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)
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
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
small bandwdth at hgh requency Passve LC lters (resonant) Coherent detecton Lockn technque 0 6 C Impedance [Ohm] 0 4 0 0 0 0 D 0 /Q V ac sn ω 0 t C x B m LPF out 0 4 0 7 0 8 0 9 0 0 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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. 094703 (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
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
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 00pA @ Hz smax = max C A 0
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
Concluson (3) To ncrease requency o operaton INT DIFF OFFERS LOW NOISE C s R DC A H(s) B 43 44