Master Degree in Electronic Engineering “ TOP-UIC ” Torino-Chicago Double Degree Project Analog and Telecommunication Electronics course Prof. Del Corso Dante A.Y. 2013-2014 Switched Capacitor Working Principles and Filters application Switched capacitor technique as filtering implementation and filter design (TI MF10) Paolo Vinella s206827 [email protected]
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Switched Capacitor : Idea and application · • BASIC SWITCH: single nMOS or pMOS ... SWITCHED CAPACITOR FILTER. TRADITIONAL (“CONTINUOUS TIME”) FILTER. ACCURACY. f0 – clk
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SWITCHED CAPACITOR: a resistor-like device!• Comparing the two expressions of currents previously found we get:
• fCLK: clock signal (switching) speed
• C: nominal value of the capacitance
GOLDEN RULE: “A capacitor, connected alternatively between two low-impedance points (two voltage sources) driven by two switches, behaves like a resistor put between these two points”
• VERSATILE: function of clock frequency
• SMALL: C=5pF ; fCLK=100kHz ⟶ REQ= 2MΩ
• A SAMPLED SYSTEM: suitable for signals with frequency fS << fCLK (typical: ratio of 5 or more)
• SWITCHES DRIVEN BY “TWO-PHASES NON OVERLAPPING CLOCK” digital signal
517 May 2014 Switched Capacitor
1
REQ I122REQ =
1C fCLK
Φ1
tΦ2
t
SWITCHES: which device?• CMOS devices are populated by MOSFET: we can use them as switches (ohmic area). OFF near GΩ ; ON tenth of Ω
• BASIC SWITCH: single nMOS or pMOS
• TRANSMISSION GATE: reduced and constant RON (VDS - independent)
617 May 2014 Switched Capacitor
Φ Φ Φ
Φ
Device turned “ON”: ohmic region for both nMOS and pMOSGON = K VAL − Vtn + Vtp
K ≐ Kn = μnCOXWnLn
= Kp = μpCOXWpLp
RON
2. Switched Capacitor in basic FILTERS
SUMMARY OF GOALS:
• Low-Pass passive cell
• Low-Pass active cell: Integrator
• Stray-Capacitive Insensitive circuits
717 May 2014 Switched Capacitor
Basic application: 1st Order LP passive cell• Simply replace the resistor of the RC LP cell with a capacitor: only capacitances in the circuit!
TRANSFER FUNCTION: H s = 11 + sRC2
= 1
1 + sC2
C1 ∙ fCLK
CUT-OFF FREQUENCY: fC = 12πRC2
= 12π
C1C2
fCLK
fC depends on RATIO among two capacitances
fC tunable varying the frequency fCLK of the signal Φ
817 May 2014 Switched Capacitor
vi
S2S1
C1 C2 vo vi C2 vo
R= 1 C1 fCLK
Φ
H(j2πf) dB
ffC
0
−20dB/dec
∠H(j2πf)
ffC
90°
0.1fC 10fC
0°
1st Order LP active cell: Integrator• The circuit behaves as analog integrator, offering a LP transfer function plus some gain
CONSIDERING SWITCHED CAPACITOR EQUIVALENT CIRCUIT: reason in terms of charge transfer from input to output!
Every clock cycle:1. Φ1 active: C1 absorbs a charge Q=C1vi 2. Φ2 active: same charge moved away from C1 to C2
Assuming vi=Vi=const, during Φ2 the output changes by C1Vi / C2 each clock cycle: Vo= − QC2
= −C1C2
ViApproximate the staircase waveform with a ramp: the circuit behaves as an integrator!Final value of Vo after every k clock cycle TCK :
Vo(kTCK) = Vo[(k−1)TCK] − Vi[(k−1)TCK]∙C1C2
1017 May 2014 Switched Capacitor
vi
R1
C2
vo
–
+
I
I
On feedback branch:
I(t)=dQ t
dtQc t =C2vc(t)
I(t)=C2dvcdt
vc=−vo I(t)=−C2dvodt
… but this is the input current!vi(t)R1
= − C2dvodt ⟶
vo 0
vo tdvo = −
0
t vi tR1C2
dt⇒
⇒ vo t = vo 0 −1
R1C20
tvi t dt
VO
C2
Vi
S 1
C1
S 2
t
VOC1
C2Vi
Limitation: parasitic capacitances!• Both C1 and C2 realized within the same integrated circuit: they exhibit parasitic components towards ground at both pins!
