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– 1 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Switched-Capacitor Circuits

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Continuous-Time Integrator – 2 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Goal: Approach: emulating resistors with switched capacitors

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Concept of Switched Capacitor – 3 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 A switched capacitor is a discrete-time resistor RC time constant set by capacitor ratio C 2 /C 1 (match considerably better than R and C) and clock period T (flexibility) so, Non-overlapping two-phase clock

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Switched Capacitors – 4 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Shunt- and series-type SCs are simple and cheap to implement Stray-insensitive SC requires 2 more switches, whats the advantage besides being more flexible (i.e., w/ or w/o the T/2 delay)? 2-phase clockSeries-typeShunt-type Stray-insensitive

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Discrete-Time Integrator (DTI) – 5 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall phase clock Series-typeShunt-type What are the VTFs (z-domain) of these DTIs, assuming no parasitic capacitance is present?

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Shunt-Type DTI – 6 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Ф1 (sample) Charge conservation law (ideal): Total charge on C 1 and C 2 during Ф 1 Ф 2 transition must remain unchanged! Ф2 (update)

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Shunt-Type DTI – 7 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Ф1 (sample) Ф2 (update)

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Series-Type DTI – 8 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Ф1 (sample/update) Ф2 (reset C 1 ) VTF:

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Stray Capacitance – 9 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Series-typeShunt-type Strays derive from D/S diodes and wiring capacitance VTF is modified due to strays Strays at the summing node is of no significance (virtual ground)

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Stray-Insensitive SC Integrator – 10 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 VTF: Capacitors can be significantly sized down to save power/area Sizes are eventually limited by kT/C noise, mismatch, etc. InvertingNon-inverting VTF:

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SC Amplifier – 11 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Non-integrating, memoryless (less the delay) Used in many applications of parametric amplification VTF:

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– 12 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 SC Applications

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CT Filter – 13 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 RLC prototype Active-RC Tow-Thomas CT biquad

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SC DT Filter – 14 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 SC DT biquad Active-RC Tow-Thomas CT biquad

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Sigma-Delta (ΣΔ) Modulator – 15 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 DTI + 1-bit comparator + 1-bit DAC = first-order ΣΔ ADC

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Pipelined ADC – 16 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 SC amplifier + 2 comparators + 3-level DAC = 1.5-bit pipelined ADC

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SC Common-Mode Feedback – 17 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 CM sense amp can be replaced by a floating voltage source since the gain through the main op-amp is high enough.

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SC Common-Mode Feedback – 18 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012

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– 19 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Noise in SC Circuits

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Noise of CT Integrator – 20 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Noise in CT circuits can be simulated with SPICE (.noise)

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Noise of SC Integrator – 21 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 SC circuits are NOT noise-free! Switches and op-amps introduce noise.

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Sampling (Ф 1 ) Ideal Voltage Source – 22 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Noise is indistinguishable from signal after sampling The noise acquired by C 1 will be amplified in Ф 2 just like signal

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Integration (Ф 2 ) – 23 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 No simulator can directly simulate the aggregated output noise!

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Sampling (Ф 1 ) Noise – Cascaded Stages – 24 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Finite op-amp BW limits the noise bandwidth, resulting in less overall kT/C noise (noise filtering). But parasitic loop delay may introduce peaking in freq. response, resulting in more integrated noise (noise peaking).

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Sampled Noise Spectrum – 25 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Total integrated noise power remains constant SNR remains constant CT DT

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– 26 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Nonideal Effects in SC Circuits

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– 27 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Capacitors (poly-poly, metal-metal, MIM, MOM, sandwich, gate cap, accumulation-mode gate cap, etc.) –PP, MIM, and MOM are linear up to bits (nonlinear voltage coefficients negligible for most applications) –Gate caps are typically good for up to 8-10 bits Switches (MOS transistors) –Nonzero on-resistance (voltage dependent) –(Nonlinear) stray capacitance added (C gs, C gd, C gb, C db, C sb ) –Switch-induced sampling errors (charge injection, clock feedthrough, junction leakage, drain-source leakage, and gate leakage) Operational amplifiers –Offset –Finite-gain effects (voltage dependent) –Finite bandwidth and slew rate (measured by settling speed)

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– 28 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Nonideal Effects of Switches

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Nonzero On-Resistance – 29 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 FET channel resistance (thus tracking bandwidth) depends on signal level Usually (R on C S ) -1 (3-5)·ω -3dB of closed-loop op-amp for settling purpose

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Clock Bootstrapping – 30 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Small on-resistance leads to large switches large parasitic caps and large clock buffers Clock bootstrapping keeps V GS of the switch constant constant on- resistance (body effect?) and less parasitics w/o the PMOS CMOSBootstrapped NMOS

