Patent Publication Number: US-11025215-B2

Title: High input impedance, high dynamic range, common-mode-interferer tolerant sensing front-end for neuromodulation systems

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with government support under Grant No. DARPA-BAA-14-08, awarded by the U.S. Department of Defense, Defense Advanced Research Projects Agency. They government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention generally relates to amplifiers and more specifically to systems and methods for increasing input impedance, increasing tolerance to differential and common-mode interference, and ripple reduction in chopped bio-signal amplifiers. 
     CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a national stage of PCT Patent Application No. PCT/US2017/065039, entitled “A High Input Impedance, High Dynamic Range, Common-Mode-Interferer Tolerant Sensing Front-End For Neuromodulation Systems” to Chandrakumar et al., filed Dec. 7, 2017, which claims priority to U.S. Provisional Application No. 62/431,420, entitled “High Input Impedance, High Dynamic Range, Common-Mode-Interferer Tolerant Sensing Front-End for Neuromodulation Systems” to Chandrakumar et al., filed Dec. 7, 2016, the disclosures of which are incorporated by reference herein in their entirety. 
     BACKGROUND 
     There has been great interest in the neuroscience community in decoding the functioning of the brain. Among the various methods used, analysis of the recordings of the electrical activity of neurons has been among the most important tools available. These recordings can be indispensable for understanding and diagnosing neurological disorders like epileptic seizures, in the creation of brain-machine interfaces, and for neuro-prosthetic technologies to aid paralyzed patients. Further, modern neuroscience is attempting to “close the loop” with the brain, by stimulating specific areas using current pulses, and recording neuronal responses to learn and adapt the stimulation patterns. For example, it has been demonstrated in a limited number of patients that stimulating certain regions of the entorhinal cortex of the brain could improve memory function. 
     Typically, extracellular recordings of neural signals occupy a frequency band from 1 Hz to about 5 kHz, and have relatively small amplitudes, ranging from 1 mV p  for Local Field Potentials (LFPs) to 100 μV p  for Action Potentials (APs). Due to their small amplitudes, neural signals are often amplified before digitization. Where the peak input-signal amplitudes are on the order of 1 mV, the input-referred noise of an amplifier should be less than 4 μV rms  for 8-bit resolution. Thus, low-noise bio-signal amplifiers could be utilized in various signal recording systems including (but not limited to) recording neural signals. 
     SUMMARY OF THE INVENTION 
     Common-mode-interferer tolerant sensing front-ends for neuromodulation systems in accordance with embodiments of the invention are discloses. In one embodiment, a chopper amplifier includes: a pair of inputs V in, CM  configured to receive a differential input signal and a common-mode (CM) signal; an input capacitor C in  connected in series with each of the pair of inputs V in, CM  having capacitance C in ; an operational amplifier g m ; and a common-mode cancellation (CMC) path to attenuate common-mode (CM) swings at V in, CM,  including: an operational amplifier g ma  with a gain A cm  and capacitors C a  and C b  configured to sense and amplify an input CM signal; C cm  capacitors configured to subtract the amplified CM signal from the input signal V in, CM  received on each of the pair of inputs. 
     In a further embodiment, the C cm  capacitors have capacitances that are the ratio of the capacitance of the input capacitors C in  and the gain A cm  of the operational amplifier. 
     In another embodiment, a gain in the CMC path is set by the capacitor ratio A cm =2 C a /C b . 
     In a still further embodiment, a C cm  capacitor is sized to be C in /A cm . 
     In still another embodiment, capacitor C in  and C cm  are matching. 
     In a yet further embodiment, capacitor C cm  is sized smaller than capacitor C in  to minimize increase in input-referred noise. 
     In still another embodiment again, the chopper amplifier further includes power supply circuitry configured to integrate a charge-pump on-chip to generate a local voltage supply for the operational amplifier g ma  in the CMC path from the available voltage supply. 
     In a still further embodiment again, bandwidth of the CMC path is greater than the bandwidth of the CM artifacts. 
     In a yet further embodiment again, the requirements of g ma  are: 
     
       
         
           
             
