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general description the MAX4206 logarithmic amplifier computes the log ratio of an input current relative to a reference current (externally or internally generated) and provides a cor- responding voltage output with a default 0.25v/decade scale factor. the device operates from a single +2.7v to +11v supply or from dual ?.7v to ?.5v supplies and is capable of measuring five decades of input cur- rent across a 10na to 1ma range. the MAX4206? uncommitted op amp can be used for a variety of purposes, including filtering noise, adding offset, and adding additional gain. a 0.5v reference is also included to generate an optional precision current reference using an external resistor, which adjusts the log intercept of the MAX4206. the output-offset voltage and the adjustable scale factor are also set using exter- nal resistors. the MAX4206 is available in a space-saving 16-pin thin qfn package (4mm x 4mm x 0.8mm), and is specified for operation over the -40? to +85? extended temper- ature range. applications photodiode current monitoring portable instrumentation medical instrumentation analog signal processing features ? +2.7v to +11v single-supply operation ? ?.7v to ?.5v dual-supply operation ? 5 decades of dynamic range (10na to 1ma) ? monotonic over a 1na to 1ma range ? 0.25v/decade internally trimmed output scale factor ? adjustable output scale factor ? adjustable output offset voltage ? internal 10na to 10? reference current source ? 0.5v input common-mode voltage ? small 16-pin thin qfn package (4mm x 4mm x 0.8mm) ? -40? to +85? operating temperature range ? evaluation kit available MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range ________________________________________________________________ maxim integrated products 1 ordering information MAX4206 v ee gnd refiin cmvin refiout logiin i in cmvout refiset scale logv2 osadj logv1 refvout v cc v cc r comp c comp r set r os r1 r2 0.1 f 0.1 f v out 0.1 f r comp c comp t ypical operating circuit 19-3071; rev 0; 12/03 for pricing, delivery, and ordering information, please contact maxim/dallas direct! at 1-888-629-4642, or visit maxim? website at www.maxim-ic.com. evaluation kit available part temp range pin-package MAX4206ete -40? to +85? 16 thin qfn-ep* *ep = exposed paddle. 16 15 14 13 cmvin logiin refiin refiout 9 10 11 12 n.c. v cc refiset cmvout 4 3 2 1 v ee gnd refvout n.c. 5678 logv1 osadj scale logv2 MAX4206 top view (leads on bottom) thin qfn pin configuration
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 2 _______________________________________________________________________________________ absolute maximum ratings stresses beyond those listed under ?bsolute maximum ratings?may cause permanent damage to the device. these are stress rating s only, and functional operation of the device at these or any other conditions beyond those indicated in the operational sections of the specificatio ns is not implied. exposure to absolute maximum rating conditions for extended periods may affect device reliability. (all voltages referenced to gnd, unless otherwise noted.) v cc .........................................................................-0.3v to +12v v ee ............................................................................-6v to +0.3v supply voltage (v cc to v ee ) .............................................. +12v refvout ....................................................(v ee - 0.3v) to +3.0v osadj, scale, refiset ...........................(v ee - 0.3v) to +5.5v refiin, logiin ........................................(v ee - 0.3v) to v cmvin logv1, logv2, cmvout, refiout ......................................(v ee - 0.3v) to (v cc + 0.3v) cmvin............................................................(v ee - 0.3v) to +1v continuous current (refiin, logiin) ................................10ma continuous power dissipation (t a = +70?) 16-pin thin qfn (derate 16.9mw/? above +70?) ....1349mw operating temperature range ...........................-40? to +85? junction temperature .....................................................+150? storage temperature range .............................-65? to +150? lead temperature (soldering, 10s) .................................