Switched-capacitor Field Programmable Analog Array SPICE simulation of frequency domain
1 Introduction
U.S. Anadigm's field programmable analog array (FPAA) using switched capacitor technology, field programmable gate array FPGA design advantages of the introduction to analog circuits. In this way, users can develop software provided by manufacturers AnadigmDesigner2 easily complete the entire analog signal processing system design, simulation, and finally loaded into the FPAA chip for authentication. However, AnadigmDesigner2 can only be realized on the FPAA circuit time domain simulation, but can not give the frequency domain characteristics of the circuit, which will filter and closed loop control system caused great inconvenience. Paper, the FPAA implementation is given by a continuous time switched capacitor network equivalent circuit model and adopt a common analysis software SPICE circuit to complete the FPAA in the frequency domain simulation. This method can be used as the complement of software development AnadigmDesigner2 allowed.
Switched-capacitor Field Programmable Analog Array SPICE simulation of frequency domain
2 FPAA principle of frequency-domain SPICE simulation
FPAA using switched capacitor circuits to perform analog signal processing, is time-varying sampling data network. As directly in the SPICE simulation can only get in the time domain characteristics of the circuit, but to understand the frequency domain characteristics, needs to carried out in the SPICE transient analysis and Zhixing Fourier transform, computational capacity, long simulation time. In 1979, CFKUTH and GSMOSCHYTZ published in two papers in the IEEE on that sample data with time-varying characteristics of the dual-port switched capacitor network can use the z domain equivalent circuit of four, said the equivalent of four of these Z domain circuit by the corresponding odd and even time slot is made of two coupled time-invariant networks, and gives six basic two-port z-domain SC network of four equivalent circuit. KRLaker so they continue to derive the other commonly used two-port SC network elements z-domain four component equivalent circuit. Through these dual-port SC network elements combinations of components can be any active or passive SC network z-domain equivalent circuit. In 1983, BERT D. NELIN generic SPICE circuit analysis software, the "element of Lossy Transmission Lines" elements established network of dual-port SC z domain equivalent circuit of four storage devices "storistor" model, so that z-domain SC network four equivalent circuit can be continuous time equivalent circuit model accurately simulated.
Anadigm's FPAA contains a large number of configurable analog blocks (CAB). Each CAB contains an electronic switch, operational amplifier, comparator and switching capacitor array. SRAM-based memory and FPAA programmable switch array is critical. AnadigmDesigner2 (Ver2.4.0.11) development software provided includes about 30 species of programmable analog circuit module (CAM) in the IP library, can cover the conventional analog signal processing, such as amplification, rectification, analog multiplier, analog divider , integral, differential and low-pass, high pass, band pass, band stop filter and so on. Thus, the establishment of the IP library of various CAM, continuous-time equivalent circuit model, you can use SPICE simulation software, the FPAA implementation of frequency domain characteristics of the circuit. Now, on to achieve the switched-capacitor FPAA PID controller, for example, set up for frequency domain characteristics of the equivalent SPICE circuit simulation module.
Switched-capacitor Field Programmable Analog Array SPICE simulation of frequency domain
3 PID continuous-time equivalent model
Figure 1 is a block diagram of PID control system calibration, which is an inherent part of the actual servo system, PID tuning device may be an FPAA FPAA chip AN221E04 to achieve. Development of software built with AnadigmDesigner2 PID controller design tools AnadigmPID, can be easily designed to achieve this in single-chip switched capacitor network, and the sampling clock frequency is 500Hz, as shown in Figure 2. It includes subtractor, integrator, with the phase amplifier, summing amplifier and the sample retainer 5 programmable analog circuit module (CAM), which is used to sample and hold reconstruction of sampled data signals. These CAM are used fully differential switched capacitor circuit structure to reduce common mode noise, reduce the even harmonic distortion signal, while increasing the output signal swing. But in order to simplify the simulation model, where a "half-circuit analysis" approach. Circuit analysis techniques such recognized that: the circuit on the signal, the symmetry of its communication channels to simplify the exchange of circuits, that is, only considering half of the signal communication pathways. The exchange of the signal path, the fully differential switched capacitor circuit structure from top to bottom completely complementary symmetry, it simplifies the use of frequency domain PID single-ended switched capacitor circuit structure, the specific circuit shown in Figure 3. In the figure, the five dashed box in the switched-capacitor circuit and Figure 2 for the five programmable analog circuit blocks (CAM)-one correspondence, φ1, φ2 phase sign is closed. After addition to sample and hold device can be established outside the discrete PID controller, four programmable analog circuit module (CAM) z-domain equivalent circuit model. For this reason, may assume the following conditions hold:
(1) all CAM is ideal capacitors, switches, voltage-controlled voltage source (that has nothing to do with the frequency of the infinite or finite gain op amp gain) consisting of linear switched capacitor network.
