Why working at higher frequencies?

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Franklin Hood
6 years ago
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1 Advanced course on ELECTRICAL CHARACTERISATION OF NANOSCALE SAMPLES & BIOCHEMICAL INTERFACES: methods and electronc nstrumentaton. MEASURING SMALL CURRENTS When speed comes nto play Why workng at hgher requences? 00 Go away rom / nose Nose (pa/sqrt(hz)) 0 sgnal 0 00 k 0k 00k M Frequency (Hz) Interestng physcs may be there Impedance Spectroscopy Impedance Magntude [] G 00M 0M M 00k C DL CPE: Q = 0F/cm n = 0.9 PBS PBS/5 CPE R Fttng 00m 0 00 k 0k 00k M Frequency [Hz] R sol Capactance (mpedance) measurements are o nterest (see next)

2 IMPEDANCE : advantage n hgh requency ( ) v( ) jc V() jc Can not be too large (bo<0mv) Gven a current resoluton ( ) v( ) At Hgher requency... jc.. smaller C can be measured 3 Impedance measurement v ( t ) ( t ) v ( t ) C p Snusodal voltage source v ( t ) ( t ) v o ( t ) v ( t ) C p Vrtual ground R Transmpedance ampler 4 V ( S) Z In phase resstance I ( S) In quadrature capactance

3 Nose S() Nose S() Nose S() Nose S() Low nose / small bandwdth Small BW small nose 5 small bandwdth at hgh requency Capactance sgnal s here Small BW small nose Small BW small nose! How to obtan a narrow bandwdth at hgh? 6 3

4 small bandwdth at hgh requency Passve LC lters (resonant) Coherent detecton Lockn technque 0 6 C Impedance [Ohm] D 0 /Q V ac sn ω 0 t C x B m LPF out Frequency [Hz] xed (hgh) requency low nose (passve) amplcaton rst stage o the detector 7 Varable requency Very selectve Complete mpedance (two multplers, 0 and 90 ) Lockn technque The longer you average, more precse wll be the mean LPF out Bandwdth Same requency V ac sn ω 0 t Coherent detecton 0 8 4

5 Nose S() Lockn technque The longer you average, more precsely you get to zero LPF out Derent requency Bandwdth 0 Small bandwdth Long averagng tme Hgh rejecton o «spurous «Long measurement tme! Low nose 9 sncronsaton o events Sgnal here Needs RECHARGEABLE events (reversble redox, pump&probe, ) Lockn technque s exactly lke lterng (very narrowband) at hgh requency! Example : V(t) Induced electronc charge on metal plates I(t) dv(t) C dt V(t) R V ( S) Z In phase resstance I ( S) In quadrature capactance 0 5

6 Classcal Transmpedance S 4kT R R I dc s small nose Hgh senstvty large R (~G ) Senstvty & precson ndependent o Classcal Transmpedance HF LF R /C Unavodable parastc capactance I dc s 30Hz R =G ( n =4A/ Hz) C =0.5pF R C Lmted bandwdth! 6

7 How to do better? T network R C c R c I n Compensated Transmpedance Ampler. I n C R C c R c R t C Integratorderentator 3 T network: prncple C R >> R c R C c R c C c >> C (R c C c = R C ) I n R R c V 4 7

8 T network: prncple C R >> R c R C c R c C c >> C (R c C c = R C ) I n R R c V c V V 5 T network: prncple C R >> R c R C c R c C c >> C I n R R c V c Vc V V V 6 8

9 T network: desgn rules C To avod stray : R c <<R C c R c R C R C c R c I n I n = R R c s C c C R c R sc R R c calbrated to obtan: (C c C ) R c R = R C I n = R R c 7 T network: stablty C R c C p,c,c c dependents I n C p A(s) R C c poles (and zero) Hyp.: C c R c R C C <<C c,c p pole OA at hgh requency! Ad hoc desgn o d A(s) G loop s A(s) 8 sc R sc p R sc c R c A(s) sc p R low req. (<00Hz) 9

10 T network: nose C R C c R c I n C p e n A(s) n e n C p 4kT R 4kTR (R R C C) LIKE A STANDARD AMP. NEGLIGIBLE Howard, RSI, 70, p.860 (999): BW=7kHz, eq.3a/ Hz up to 00Hz 9 Compensated Transmpedance Ampl. C R C c R t I n = R t R R c sc c R c sc R I n R c C c R c = C R / n Needs careull tunng o R c I n = R t R R c Carlà, RSI, 75, p.497 (004), Co, IEEE Instr.&Meas. 55, p.84 (006) Carmnat, Analog IC Sg. Process (03) 0 0