+300? dc electrical characteristics?ingle-supply operation (v cc = +5v, v ee = gnd = 0v, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = -40? to +85?. typical values are at t a = +25?, unless otherwise noted.) (note 1) parameter symbol conditions min typ max units supply voltage v cc (note 2) 2.7 11.0 v t a = +25? 3.9 5 supply current i cc t a = -40? to +85? 7 ma minimum 10 na lo giin c ur r ent rang e ( n otes 3, 4) i log maximum 1 ma minimum 10 na re fiin c ur r ent rang e ( n otes 3, 4) i ref maximum 1 ma common-mode voltage v cmvout 480 500 520 mv common-mode voltage input range v cmvin 0.5 1.0 v t a = +25? ? ? log conformity error v lc i ref = 10na, i log = 10na to 1ma, k = 0.25v/decade (note 4) t a = -40? to +85? ?0 mv t a = +25? 237.5 250 262.5 logarithmic slope (scale factor) k t a = -40? to +85? (note 4) 231.25 268.75 mv/ decade logarithmic slope (scale factor) temperature drift t a = -40? to +85? 80 ?/ d ecad e/ ? input offset voltage v io t a = +25?, |v cmvin - v refiin |, |v cmvin - v logiin | 15mv input offset voltage temperature drift v ios |v cmvin - v refiin |, |v cmvin - v logiin |6 ?/? t a = +25? 1.218 1.238 1.258 voltage reference output v refvout t a = -40? to +85? (note 4) 1.195 1.275 v v ol tag e refer ence o utp ut c ur r ent i refvout 1ma t a = +25? 490 500 510 c ur r ent refer ence o utp ut v ol tag ev refiset t a = -40? to +85? (note 4) 482 518 mv
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range _______________________________________________________________________________________ 3 ac electrical characteristics?ingle-supply operation (v cc = +5v, v ee = gnd = 0, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = +25?, unless otherwise noted.) dc electrical characteristics?ingle-supply operation (continued) (v cc = +5v, v ee = gnd = 0v, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = -40? to +85?. typical values are at t a = +25?, unless otherwise noted.) (note 1) parameter symbol conditions min typ max units logv2 buffer t a = +25? 0.4 2 input offset voltage v io t a = -40? to +85? (note 4) 6 mv input bias current i b (note 4) 0.01 1 na v oh r l to gnd = 2k ? v cc - 0.2 v cc - 0.3 output voltage range v ol r l to gnd = 2k ? 0.2 0.08 v i out+ sourcing 34 output short-circuit current i out- sinking 58 ma slew rate sr 12 v/? unity-gain bandwidth gbw 5 mhz parameter symbol conditions min typ max units logv2 total noise 0.1hz to 10hz, total output-referred noise, i ref = 10na, i log = 100na 17 ? rms logv2 spot noise density f = 5khz, i ref = 10na, i log = 100na 0.8 ?/ hz refvout total noise 1hz to 10hz, total output-referred noise 3.3 ? rms refvout spot noise density f = 5khz 266 nv/ hz refiset total noise 1hz to 10hz, total output-referred noise 0.67 ? rms refiset spot noise density f = 5khz 23 nv/ hz small-signal unity-gain bandwidth i ref = 1?, i log = 10?, r comp = 300 ? , c comp = 32pf 1mhz dc electrical characteristics?ual-supply operation (v cc = +5v, v ee = -5v, gnd = 0, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = -40? to +85?. typical values are at t a = +25?, unless otherwise noted.) (note 1) parameter symbol conditions min typ max units v cc 2.7 5.5 supply voltage (note 2) v ee -2.7 -5.5 v t a = +25? 5 6 supply current i cc t a = -40? to +85? 7.5 ma minimum 10 na lo giin c ur r ent rang e ( n otes 3, 4) i log maximum 1 ma minimum 10 na re fiin c ur r ent rang e ( n otes 3, 4) i ref maximum 1 ma common-mode voltage v cmvout 480 500 520 mv
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 4 _______________________________________________________________________________________ dc electrical characteristics?ual-supply operation (continued) (v cc = +5v, v ee = -5v, gnd = 0, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = -40? to +85?. typical values are at t a = +25?, unless otherwise noted.) (note 1) parameter symbol conditions min typ max units common-mode voltage input range v cmvin 0.5 1.0 v t a = +25? ? ? log conformity error v lc i ref = 10na, i log = 10na to 1ma, k = 0.25v/decade (note 4) t a = -40? to +85? ?0 mv t a = +25? 237.5 250 262.5 logarithmic slope (scale factor) k t a = -40? to +85? 231.25 268.75 mv/ decade logarithmic slope (scale factor) temperature drift t a = -40? to +85? 80 ?/ decade/ ? input offset voltage v io t a = +25?, |v cmvin - v refiin |, |v cmvin - v logiin | 15mv input offset voltage temperature drift v ios |v cmvin - v refiin |, |v cmvin - v logiin |6 ?/? t a = +25? 1.218 1.238 1.258 voltage reference output v refvout t a = -40? to +85? (note 4) 1.195 1.275 v voltage reference output current i refvout 1ma t a = +25? 490 500 510 current reference output voltage v refiset t a = -40? to +85? (note 4) 482 518 mv logv2 buffer t a = +25? 0.4 2 input offset voltage v io t a = -40? to +85? (note 4) 6 mv input bias current i b (note 4) 0.01 1 na v oh r l to gnd = 2k ? v cc - 0.2 v cc - 0.3 output voltage range v ol r l to gnd = 2k ? v ee + 0.2 v ee + 0.08 v i out+ sourcing 34 output short-circuit current i out- sinking 58 ma slew rate sr 12 v/? unity-gain bandwidth gbw 5 mhz