               
                 
                   g 
                   ma 
                 
                 ⁡ 
                 
                   ( 
                   
                     
                       C 
                       b 
                     
                     
                       
                         C 
                         b 
                       
                       + 
                       
                         2 
                         ⁢ 
                         
                           C 
                           a 
                         
                       
                     
                   
                   ) 
                 
               
               ⁢ 
               
                 1 
                 
                   2 
                   ⁢ 
                   
                     π 
                     ⁡ 
                     
                       ( 
                       
                         
                           C 
                           b 
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             C 
                             cm 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             &gt; 
             
               30 
               ⁢ 
               
                   
               
               ⁢ 
               kHz 
             
           
         
       
     
     In a yet further additional embodiment, there is no chopping at an output of the CMC path such that the CM-to-DM single at the CMC output remains at baseband as compared to the up-modulated differential input signal. 
     In still another embodiment, the chopper amplifier further includes at least one feedback loop including a multi-rate duty-cycled resistor (MDCR), wherein the MDCR comprises a first anti-alias filter (AAF) comprising a duty-cycled resistor (DCR) formed by R 1  switching at f 1 , and a capacitor C 1  followed by a second low-pass filter formed by a DCR R 2  switching at f 2 , and a capacitor C 2 , wherein the AAF allows for a significantly reduced switching frequency f 2 , as the AAF reduces the bandwidth of the signal flowing into the second low-pass filter. 
     In yet another embodiment again, a lower limit on the switching frequency f 2  is determined by the bandwidth f aaf  of the AAF and the required attenuation of the aliased components. 
     In still another embodiment, the chopper amplifier further includes an auxiliary path comprising two storage capacitors with capacitance C aux  and switching circuitry configured using offset modulation to pre-charge the input capacitors C in  during a pre-charging phase. 
     In a further additional embodiment, the chopper amplifier includes passive mixers M 1,2  in the auxiliary path, where a frequency of a ripple at electrodes is equal to the clock frequency F aux  used in the mixers M 1,2 . 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1 a    is a schematic diagram illustrating a response of a conventional chopper amplifier to common mode inputs. 
         FIG. 1 b    illustrates an equivalent circuit of a low-pass filter using a duty-cycled resistor (DCR) in accordance with an embodiment of the invention. 
         FIG. 1 c    illustrates a chopper amplifier with a common-mode cancellation (CMC) path in accordance with an embodiment of the invention. 
         FIG. 1 d    illustrates a multi-rate duty-cycled resistor (MDCR) to realize large resistance while overcoming a limitation due to parasitic capacitance in accordance with an embodiment of the invention. 
         FIG. 1 e    illustrates a chopper amplifier with capacitive feedback and a servo-loop in accordance with an embodiment of the invention. 
         FIG. 1 f    illustrates an equivalent common-mode circuit for a chopper amplifier for common mode signals in accordance with an embodiment of the invention. 
         FIG. 1 g    plots a transfer function from the common mode input at an electrode to an operational amplifier input in accordance with an embodiment of the invention. 
         FIG. 1 h    illustrates a current-reuse operational amplifier in accordance with an embodiment of the invention. 
         FIG. 1 i    illustrates a low-bandwidth integrator using a convention DCR in accordance with an embodiment of the invention. 
         FIG. 1 j    illustrates a schematic of an operational amplifier used to realize g ma  in accordance with an embodiment of the invention. 
         FIG. 1 k    illustrates an equivalent circuit of a composite low-pass filter in accordance with an embodiment of the invention. 
         FIG. 1 l    illustrates a low-bandwidth integrator using an MDCR in accordance with an embodiment of the invention. 
         FIG. 1 m    illustrates a chopper amplifier with capacitive feedback and a servo-loop. 
         FIG. 2 a    illustrates a transfer function in accordance with an embodiment of the invention. 
