Switched Capacitor: Sampled Data Systems

Transcription

1 Switched Capacitor: Sampled Data Systems Basic switched capacitor theory How has Anadigm utilised this. Theory-Basic SC and Anadigm-1

2 Resistor & Charge Relationship I + V - I Resistance is defined in terms of current (I) and voltage (V). I = Q t Current is the rate of change of charge. R = V I = V t Q R = V/I Theory-Basic SC and Anadigm-2

3 Switching Charge to a Capacitor Theory-Basic SC and Anadigm-3

4 Switched Capacitor as a Resistor Equivalent resistance Contains no R Goes UP as C goes down Function only of C and clock period (T) Ratios Independent of clocks Depends on capacitor matching Theory-Basic SC and Anadigm-4

5 Why Switched Capacitor? RC constants with only C s Area savings - much smaller for large R Better resistor values Better tolerance; typically ± 1.0% Better matching - typically ± 0.1% Better Linearity Wider range The extras Phase swapping Frequency dependent RC s Theory-Basic SC and Anadigm-5

6 Phase Swapping Theory-Basic SC and Anadigm-6

7 The Clock as a System Reference Corner frequency can be changed by changing the clock frequency Theory-Basic SC and Anadigm-7

8 Switched Capacitor Circuits are Sampled Data Systems Inputs and outputs may be valid only on certain phases Subject to sampled data system constraints φ1 φ2 φ1 φ2 φ1 φ2 Theory-Basic SC and Anadigm-8

9 Expression of Sampled Data Function V t Q t Q 1 = CV 1 V t Q = CV 0 1 Q t φ1 φ2 φ1 φ2 φ1 φ2 Theory-Basic SC and Anadigm-9 t=-2 t=-1 t=0 (= now )

10 Sampled Data Example C2 Qfb0 = C2 Vout 0 Vin C1 Qin Qfb Qi Ci Qi0 = Ci ( Vout0 Vout 1) Vout Qin = C Vin C 1 Vin C2 Vout0 + Ci ( Vout0 Vout ) = 0 Theory-Basic SC and Anadigm-10

11 And we get : AnadigmDesigner Simulator Equation! Vin C1 C2 Ci Vout nc i All SC functions are about ratios of capacitors. Normalise all caps connected to an integrator stage to the integrator cap (=C 2 here). So: =1 C1 nc 1 = C i C2 nc2 = C i On φ2 : On φ1 : Vout 1 = ( 1 1 (1 + ) Vout + nc Vin nc Vout0 = Vout 1 ) Theory-Basic SC and Anadigm-11

12 Performance: Programming Boundaries Op-amp dynamics Gain-bandwidth product Op-amp slew rate Loading limits Input offset Limit on filter order Capacitance spread Theory-Basic SC and Anadigm-12

13 Opamp Gain Bandwidth Product 80dB 40dB 0dB 120kHz There is a natural trade-off between bandwidth and gain This knowledge is built into the IPmodules Theory-Basic SC and Anadigm-13

14 Op-amp Slew Rate Defines speed at which large transitions in output voltage are made. The op-amp is no longer operating in small-signal mode (the virtual ground is destroyed temporarily) This is separate to GB product It arises from internal features of the op-amp, and is not a feature of capacitive loading Note: excess capacitive load causes op-amp instability (ringing) Anadigm op-amp s are designed to drive 100pF load at unity gain About 6 or 7 full-size input caps Theory-Basic SC and Anadigm-14

15 Input Offset C3 C2 Vin = 0 C1 Vos Vout V out = V os ( C 1 + C3) C 3 Anadigm 3.3volt products have an internal offset nulling circuit this reduces the effective offset from a few mil-volts to less than 250 microvolts. 5 volt products do not have this feature Theory-Basic SC and Anadigm-15

16 Filter Order In theory, very large filters can be constructed with Anadigm s dpasp and FPAA products, 8 poles with each device and multiple devices can be used. All the previous effects are cumulative and will put a practical limit on filters that can be built. A rule of thumb, a maximum order of about can be realised without special consideration of the second order effects mentioned previously (e.g. C-message telecoms filter) Higher order filters with poles in their transfer function (IIR filters) are not often called for anyway. Theory-Basic SC and Anadigm-16

17 Capacitance Spread The ratio of C max to C min in a given Switched Capacitor stage Limits CAM parameter ranges Lowest filter cut-off frequency Minimum and maximum gain settings Maximum length of integrator time-constant Theory-Basic SC and Anadigm-17

18 Extending Capacitance Spread C3 C2a C2b Vin C1 Vout Uses parallel combinations of available capacitors Many of Anadigm s CAM use this technique. Theory-Basic SC and Anadigm-18