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range _______________________________________________________________________________________ 5 ac electrical characteristics?ual-supply operation (v cc = +5v, v ee = -5v, gnd = 0, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = +25?, unless otherwise noted.) parameter symbol conditions min typ max units logv2 total noise 0.1hz to 10hz, total output-referred noise, i ref = 10na, i log = 100na 17 ? rms logv2 spot noise density f = 5khz, i ref = 10na, i log = 100na 0.8 ?/ hz refvout total noise 1hz to 10hz, total output-referred noise 3.3 ? rms refvout spot noise density f = 5khz 266 nv/ hz refiset total noise 1hz to 10hz, total output-referred noise 0.67 ? rms refiset spot noise density f = 5khz 23 nv/ hz small-signal unity-gain bandwidth i ref = 1?, i log = 10?, r comp = 300 ? , c comp = 32pf 1 mhz note 1: all devices are 100% production tested at t a = +25?. all temperature limits are guaranteed by design. note 2: guaranteed and functionally verified. note 3: log conformity error less than ?mv with scale factor = 0.25v/decade. note 4: guaranteed by design. t ypical operating characteristics (v cc = +5v, v ee = gnd = 0v, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = +25?, unless otherwise noted.) v logv1 vs. i log MAX4206 toc01 i log (a) v logv1 (v) 1m 100 100n 1 10 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 -0.25 10n 10m i ref = 10na t a = -40 c to +85 c v cc = +5v v ee = gnd 1m 100 10n 100n 1 10 1n 10m v logv1 vs. i log MAX4206 toc02 i log (a) v logv1 (v) 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 -0.25 i ref = 10na t a = -40 c to +85 c v cc = +5v v ee = -5v 1m 100 10n 100n 1 10 10m v logv1 vs. i log MAX4206 toc03 i log (a) v logv1 (v) 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 -0.25 i ref = 10na t a = -40 c to +85 c v cc = +2.7v v ee = gnd
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 6 _______________________________________________________________________________________ -0.25 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 -0.50 v logv1 vs. i log (i ref = 10na to 1ma) MAX4206 toc04 i log (a) v logv1 (v) 1m 100 100n 1 10 10n 10m 10na 100na 1 a 10 a 100 a 1ma v logv1 vs. i ref (i log = 10na to 1ma) MAX4206 toc05 i ref ( a ) v logv1 (v) 100 10 1 100n 10n -0.3 0 0.3 0.5 0.8 1.0 1.3 1.5 1.8 2.0 -0.5 1n 1m 10na 100na 1 a 10 a 100 a 1ma -15 -10 -5 0 5 10 15 20 -20 normalized log conformance error vs. i log MAX4206 toc06 i log ( a ) error (mv) 1m 100 100n 1 10 10n 10m i ref = 10na t a = -40 c to +85 c v cc = +5v v ee = gnd 1m 100 10n 100n 1 10 1n 10m -15 -10 -5 0 5 10 15 20 -20 normalized log conformance error vs. i log MAX4206 toc07 i log (a) error (mv) i ref = 10na t a = -40 c to +85 c v cc = +5v v ee = -5v t a = -40 c -15 -10 -5 0 5 10 15 20 -20 normalized log conformance error vs. i log MAX4206 toc08 i log (a) error (mv) 1m 100 100n 1 10 10n 10m i ref = 10na t a = -40 c to +85 c v cc = +2.7v v ee = gnd t a = -40 c -15 -10 -5 0 5 10 15 20 -20 normalized log conformance error vs. i log MAX4206 toc09 i log (a) error (mv) 1m 100 100n 1 10 10n 10m i ref = 10na single supply: v cc = +2.7v, +5v, 11v, v ee = gnd dual supply: v cc = +5v v ee = -5v v logiin - v cmvin vs. i log MAX4206 toc10 i log (a) v logiin - v cmvin (mv) 1m 100 100n 1 10 5 4 3 2 1 0 -1 -2 -3 -4 -5 10n 1n 10m i ref = 10na v logv2 voltage-noise density vs. frequency MAX4206 toc11 frequency ( hz ) 1m 100k 10k 1k 100 10 0.1 1 10 0.01 110m noise density ( v/ hz) i ref = i log 100na 10na 1 a 10 a total wideband voltage noise at v logv2 vs. i log MAX4206 toc12 i log ( a ) voltage noise (mv rms ) 100 10 1 100n 1 2 3 4 5 0 10n 1m i ref = i log f = 1hz to 1mhz t ypical operating characteristics (continued) (v cc = +5v, v ee = gnd = 0v, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = +25?, unless otherwise noted.)