Ideal behavior of the device clearly influenced by parasitic: charge dispersion!
All critical? NO, only CP11!
• CP12 between GND and GND: no effect!
• CP21 between virtual GND of the OPAMP and GND: no effect!
• CP22 in parallel to (driven by) vO : no effect on C2 charge!
• CP11 in parallel with C1 => the “real” C1 is C1+CP11: problematic!
…we can do better. Let’s see how
1117 May 2014 Switched Capacitor
vi
C2
vo
–
+Φ2C1Φ1
CP21 CP22
CP11CP12
4-switch cell: an help we need• IDEA: to avoid influence of parasitic let’s try to put C1 in series instead of parallel use 4-switch CELL
• Still seen as equivalent resistor:
1. Φ1 active: C charges with Q=C vi 2. Φ2 active: C discharged to GND. We take Io fCLK/sec times IO=QfCLK
Req =viI0
⟹ REQ = 1CfCLK
SAME RESULT!
INVERTING 4-SWITCH CELL: exchange position of Φ1 and Φ2 in output branch: now IO=-QfCLK (current with opposite sign)
1217 May 2014 Switched Capacitor
Φ2
C
Φ1 Φ1
Φ2vi
IOoutput MUST see a GND!
Stray Insensitive Active Integrator• Plug the 4-switch CELL inside the active integrator:
• We get rid of parasitic effects!
1317 May 2014 Switched Capacitor
vi
C2
vo
–
+
Φ2
C1
Φ1 Φ1
Φ2
vi
C2
vo
–
+
Φ2
C1
Φ1 Φ1
Φ2
CP22CP21
CP11 CP12
Non-Inverting Active Integrator• Using the INVERTING 4-switch CELL we can realize a NON-INVERTING integrator:
It overcomes the inverting limitation of the standard integrator!
1417 May 2014 Switched Capacitor
vi
C2
vo
+
–
Φ2
C1
Φ1 Φ2
Φ1
3. Switched Capacitor in COMPLEXFILTERS
SUMMARY OF GOALS:
• II Order Filters recall
• Tow-Thomas (State Variable) filter with SC
• IC Texas Instrument TI MF-10
implementation
1517 May 2014 Switched Capacitor
II order filters: recall (1)
BAND-PASS
LOW-PASS
HIGH-PASS
1617 May 2014 Switched Capacitor
II order filters: recall (2)
NOTCH
ALL-PASS
1717 May 2014 Switched Capacitor
II order filters: recall (3)
BANDPASS LOWPASS HIGH-PASS
NOTCH ALL-PASS
1817 May 2014 Switched Capacitor
State Variable Filter: recall• Device Block Diagram:
• Circuital implementation:
1917 May 2014 Switched Capacitor
Vi
∫∫
Σ -1V0
V11
A2
-A2VA
VA
B2B1B0
A0
A1
VLP VBPVHP
Commercial SC Active Filter: Texas Instrument MF10• 2 filter blocks (A and B) general purpose (State-Variable filters) up to 4th order filters
• Can realize any filter response type (Butterworth, Bessel, Cauer and Chebyshev)
• Each BLOCK: LP, BP, HP, N, A.P (called “MODES” OF OPERATION):
• f0 dependent on CLK ; QMAX depends on MODE (up to 150)
• f0 × Q Range up to 200÷300 kHz
• Operation up to 20÷30 kHz ; CLK up to 1÷1.5 MHz
• Supply ±7V or +14V. Can source 3 mA and sink 1.5 mA
2017 May 2014 Switched Capacitor
Mode BP LP HP N AP No. ofResistors Adjustable fCK/f0 Notes
1 * * * 3 No
1a HOBP1 = −QHOBP2 = +1 HOLP + 1 2 No May need input buffer. Poor