Switched-capacitor Field Programmable Analog Array SPICE simulation of frequency domain
(2) switched-capacitor network input and output are sampled data signal, the switch control signal are two non-overlapping clock. Is shown in Figure 4, one of the four CAM gain stage with offset compensation as one example. First, the switched capacitor network is divided into eight basic components dual-port SC network elements, surrounded by the dotted line in Figure 4 in parts. Then the SC network elements for each dual-port with its z-component domain equivalent circuit instead of four, to get the gain stage with offset compensation z-domain equivalent circuit model. Thus, to establish a good four programmable analog circuit module (CAM) z-domain equivalent circuit in Figure 3, link FPAA can be achieved by a discrete PID controller, z-domain equivalent circuit, Figure 5 in the rough part of the circuit surrounded crossed. The z-domain equivalent circuit consists of three basic components: an inverse relationship with the switched-capacitor equivalent resistor (CRES), is "memory" (PSTR) and negative "memory" (NSTR). FPGA can be introduced according to Figure 5, the discrete PID controller to achieve z-domain transfer function, but to achieve the frequency SPICE simulation, but also developed a z-domain equivalent circuit of the continuous-time equivalent circuit model. This also requires the establishment of the equivalent resistor (CRES), is "memory" (PSTR) and the negative "memory" (NSTR) equivalent circuit model of continuous time.
Switched-capacitor Field Programmable Analog Array SPICE simulation of frequency domain
The role of the output sample and hold device is re-discrete sampling data signals constitute a continuous-time signal, its transfer function as follows:
H (s) = (1-e-sT) / (sT)
The signal frequency response is a sinx / x function characteristics, can play the role of low-pass filter. The continuous-time equivalent circuit model shown in Figure 6. The figure, CAM in the op amp with voltage-controlled voltage source equivalent, equal to FPAA voltage transmission system in the op amp's open loop gain le4. Servo System theory of the transfer function can be used SPICE behavioral model in the Laplace said. To Figure 5, the equivalent resistor (CRES), is "memory" (PSTR), negative "memory" (NSTR), as well as sample and hold devices are used to their continuous-time equivalent circuit instead of, you can get the PID correction open-loop control system frequency domain SPICE simulation model, the simulation results shown in Figure 7. ① figure representative of FPAA PID controller to achieve the discrete frequency response, ② behalf by the sample and hold output of the PID controller frequency response, ③ and ④, said the series tuning PID control system of open-loop amplitude-frequency and phase frequency curve can be read from the graph through the frequency is 5.28Hz, phase margin is 41 °. PID correction in the series before, with the dynamic system through the frequency is 2.03Hz, phase margin is 10 °.
Switched-capacitor Field Programmable Analog Array SPICE simulation of frequency domain
4 Conclusion
The paper presented by an illustration of the switched-capacitor FPAA Field Programmable Analog Array SPICE simulation of frequency domain methods. This method can be achieved through SPICE simulation software to the FPAA circuit AC small signal analysis, thus, such as filters and closed-loop control systems analysis and design convenience.
Switched-capacitor Field Programmable Analog Array SPICE simulation of frequency domain