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range _______________________________________________________________________________________ 7 i log pulse response (i ref = 100na, v cc = 5v, v ee = gnd) MAX4206 toc13 v logv1 (v) 20 s/div 0.50v 1.0v 100 a to 1ma 10 a to 100 a 1 a to 10 a 100na to 1 a 0.25v 0.75v 0.75v 0.50v 0.25v 0 i log pulse response (i ref = 100na, v cc = 5v, v ee = -5v) MAX4206 toc14 v logv1 (v) 20 s/div 0.50v 1.0v 100 a to 1ma 10 a to 100 a 1 a to 10 a 100na to 1 a 0.25v 0.75v 0.75v 0.50v 0.25v 0 i ref pulse response (i log = 1ma) MAX4206 toc15 v logv1 (v) 20 s/div 0.50v 1.0v 1 a to 100na 10 a to 1 a 100 a to 10 a 1ma to 100 a 0.25v 0.75v 0.75v 0.50v 0.25v 0 0 10 5 20 15 25 30 240 250 245 255 logarithmic slope distribution MAX4206 toc16 slope (mv/decade) count (%) 260 0 5 15 10 20 25 1.232 1.238 1.240 1.234 1.236 1.242 v refvout distribution MAX4206 toc17 v refvout (v) count (%) r l = 100k ? 1.244 0 6 4 2 12 8 10 14 16 -1.0 0.5 1.0 -0.5 0 1.5 2.0 2.5 input offset voltage distribution MAX4206 toc18 input offset voltage (mv) count (%) input offset voltage = v logiin - v cmvin 3.0 t ypical operating characteristics (continued) (v cc = +5v, v ee = gnd = 0v, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = +25?, unless otherwise noted.)
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 8 _______________________________________________________________________________________ 0 -100 10 100 1k 10k 100k 1m reference power-supply rejection ratio vs. frequency -80 MAX4206 toc22 frequency (hz) reference psrr (db) -60 -40 -20 -90 -70 -50 -30 -10 c refvout = 0.1 f i refvout = 1ma reference line-transient response MAX4206 toc23 10 s/div 1.238v 0v v cc 2v/div v refvout 200mv/div c refvout = 0f reference load-transient response MAX4206 toc24 100 s/div 1.238v 0ma i refvout 1ma/div v refvout 100mv/div c refvout = 0f reference turn-on transient response MAX4206 toc25 10 s/div 0v 0v v cc 2.5v/div v refvout 500mv/div t ypical operating characteristics (continued) (v cc = +5v, v ee = gnd = 0v, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = +25?, unless otherwise noted.) 1.20 1.23 1.22 1.21 1.24 1.25 1.26 1.27 1.28 1.29 1.30 -50 0 -25 25 50 75 100 reference output voltage (v refvout ) vs. temperature MAX4206 toc19 temperature ( c) reference output voltage (v) 1.00 1.15 1.10 1.05 1.20 1.25 1.30 1.35 1.40 1.45 1.50 -1.0 -0.5 0.5 01.0 reference output voltage (v refvout ) vs. load current MAX4206 toc20 load current (ma) reference output voltage (v) 1.200 1.215 1.210 1.205 1.220 1.225 1.230 1.235 1.240 1.245 1.250 23 5 46 reference output voltage (v refvout ) vs. supply voltage MAX4206 toc21 supply voltage (v) reference output voltage (v)
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range _______________________________________________________________________________________ 9 small-signal ac response i log to v logv1 MAX4206 toc26 frequency (hz) normalized gain (db) 1m 100k 10k 1k -50 -40 -30 -20 -10 0 10 -60 100 10m i log = 100 a i log = 1ma i log = 10 a i log = 1 a i log = 100na c comp = 33pf r comp = 330 ? small-signal ac response i log to v logv1 MAX4206 toc27 frequency (hz) normalized gain (db) 1m 100k 10k 1k -50 -40 -30 -20 -10 0 10 -60 100 10m i log = 100 a i log = 1ma i log = 10 a i log = 1 a i log = 100na c comp = 100pf r comp = 1k ? small-signal ac response of buffer MAX4206 toc28 frequency (hz) normalized gain (db) 10m 1m 100k -9 -6 -3 0 3 -12 10k 100m a v = 2v/v a v = 4v/v a v = 1v/v t ypical operating characteristics (continued) (v cc = +5v, v ee = gnd = 0v, i ref = 1?, i log = 10?, logv2 = scale, logv1 = osadj, cmvin = cmvout, r set > 1m ? , t a = +25?, unless otherwise noted.) pin description pin name function 1, 9 n.c. no connection. not internally connected. 2 refvout 1.238v reference voltage output. bypass refvout to gnd with a 0 to 1? capacitor (optional). 3 gnd ground 4v ee negative power supply. bypass v ee to gnd with a 0.1? capacitor. 5 logv1 logarithmic amplifier voltage output 1. the output scale factor of logv1 is 0.25v/decade. 6 osadj offset adjust input. when operating from a single power supply, current applied to osadj adjusts the output offset voltage (see the output offset section). 7 scale scale factor input. adjust the output scale factor for logv2 using a resistive divider (see the scale factor section). 8 logv2 logarithmic amplifier voltage output 2. adjust the output scale factor for logv2 using a resistive divider (see the scale factor section). 10 v cc positive power supply. bypass v cc to gnd with a 0.1? capacitor. 