Background
Precision time measurement is widely applied to particle physics experiments, such as time-of-flight detector systems, neutron measurement experiments, gamma ray measurement, and plays a very important role in Positron Emission Tomography (PET) systems in the medical imaging field. The conventional Time measurement method is implemented based on a leading edge timing, multi-threshold discrimination or Constant Fraction timer (CFD) technique in conjunction with a Time To Digital Converter (TDC). In these methods both the timing circuit and the TDC circuit affect the final time measurement accuracy. Research in recent years shows that higher time measurement accuracy can be realized by firstly obtaining a complete waveform by using a full-waveform digitization technology and then obtaining time information by using a digital signal processing method. A classical waveform digitizing method is based on an analog-to-Digital converter (ADC), but as an alternative, a waveform digitizing technology based on a Switched Capacitor Array (SCA) Application Specific Integrated Circuit (ASIC) is receiving more and more attention and research due to its advantages of high sampling rate, low power consumption, high channel integration, and relatively low price.
In the current high-speed SCA chip, the sampling clock is generated by an inverter delay chain, which is schematically shown in fig. 1, so the sampling interval between adjacent sampling units is determined by the delay of the corresponding inverter. However, due to the influence of process variations, the delays of inverters at different levels in an actual chip are different, which results in a certain inconsistency between sampling intervals. This inconsistency, if not corrected, can limit the accuracy of the time measurement. So far, some documents have discussed this problem and proposed respective time correction schemes, wherein the most representative is "sine wave zero crossing" time correction method, which uses the characteristic that the slope of different sampling units at the sine wave "zero crossing" is not changed, i.e. the ratio of the sampling amplitude difference to the sampling time interval is fixed, and calculates the true sampling interval by measuring the amplitude difference, and the schematic diagram of the principle is shown in fig. 2. The method can be expressed simply as follows:
where N is the number of sampling units, Δ VnAnd Δ tnRespectively, the amplitude interval and the time interval between the nth sampling unit and the (n + 1) th sampling unit, and the zero point is positioned between the nth sampling unit and the (n + 1) th sampling unit, TclcIs the period of the Delay-chain phase-Locked Loop (DLL) input reference clock, and p is the sine wave slope at zero.
The method has a certain effect of improving the time measurement precision, but the method is easily influenced by the gain deviation and the bandwidth of each sampling unit, and the formula (1) is not strictly established, so that a certain deviation still exists between the obtained sampling interval and the real sampling interval, and the method has a limited improvement on the time measurement precision, and the effect is not obvious enough when the method is particularly applied to chips with lower bandwidth and larger gain deviation of each sampling unit.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention provides a time correction method for a switched capacitor array chip, which comprises the following processes: inputting sine waves with known frequency to an SCA chip, carrying out necessary amplitude correction on waveforms obtained by sampling, firstly calculating time values corresponding to each zero crossing point by using a linear difference method, then expressing the time interval between two adjacent zero crossing points on the same rising edge (or the same falling edge) in a linear addition mode by using each sampling interval, and establishing an equation by using the relationship between the time interval between the two adjacent zero crossing points and the period of an input signal. Repeating the above process for enough times to obtain an overdetermined linear equation set, solving the equation set by using a least square method, wherein the solution of the equation set is a real sampling interval, and then applying the sampling interval to a time measurement result. The innovation point of the scheme is that an overdetermined linear equation set is constructed and solved by utilizing the relation between the sampling signal period and the sampling interval so as to obtain the actual sampling interval of the switched capacitor array chip, and the time measurement result is corrected by utilizing the sampling interval. The method has the characteristics of simple and efficient algorithm, high precision and the like, and the calculation result is not limited by the analog bandwidth of the chip and the gain deviation of each sampling unit; the method can be applied to the field of high-precision time measurement based on the switched capacitor array chip, including flight time detection systems in high-energy physical experiments, neutron measurement, PET instruments in the field of medical imaging and the like.
The flow of the time correction method for the switched capacitor array chip according to the embodiment of the present invention is shown in fig. 3, and mainly includes the following steps:
step 1, inputting a sine wave with a known frequency as an input signal to a switched capacitor array chip, and calculating the zero crossing time of the sine wave sampled by the switched capacitor array chip.
In the embodiment of the invention, a signal generator is used for generating a sine wave with a known frequency as an input signal; and sampling the input signal by using a switched capacitor array chip, performing amplitude correction on the sine waveform obtained by sampling, and calculating the zero crossing time by using a linear difference method.
For example, a SCA waveform digitizing chip with a maximum sampling rate of 5.2Gsps, which is independently designed by nuclear detection and nuclear electronics national emphasis laboratories, and which has 256 sampling units in a single channel, can be used, and the signal generator used is the RoHDE & SCHWARZ RF signal generator ROHDE & SCHWARZ SMA 100A. The method comprises the steps of generating a sine wave with a signal frequency of 139MHz by using a signal generator as an input signal, sampling the input signal by using an SCA chip, and performing necessary amplitude correction on a waveform obtained by sampling, wherein the amplitude correction comprises the steps of converting a quantized code value into an amplitude value and correcting the inherent direct current deviation of each sampling unit.
