T962 we will need to use some of each species. The only difference between the species is the sensitivity of the analog input signal, i.e. the Volts input to ADC counts output factor. Recall that the ADF-2 cards were originally made for a totally different application were this difference in sensitivity is used as part of the E to Et conversion. The 4 species of ADF-2 cards are called: A, B, C, and D. Their inputs have the following characteristics: Volts Differential Full Scale "Exact" ---------------------------------- mVolts Diff "Nominal" "Exact" per LSBit ADF-2 ------------- --------------- --------------- Species EM HD EM HD EM HD ------- ---- ---- ----- ----- ----- ----- A 4.0 2.0 4.087 2.120 3.995 2.072 B 5.5 3.5 5.439 3.491 5.317 3.413 C 4.0 4.0 4.087 4.087 3.995 3.995 D 5.5 5.5 5.439 5.439 5.317 5.317 The ADF-2 cards will see an input of about 48 mV per femto Coulomb input to the Preamp. Thus using a "C" species ADF-2 card as an example, one femto Coulomb input to the Preamp will make about 12 ADC counts, and about 85 femto Coulomb input will make a full scale ADC output of 1023 counts. Recall that because the input signal swings both positive and negative the ADF-2 card is typically setup for LArTPC operation with a pedestal of 400 counts. The sign of the input signal has been setup so that as the cloud of electrons comes towards a wire or is collected by a wire the output of the ADC will increase. The ADC's make a conversion about once every 33 nsec. The clock that controls this is actually locked to the Tevatron RF system. A clock is synthesized at 8/7 times the 53.104 MHz Tevatron RF frequency and the ADC's makes a conversion on every other cycle of this synthesized clock. In the LArTPC application the digital data from only every 6th ADC conversion is stored in the 2048 step long circular buffer. Thus adjacent samples in the circular buffer are spaced about 198 nsec apart. The sampling rate for the LArTPC application can be adjusted to any reasonable integer relationship to the Tevatron RF. The fundamental clock to the ADF-2 card must be the 53.104 MHz Tevatron RF. All of the ADF-2 cards in a crate and across multiple crates clock together synchronously. When a trigger signal is used to stop the recording of data in their circular buffers all of the cards (even across multiple crates) stop on the same clock cycle. The contents of the 2048 step long circular buffer for each of the 32 channels on the ADF-2 card can be readout over VME. The ADF-2 card records the address of the last location that was written in the circular buffer so that these 2048 samples can be put in monotonic time order.