11 refiset current reference adjust input. a resistor, r set , from refiset to gnd adjusts the current at refiout (see the adjusting the logarithmic intercept section). 12 cmvout 0.5v common-mode voltage reference output. bypass cmvout to gnd with a 0.1? capacitor. 13 refiout current reference output. the internal current reference output is available at refiout . 14 refiin current reference input. apply an external reference current at refiin. i refiin is the reference current used by the logarithmic amplifier when generating logv1. 15 logiin current input to logarithmic amplifier. logiin is typically connected to a photodiode anode or other external current source. 16 cmvin common-mode voltage input. v cmvin is the common-mode voltage for the input and reference amplifiers (see the common mode section).
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 10 ______________________________________________________________________________________ detailed description theory figure 2 shows a simplified model of a logarithmic amplifier. two transistors convert the currents applied at logiin and refiin to logarithmic voltages accord- ing to the following equation: where: v be = base-emitter voltage of a bipolar transistor k = 1.381 x 10 -23 j/k t = absolute temperature (k) q = 1.602 x 10 ?9 c i c = collector current i s = reverse saturation current the logarithmic amplifier compares v be1 to the refer- ence voltage v be2 , which is a logarithmic voltage for a known reference current, i ref . the temperature depen- dencies of a logarithmic amplifier relate to the thermal voltage, (kt/q), and i s . matched transistors eliminate the i s temperature dependence of the amplifier in the following manner: vvv kt q i i kt q i i kt q i i i i kt q i i out be be log s ref s log s ref s log ref = ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 12 ln ln ln ln ln ? ? ? ? ? = ? ? ? ? ? ? () ? ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? ? ? kt q i i k i i see figure log ref log ref ln( ) log log ( ) 10 3 10 10 v kt q i i be c s = ? ? ? ? ? ? ? ? ? ? ? ? ln MAX4206 logiin cmvin v cc refiin v cc current correction v cc logv1 scale osadj logv2 v cc v cc refiset current mirror cmvout refvout refiout gnd v ee 0.5v 1.238v v ee v ee summing amplifier and temperature compensation figure 1. functional diagram
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range ______________________________________________________________________________________ 11 where: k = scale factor (v/decade) i log = the input current at logiin i ref = the reference current at refiin the MAX4206 uses internal temperature compensation to virtually eliminate the effects of the thermal voltage, (kt/q), on the amplifier? scale factor, maintaining a constant slope over temperature. definitions transfer function the ideal logarithmic amplifier transfer function is: adjust k (see the scale factor section) to increase the transfer-function slope as illustrated in figure 3. adjust i ref using refiset (see the adjusting the logarithmic intercept section) to shift the logarithmic intercept to the left or right as illustrated in figure 4. log conformity log conformity is the maximum deviation of the MAX4206? output from the best-fit straight line of the v logv1 versus log (i log /i ref ) curve. it is expressed as a percent of the full-scale output or an output voltage. referred-to-input and referred-to-output errors the log nature of the MAX4206 insures that any addi- tive error at logv1 corresponds to multiplicative error at the input, regardless of input level. total error total error, te, is defined as the deviation of the output voltage, v logv1 , from the ideal transfer function (see the ideal transfer function section): total error is a combination of the associated gain, input offset current, input bias current, output offset voltage, and transfer characteristic nonlinearity (log conformity) errors: where v lc and v osout are the log conformity and out- put offset voltages, respectively. output offset is defined as the offset occurring at the output of the MAX4206 when equal currents are presented to i log and i ref . because the MAX4206 is configured with a gain of k = 0.25v/decade, a 4 should multiply the (? lc ? osout ) term, if v lc and v osout were derived from this default configuration. vkk ii ii vv logv log bias ref bias lc osout 210 1 2 14 = ? ? ? ? ? ? ? ? () ? ? ? ? ? ? ? ? () log ? vvte logv ideal 1 = vk i i ideal log ref = ? ? ? ? ? ? log 10 logiin cmvin v cc refiin v cc v be1 v be2 v ee v ee i log i ref figure 2. simplified model of a logarithmic amplifier ideal transfer function with varying k MAX4206 fig03 current ratio (i log /i ref ) normalized output voltage (v) 10 0.1 -2 -3 -1 0 1 2 3 4 -4 0.001 1000 v out = k log (i log /i ref ) k = 1 k = 0.5 k = 0.25 figure 3. ideal transfer function with varying k
