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**On-Chip Processing for the Wave Union TDC Implemented in FPGA**

Jinyuan Wu Fermi National Accelerator Laboratory, Batavia, IL 60510, USA An FPGA TDC with 20ps or 10ps RMS Resolution There are two major issues in the delay chain based FPGA TDC due to uneven internal delay in the carry chain. (1) The bin widths are uneven and depend on temperature and power supply voltage, which must be calibrated as frequently as possible. The auto-calibration functional block developed in this work provides semi-continuous calibration that converts the TDC measurements from bins to picoseconds. (2) In many applications, the TDC resolution is limited by the “ultra-wide bins”, corresponding to the carry chain crossing at the boundaries of the logic array blocks. The apparent widths of these ultra-wide bins can be several times bigger than the average bin width. The “wave union launchers” described in this paper are designed to make multiple measurements with a single delay chain structure, effectively to sub-divide the ultra-wide bins in each raw measurement. Several TDC schemes with resolutions in 20 to 10 picoseconds range implemented in today’s low cost FPGA have been tested. The Wave Union TDC Wave Union Launcher B In CLK 1: Oscillate 0: Hold In CLK 1: Unleash 0: Hold Wave Union Launcher A 1 2 The “wave union launchers” are designed to make multiple measurements with a single delay chain structure, effectively to sub-divide the ultra-wide bins in each raw measurement. A wave union launcher creates a pulse train or “wave union” with several 0-to-1 or 1-to-0 logic transitions for each input hit. 2 1 Implementation Details The Wave Union Launcher A The Automatic Calibration Block The Wave Union Launcher B DNL Histogram In (bin) LUT S Out (ps) After arrival of the input, the wave union launcher B starts to oscillate launching a wave union into the carry chain. The carry chain/register array structure takes 16 snap shots of the oscillation bit patterns in 16 clock cycles at 400MHz. The phase of the oscillation is determined by the arrival time of the input signal. If the drift of temperature and power supply voltage is sufficiently slow, it is reasonable to assume that the oscillation frequency is stable and can be measured to a good accuracy after long time. Then in the 16 snap shots, the locations of the logic transitions can be utilized to compute the arrival time of the input signal to a higher resolution through the processing block “SumHitD”. The “wave union launcher A” generates a pulse train with three logic transitions of which two are encoded. The “wave union launcher B” is simply a ring oscillator enabled by the input and after the input level turns from 0 to 1, a pulse train with unlimited length and logic transitions is generated. A DNL histogram is booked in the FPGA internal memory. Once all hits are booked into the histogram, the lookup table (LUT) is integrated from the DNL histogram so that it outputs the actual time of the center of the addressed bin. The outputs of the LUT are the TDC times calibrated to the temperature and power supply condition during booking the previous 16K hits. Test Result Remarks on Coarse Time Counters 1 2 RMS 10ps 140ps Data Output via Ethernet Two NIM inputs 000 001 011 010 110 111 101 100 Coarse Time Counter Fine Encoder In CLK ENA Fine Time Coarse Time Data Ready Hit Detect Logic Coarse Time Counter Gray Code Counter The left-most peak (which partially rolls over to the right edge) corresponds to the time difference of two input NIM signals without any BNC adapters. The second peak from left corresponds to one BNC adapter inserted into one of the NIM signal and the third peak corresponds two BNC adapters inserted, respectively, as shown in the photograph of the module. As expected, the separation between peaks is about 140ps. Each peak contains 16K events and the RMS resolution of each peak is about 10ps. BNC adapters to add 140ps step. BNC Adapter to add 140ps step. FPGA with 8ch TDC While the fine time is being encoded, a hit valid signal is being generated by the hit detect logic. It is used to enable latching of the coarse time. The uncertainty of the relative timing between the hit and the CLK is confined in the register array and all other signals are derived from the output of the register array. Their timing is well-defined by the CLK and they are staged into the process pipeline. Double counters driven by both edges of the system clock and the Gray code counters are popular choice for TDC coarse time counters, but they are only necessary for one type of TDC architecture found in ASCI TDC. For FPGA TDC, plain binary counter is sufficient. LeCroy 429A NIM Fan-out NIM/ LVDS - Wave Union TDC B +

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