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Simplified Clock Bootstrapper – 31 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Pros Linearity Bandwidth Cons Device reliability Complexity

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Switch-Induced Errors – 32 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Channel charge injection and clock feedthrough (on drain side) result in charge trapped on C S after switch is turned off. Clock feedthrough Charge injection

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Clock Feedthrough and Charge Injection – 33 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Both phenomena sensitive to Z i, C S, and clock rise/fall time Offset, gain error, and nonlinearity introduced to the sampling Clock feedthrough can be simulated by SPICE, but charge injection cannot be simulated with lumped transistor models

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Clock Rise/Fall-Time Dependence – 34 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Clock feedthroughCharge injection Fast turn-off Slow turn-off

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Dummy Switch – 35 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Difficult to achieve precise cancellation due to the nonlinear dependence of ΔV on Z i, C S, and clock rise/fall time Sensitive to the phase alignment between Ф and Ф_

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CMOS Switch – 36 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Very sensitive to phase alignment between Ф and Ф_ Subject to threshold mismatch between PMOS and NMOS Exact cancellation occurs only for one specific V in (which one?) Same size for P and N FETs

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Differential Signaling – 37 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Signal-independent errors (offset) and even-order distortions cancelled Gain error and odd-order nonlinearities remain Balanced diff. input

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Switch Performance – 38 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Charge injection: Bandwidth: Performance FoM: Technology scaling improves switch performance! On-resistance:

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Leakage in SC Circuits – 39 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 I1 – diode leakage (existing in the old days too) I2 – sub-threshold drain-source leakage of summing-node switch I3 – gate leakage (FN tunneling) of amplifier input transistors Leakage currents are highly temperature- and process-dependent; the lower limit of clock frequency is often determined by leakage Φ 1 = high, Φ 2 = low

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DS Leakage – 40 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall μm CMOS A 0 = G m ·R o = 90dB R o 2MΩ R leak 0.6V/3μA 0.2MΩ A 0 = G m ·(R leak //R o ) 70dB

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Gate Leakage – 41 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Direct tunneling through the thin gate oxide Short-channel MOSFET behaves increasingly like BJTs Violates the high-impedance assumption of the summing node

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Switch Size Optimization – 42 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 To minimize switch-induced error voltages, small transistor size, slow turn-off, low source impedance should be used. For fast settling (high-speed design), large W/L should be used, and errors will be inevitably large as well. Guidelines Always use minimum channel length for switches as long as leakage allows. For a given speed, switch sizes can be optimized w/ simulation. Be aware of the limitations of simulators (SPICE etc.) usinglumped device models.

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– 43 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Nonideal Effects of Op-Amps

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– 44 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Offset Finite-gain effects (voltage dependent) Finite bandwidth and slew rate (measured by settling speed)

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Offset Voltage – 45 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 V i = 0

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Autozeroing – 46 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Also eliminates low-frequency noise, e.g., 1/f noise A.k.a. correlated double sampling (CDS)

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Chopper Stabilization – 47 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Ref: K. C. Hsieh, P. R. Gray, D. Senderowicz, and D. G. Messerschmitt, A low-noise chopper-stabilized differential switched-capacitor filtering technique, IEEE Journal of Solid-State Circuits, vol. 16, issue 6, pp , 1981.

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Chopper Stabilization – 48 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Also eliminates DC offset voltage of A 1

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Chopper-Stabilized Differential Op-Amp – 49 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Integrators/amplifiers can be built using these op-amps Some oversampling is useful to facilitate the implementation

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Ideal SC Amplifier – 50 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Closed-loop gain is determined by the capacitor ratio by design But this is assuming X is an ideal summing node (the op-amp is ideal)

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Finite-Gain Effect in SC Amplifier – 51 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012

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– 52 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Practical Issues

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Analog vs. Digital Supply Lines – 53 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Sharing sensitive analog supplies with digital ones is a very bad idea.

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Analog vs. Digital Supply Lines – 54 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Dedicated pads for analog and digital supplies On-chip bypass capacitors help (watch ringing) Off-chip chokes (large inductors) can stop noise propagation at board level

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Supply Capacitance – 55 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Any summing-node stray capacitance can be a potential coupling path. V DD, V SS, substrate, clock line, and digital noises, body effect, etc. Fully differential circuits help to reject common-mode noise and coupling.

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Supply Capacitance – 56 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Avoid connecting bottom-plate parasitics to the summing node Avoid crossing other signal lines with the summing node Shielding can mitigate substrate noise coupling

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Clock Generation – 57 – Data ConvertersSwitched-Capacitor CircuitsProfessor Y. Chiu EECT 7327Fall 2012 Clock-gated ring structure Non-overlapping time determined by inverter delays, sensitive to process, voltage, and temperature (PVT) variations DLL is an alternative, often used in high-speed designs

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