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 12 ______________________________________________________________________________________ i bias1 and i bias2 are currents on the order of 20pa, significantly smaller than i log and i ref , and can there- fore be eliminated: expanding this expression: the first term of this expression is the ideal component of v logv1 . the remainder of the expression is the total error, te: in the second term, one can generally remove the products relating to ? k, because ? k is generally much less than 1. hence, a good approximation for te is given by: as an example, consider the following situation: full-scale input = 5v i log = 100? i ref = 100na k = 1 ?% v/decade (note that the uncommitted ampli- fier is configured for a gain of 4) v lc = ?mv (obtained from the electrical character- istics table) v osout = ?mv (typ) t a = +25? substituting into the total error approximation, te ? (1v/decade)(0.05log 10 (100?/100na) ? (?mv ?mv) = ?0.15v ?(?mv)] as a worst case, one finds te ? ?78mv or ?.6% of full scale. when expressed as a voltage, te increases in proportion with an increase in gain as the contributing errors are defined at a specific gain. calibration using a look-up table eliminates the effects of gain and output offset errors, leaving conformity error as the only factor con- tributing to total error. for further accuracy, consider tem- perature monitoring as part of the calibration process. applications information input current range five decades of input current across a 10na to 1ma range are acceptable for i log and i ref . the effects of leakage currents increase as i log and i ref fall below 10na. bandwidth decreases at low i log values (see the frequency response and noise considerations section). as i log and i ref increase to 1ma or higher, transistors become less logarithmic in nature. the MAX4206 incorporates leakage current compensation and high-current correction circuits to compensate for these errors. frequency compensation the MAX4206? frequency response is a function of the input current magnitude and the selected compensation network at logiin and refiin. the compensation net- work comprised of c comp and r comp ensures stability over the specified range of input currents by introducing an additional pole/zero to the system. for the typical application, select c comp = 100pf and r comp = 100 ? . where high bandwidth at low current is required, c comp = 32pf and r comp = 330 ? are suitable compen- sation values. te k k i i vv log ref lc osout ? ? ? ? ? ? ? () ? ? ? ? ? ? ? ? ? log 10 4 te k k i i kkvv log ref lc osout ? ? ? ? ? ? ? () ?? log ( ) 10 41 vk i i kk i i kkvv logv log ref log ref lc osout 210 10 41 ? ? ? ? ? ? ? ? ? ? ? ? ? () log log ( ) ? ? vkk i i vv logv log ref lc osout 210 14 ? ? ? ? ? ? ? () ? ? ? ? ? ? ? ? () log ? ideal transfer function with varying i ref MAX4206 fig04 i log (a) output voltage (v) 100 1 10 100n 10n -1.0 -0.5 0 0.5 1.0 1.5 -1.5 1n 1m i ref = 100 a i ref = 1 a i ref = 10na figure 4. ideal transfer function with varying i ref
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range ______________________________________________________________________________________ 13 frequency response and noise considerations the MAX4206 bandwidth is proportional to the magni- tude of the i ref and i log currents, whereas the noise is inversely proportional to i ref and i log currents. common mode a common-mode input voltage, v cmvout , of 0.5v is available at cmvout and can be used to bias the log- ging and reference amplifier inputs by connecting cmvout to cmvin. an external voltage between 0.5v and 1v can be applied to cmvin to bias the logging and reference transistor collectors and to optimize the performance required for both single- and dual-supply operation. adjusting the logarithmic intercept adjust the logarithmic intercept by changing the refer- ence current, i ref . a resistor from refiset to gnd (see figures 5 and 6) adjusts the reference current, according to the following equation: where v refiset is 0.5v. select r set between 5k ? and 5m ? . refiout current range is 10na to 10? only. single-supply operation