In the sampled waveform, there are sampling points on both sides of the zero point of the waveform, such as the sampling points 54 and 55, 92 and 93 in fig. 4, and the time values of the "zero-crossing" points a and b can be calculated by a linear difference method using these special sampling points.
And 2, establishing an equation by utilizing the relation between the time interval of two adjacent zero-crossing time and the period of the input signal.
In the embodiment of the present invention, it is assumed that: the zero crossing point a is at the sampling point n1And n1+1, with the zero crossing b at sample point n2And n2+ 1;
the time interval Δ t between two adjacent zero crossings a and ba,bExpressed as:
wherein, Δ t
iRepresents the sampling time interval between sample point i and sample point i +1, then
Corresponds to a sampling point n
1And n
1+1, sample point n
2And n
2The sampling time interval between +1, α and β are both coefficients:
wherein, V
DCRepresents the dc value of the input sine wave;
corresponds to a sampling point n
1+1, sample point n
2The voltage value of (d);
corresponds to a sampling point n
1And n
1+1, sample point n
2And n
2A voltage difference between + 1;
and a time interval Δ ta,bEqual to the period T of the known input signalSThus, the following equation is established:
for ease of understanding, the above process is described below with reference to the example shown in fig. 4. Time interval delta t between two adjacent zero-crossing points a and b in fig. 4a,bIt can be expressed in the form of a linear addition of all the sampling intervals between sample point 54 and sample point 93:
wherein, Δ tiRepresenting the sampling time interval between sample point i and sample point i +1, then Δ t54、Δt92Corresponding to the sample time interval between samples 54 and 55 and between samples 92 and 93, α and β are coefficients:
wherein, VDCRepresents the dc value of the input sine wave; v55、V92Corresponding to the voltage values at sample point 55 and sample point 92; Δ V54、ΔV92Corresponding to the difference in voltage between sample points 54 and 55 and between sample points 92 and 93.
The time interval between the zero-crossing points a and b is equal to the period T of the known input signalSThus, the following equation is established:
and 3, establishing an overdetermined linear equation set by using enough equations, and solving to obtain the actual sampling interval of the switched capacitor array chip.
Sufficient equations can be obtained through the preceding steps to establish an overdetermined system of linear equations. In the embodiment of the invention, 3000 equations are obtained, an over-determined linear equation set is established according to the 3000 equations, and the equation set is expressed in a matrix equation form as follows:
wherein M represents the number of equations, and N represents the number of sampling units. If the SCA waveform digitizing chip mentioned in step 1 is adopted, the number of sampling units (i.e., sampling points) is 256, so the size of the equation coefficient matrix is 3000 × 256.
And then, solving an overdetermined linear equation set by using a least square method, wherein the solution of the overdetermined linear equation set is the actual sampling interval of the switched capacitor array chip.
As shown in fig. 5, the average of the finally obtained sampling intervals provided by the embodiment of the present invention is 0.192ns, which corresponds to a sampling frequency of 5.2 Gsps.
And 4, correcting the time measurement result by utilizing the actual sampling interval.
There are various ways to measure time using the SCA chip, and the method used in this example is as follows:
a narrow pulse waveform with the rising edge and the falling edge of 1.0ns is generated by an arbitrary waveform signal generator Keysight 81160A, the waveform is divided into two parts by a power divider, and the two divided waveforms are accessed into two sampling channels of a chip through two cables with different lengths for sampling. Firstly, amplitude calibration is carried out on the sampled signals, and then the time of each sampling point is corrected by using the actual sampling interval obtained by calculation in the step 4. And then respectively carrying out polynomial fitting on the leading edges of the two corrected waveforms, setting a voltage threshold value of 400mV, and respectively calculating time values of overvoltage threshold value points, wherein two threshold crossing time intervals are signal delay time, and a schematic diagram of the principle is shown in FIG. 6. Repeating the process 3000 times, a statistical result can be obtained, the average value of the measurement result is 3.36ns, the average value is the actual delay value of the two channel signals, and the root mean square value can represent the time measurement precision. Compared with the result of no time correction, as shown in fig. 7, it can be seen that the time measurement accuracy is improved from 27.7ps to 7.8ps by the sampling interval correction, and the effect is significant.
Compared with the traditional 'sine wave zero-crossing' time correction method, the scheme provided by the embodiment of the invention completes the final sampling interval calculation by measuring the amplitude difference of the sampling points at two sides of the zero point, but has the difference that the amplitude difference in the method does not directly participate in the final calculation, but is used for obtaining a voltage ratio as the coefficient of a variable in an equation. Although the bandwidth and gain deviation can affect the voltage amplitude value, the bandwidth and gain deviation can not affect the voltage ratio value, so the method can perfectly restore the real sampling interval theoretically. Compared with the traditional sine wave zero-crossing time correction method, the method is more accurate and stable, and has wider application range
Through the above description of the embodiments, it is clear to those skilled in the art that the above embodiments can be implemented by software, and can also be implemented by software plus a necessary general hardware platform. With this understanding, the technical solutions of the embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a usb disk, a removable hard disk, etc.), and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods according to the embodiments of the present invention.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.