11 Gan Gan Integratorderentator scheme s C s C C v u s C d Integrator Derentator C Log Stable, easy to be set, lnear, no calbraton Int. d. : nose n C =p G=00 =00p = 00k Only on sgnal path n addton to OpAmp low nose S 4kT R d C C d Equvalent to G

12 Int. d. : hgh requency lmt C C C p A() G loop C C C p C G loop s A s C C C p C GBP No stablty problems C GBP C C p C Easly n the MHz range 3 Int.d.: hgh requency lmt C = pf =00k C C p =5pF = 00pF GBP = 0MHz 0.5 pf Gan Maxmum operatng requency o the system G 30Hz 3MHz Same equvalent nput nose! 4

13 Integratorderentator : dc current I dc C V t) I t C d out ( dc I C dc t Unavodable OpAmp saturaton 5 Integratorderentator : pulsed reset C = pf =00k I dc = 00pF Gan but lmted tme or measurement : I I dc =0nA, V max =0V 3MHz 6 T m = ms Axopatch 00B 3

14 DC current dscharge () C I DC A H(s) R DC B Hgh DC gan rom A to B H(s) DC current collected through R DC ACTIVE ONLY at very low requences 7 DC current dscharge () C s A H(s) R DC B H(s) Zero gan rom A to B (H(S) NOT actve) when sgnal s present 8 4

15 Stablty remarks I test G loop sc H(s) R DC I out G loop 0dB/dec R DC H(s) H(s) 9 Stablty remarks I test G loop sc H( s) R DC I out G loop R DC H(s) H(s) 40dB/dec low phase margn! 30 5

16 Stablty remarks I test G loop sc H( s) R DC G loop I out dc dscharge R DC H(s) sgnal bandwdth H(s) 0dB p z 0dB/dec w p z /g w m C R DC STABILITY o the crcut IMPOSES the same number o poles and zeros n H(s) g 3 DC output AC output C I dc s s I dc AC out R DC H(s) DC out = R DC I dc T() c C C d Rd 3 z m w h C GBP C C p 6

17 Hgh value resstor Nose current MIXES to nput sgnal I dc s s I dc C ac eedback A R DC as BIG as possble low nose DC out B R DC H(s) Dc eedback R DC not too bg large dynamc o I 4kT c R Doesn t aect BW Very good! R DC ~ G 33 H(s) : desgn consderatons Poles/zeros at very low requency: A 0 H(s) Hz C z R z Sgnal bandwdth X A 0 R p C z 0.Hz R C z z R R z p V n R p A(s) In case o saturaton, recovery tmes proportonal to t z 34 7

18 Derentator: desgn consderatons G loop V nt 35 Constrants: π = B C GBP > = R eq nose Example: C =.5pF, R eqnose =G, =0pF 0 GBP GBP > πb C R eq nose π B=MHz =47k =pf GBP>60MHz Example o realzaton Output stage DC out AC out Ferrar, RSI, 78, p (007) 36 C C d H(s): 40 R F =47k R DC =G Bandwdth: Hz MHz second order lter, g = 3; zero <0.Hz 8

19 Expermental results bandwdth G 00M.8Hz.4MHz Gan [] 0M M Classc transmp. amp. wth the same nose 37 00k 00m 0 00 k 0k 00k M 0M Frequency [Hz] Nose Analyss C n R DC e n H(s) C e H e n Reduced by the capactve gan /C 4kT e H en C 4 eq n en Cn C en C Rdc Rdc Rd Cd Input equvalent nose: kt C Rd Cd 38 Same o a classcal transmp. ampler neglgble or c >00k 9

20 Expermental results nose 39 Current nose[a/sqrt(hz)] p 00 0 Classc transmp. amp. wth the same bandwth (R F 800k) Measured nose 4kT 4 n Rdc kt C R d C d 00 k 0k 00k M Frequency [Hz] e C n n Theroretcal predcton C Dynamc range consderatons C s I dc R DC A H(s) B 40 DC: node B I dc max = V Hmax c 0nA Low requency: node A Hgh requency: node Vout smax = V max πc Hz smax = max C A 0

21 Current Nose Concluson () Read currents wth a TRANSIMPEDANCE AMPLIFIER ( t ) R V o (t)= (t). R R C TOT Low output mpedance senstvty large R precson stable R 4 Concluson () Be aware o nput capactance KEEP C n SMALL I nose dv C dt G Z C n Increases wth requency 4

22 Concluson (3) To ncrease requency o operaton INT DIFF OFFERS LOW NOISE C s R DC A H(s) B 43 44

Chapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals.

Chapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals. 6 Operatonal mpler Chapter 6 Operatonal mpler CC Symbol: nput nput Output EE () Non-nvertng termnal, () nvertng termnal nput mpedance : Few mega (ery hgh), Output mpedance : Less than (ery low) Derental