when operating from a single +2.7v to +11v supply, i log must be greater than i ref , resulting in a positive slope of the log output voltages, logv1 and logv2. bias the log and reference amplifiers by connecting cmvout to cmvin or connecting an external voltage reference between 0.5v and 1v to cmvin. for single- supply operation, connect v ee to gnd. output offset select r os and i os to adjust the output offset voltage (see figure 5). the magnitude of the offset voltage is given by: v os = r os ? i osadj scale factor the scale factor, k, is the slope of the logarithmic out- put. for the logv1 amplifier, k = 0.25v/decade. when operating in a single-supply configuration, adjust the overall scale factor for the MAX4206 using the uncom- mitted logv2 amplifier and the following equation, which refers to figure 5: select r1 between 1k ? and 100k ? , with an ideal value of 10k ? . the noninverting amplifier ensures that the overall scale factor is greater than or equal to 0.25v/decade for single-supply operation. design example desired: single-supply operation logarithmic intercept: 100na overall scale factor = 1v/decade because there is no offset current applied to the circuit (r os = 0 ? ), the reference current, i ref , equals the log intercept of 100?. therefore, select r 1 = 10k ? : dual-supply operation when operating from dual ?.7 to ?.5v supplies, it is not required that i log be greater than i ref . a positive output voltage results at logv1 when i log exceeds i ref . a negative output voltage results at logv1 when i log is less than i ref . bias the log and reference amplifiers by connecting cmvout to cmvin or con- nect an external 0.5v to 1v reference to cmvin. for dual-supply operation with cmvin < 0.5v, refer to the max4207 data sheet. output offset the uncommitted amplifier in the inverting configuration utilized by the MAX4206 facilitates large output-offset voltage adjustments when operated with dual supplies. the magnitude of the offset voltage is given by the fol- lowing equation: a resistive divider between refvout, osadj, and gnd can be used to adjust v osadj (see figure 6). vv r rr osadj refout = + ? ? ? ? ? ? 4 34 vv r r os osadj =+ ? ? ? ? ? ? 1 2 1 rk vv k 210 1 025 130 = ? ? ? ? ? ? ? = ?? / . r v na k set = = 05 10 100 500 . ? rr k 21 025 1 = ? ? ? ? ? ? ? . r v i set refiset ref = 10
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 14 ______________________________________________________________________________________ scale factor the scale factor, k, is the slope of the logarithmic output. for the logv1 amplifier, k = 0.25v/decade. when oper- ating from dual supplies, adjust the overall scale factor for the MAX4206 using the uncommitted logv2 amplifi- er and the following equation, which refers to figure 6: select r 2 between 1k ? and 100k ? . design example desired: dual-supply operation logarithmic intercept: 1? overall scale factor = 1v/decade select r 1 = 10k ? : measuring optical absorbance a photodiode provides a convenient means of measur- ing optical power, as diode current is proportional to the incident optical power. measure absolute optical power using a single photodiode connected at logiin, with the MAX4206? internal current reference driving refiin. alternatively, connect a photodiode to each of the MAX4206? logging inputs, logiin and refiin, to measure relative optical power (figure 7). in absorbance measurement instrumentation, a refer- ence light source is split into two paths. the unfiltered path is incident upon the photodiode of the reference channel, refiin. the other path passes through a sam- ple of interest, with the resulting filtered light incident on the photodiode of the second channel, logiin. the MAX4206 outputs provide voltages proportional to the log ratio of the two optical powers?n indicator of the optical absorbance of the sample. in wavelength-locking applications, often found in fiberoptic communication modules, two photodiode cur- rents provide a means of determining whether a given optical channel is tuned to the desired optical frequency. in this application, two bandpass optical filters with over- lapping ?kirts?precede each photodiode. with proper fil- ter selection, the MAX4206 output can vary monotonically (ideally linearly) with optical frequency. rk v decade k 210 1 025 40 = ? ? ? ? ? ? = ?? / . r v a k set = = 05 10 1 50 . ? rr k 21 025 = ? ? ? ? ? ? . MAX4206 v ee gnd refiin logiin i in cmvin refiout cmvout refiset scale logv2 osadj logv1 refvout v cc v cc r comp 100 ? c comp 100pf r set 500k ? r os 0 ? r1 10k ? r2 30k ? 0.1 f 0.1 f v out 0.1 f r comp 100 ? c comp 100pf figure 5. single-supply typical operating circuit MAX4206 v ee v ee gnd refiin refiout logiin i in refiset scale logv2 logv1 cmvin cmvout v cc v cc r comp 100 ? c comp 100pf r set 50k ? r1 10k ? r2 40k ? 0.1 f 0.1 f 0.1 f v out r comp 100 ? c comp 100pf osadj refvout r4 r3 figure 6. dual-supply typical operating circuit
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range ______________________________________________________________________________________ 15 photodiode current monitoring figure 8 shows the MAX4206 in a single-supply, optical- power measurement circuit, common in fiberoptic applications. the max4007 current monitor converts the sensed apd current to an output current that drives the MAX4206 logiin input (apd current is scaled by 0.1). the max4007 also buffers the high-voltage apd voltages from the lower MAX4206 voltages. the MAX4206? internal current reference sources 10na (r set = 5m ? ) to the refiin input. this configuration sets the logarithmic intercept to 10na, corresponding to an apd current of 100na. the unity-gain configuration of the output buffer maintains the 0.25v/decade gain present at the logv1 output. capacitive loads the MAX4206 drives capacitive loads of up to 50pf. reactive loads decrease phase margin and can pro- duce excessive ringing and oscillation. use an isolation resistor in series with logv1 or logv2 to reduce the effect of large capacitive loads. recall that the combi- nation of the capacitive load and the small isolation resistor limits ac performance. power dissipation the logv1 and logv2 amplifiers are capable of sourcing or sinking in excess of 30ma. ensure that the continuous power dissipation rating for the MAX4206 is not exceeded. tqfn package the 16-lead thin qfn package has an exposed paddle that provides a heat-removal path, as well as excellent electrical grounding to the pc board. the MAX4206? exposed pad is internally connected to v ee , and can either be connected to the pc board v ee plane or left unconnected. ensure that only v ee traces are routed under the exposed paddle. layout and bypassing bypass v cc and v ee to gnd with ceramic 0.1? capacitors. place the capacitors as close to the device as possible. bypass refvout and/or cmvout to gnd with a 0.1? ceramic capacitor for increased noise immunity and a clean reference current. for low- current operation, it is recommended to use metal guard rings around logiin, refiin, and refiset. connect this guard ring to cmvout. evaluation kit an evaluation kit is available for the MAX4206. the kit is flexible and can be configured for either single-supply or dual-supply operation. the scale factor and reference current are selectable. refer to the MAX4206 evaluation kit data sheet for more information. chip information transistor count: 754 process: bicmos MAX4206 v ee gnd 0.1 f 0.1 f 0.1 f refiin logiin v cc cmvin refiout cmvout refiset v cc r 1 r 3 r 2 r 4 v cc scale logv1 logv2 osadj refvout 100pf 100 ? 100 ? 100pf figure 7. measuring optical absorbance
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range 16 ______________________________________________________________________________________ v ee gnd refvout cmvin refiout cmvout refiset v cc scale logv2 osadj logv1 refiin fiber cable apd +2.7v to +76v 2.2 h 2.2 f 0.22 f bias ref clamp out tia gnd to limiting amplifier high-speed data path 0.1 f 100pf v cc 5m ? 100pf 100 ? 100 ? output photodiode bias 0.1 f i apd /10 i apd 0.1 f MAX4206 max4007 figure 8. logarithmic current-sensing amplifier with sourcing input
MAX4206 precision transimpedance logarithmic amplifier with over 5 decades of dynamic range maxim cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in a maxim product. no circu it patent licenses are implied. maxim reserves the right to change the circuitry and specifications without notice at any time. maxim integrated products, 120 san gabriel drive, sunnyvale, ca 94086 408-737-7600 ____________________ 17 2003 maxim integrated products printed usa is a registered trademark of maxim integrated products. package information (the package drawing(s) in this data sheet may not reflect the most current specifications. for the latest package outline info rmation, go to www.maxim-ic.com/packages .) 24l qfn thin.eps b 1 2 21-0139 package outline 12,16,20,24l qfn thin, 4x4x0.8 mm b 2 2 21-0139 package outline 12,16,20,24l qfn thin, 4x4x0.8 mm

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