         FIG. 2 b    illustrates implementation of auxiliary-buffer assistance using storage caps in accordance with an embodiment of the invention. 
         FIG. 2 c    illustrates a half-circuit of an auxiliary path to analyze positive feedback in accordance with an embodiment of the invention. 
         FIG. 2 d    illustrates an equivalent circuit using switched-cap approximation in accordance with an embodiment of the invention. 
         FIG. 2 e    illustrates setting errors in a precharge phase leading in accordance with an embodiment of the invention. 
         FIG. 3 a    illustrates a complete implementation of a front-end chopper amplifier in accordance with an embodiment of the invention. 
         FIG. 3 b    illustrates schematics for operational amplifier g m1  and operational amplifier g m2  in accordance with an embodiment of the invention. 
         FIG. 4 a    illustrates a measured signal transfer function of a fabricated chopper amplifier, with programmable high-pass corner frequency in accordance with an embodiment of the invention. 
         FIG. 4 b    illustrates measured input-referred noise of a chopper amplifier in accordance with an embodiment of the invention. 
         FIG. 4 c    illustrates measured input impedance of a chopper amplifier using different impedance boost techniques in accordance with an embodiment of the invention. 
         FIG. 5 a    illustrates measured harmonic distortion of a chopper amplifier in accordance with an embodiment of the invention. 
         FIG. 5 b    illustrates response of a front-end to two-tone tests with a large CM interferer, showing the severity of distortion (without CMC), and the efficacy of the CMC path in reducing distortion with a high-frequency interferer. 
         FIG. 5 c    illustrates response of a front-end to two-tone tests with a large CM interferer, showing the severity of distortion (without CMC), and the efficacy of the CMC path in reducing distortion with a low-frequency interferer. 
         FIG. 6  illustrates a comparison an embodiment of the invention with the current state-of-the-art. 
         FIG. 7 a    illustrates a micrograph of a fabricated prototype showing eight chopper amplifiers implemented in 40-nm CMOS in accordance with an embodiment of the invention. 
         FIG. 7 b    illustrates a test setup for characterizing a fabricated chopper amplifier in accordance with an embodiment of the invention. 
         FIG. 8  illustrates in vitro measurements using pre-recorded human neural recordings (no stimulation). 
         FIG. 9 a    illustrates large offsets observed at an electrode when aux-path chopping is disabled in accordance with an embodiment of the invention. 
         FIG. 9 b    illustrates measured electrode input when aux-path chopping was enabled in accordance with an embodiment of the invention. 
         FIG. 9 c    illustrates measured input-referred noise showing reduced aux-buffer flicker noise when auxiliary-chopping is enabled in accordance with an embodiment of the invention. 
         FIG. 10 a    illustrates an input arm of the chopper amplifier, consisting of capacitors C in  and a passive mixer in accordance with an embodiment of the invention. 
         FIG. 10 b    illustrates a charge provided by an electrode during chopping in accordance with an embodiment of the invention. 
         FIG. 10 c    illustrates an auxiliary path technique in accordance with an embodiment of the invention. 
         FIG. 11  illustrates an auxiliary-path chopping using mixers M 1,2  to mitigate the effect of positive feedback in accordance with an embodiment of the invention. 
         FIG. 12  illustrates common-mode rejection ratio (CMRR) and power supply rejection ration (PSRR) measurements of a complete front-end chopper amplifier in accordance with an embodiment of the invention. 
         FIG. 13  illustrates a measurement setup in accordance with an embodiment of the invention. 
         FIG. 14  illustrates stimulation waveforms used for in vitro measurements in accordance with an embodiment of the invention. 
         FIG. 15 a    illustrates measured waveforms when differential stimulation is enabled without injecting pre-recorded neural signals; recording site waveforms in accordance with an embodiment of the invention. 
         FIG. 15 b    illustrates measured waveforms when differential stimulation is enabled without injecting pre-recorded neural signals; differential signal at recording site in accordance with an embodiment of the invention. 
         FIG. 15 c    illustrates measured waveforms when differential stimulation is enabled without injecting pre-recorded neural signals; measured output using CCIA (gain normalized to unity) in accordance with an embodiment of the invention. 
         FIG. 16  illustrates measured output (LP filtered up to 50 Hz) of CCIA during stimulation; A 25-Hz sinusoid was injected to represent a neural signal in accordance with an embodiment of the invention. 
         FIG. 17 a    illustrates measured waveforms (HP filtered from 800 Hz) during stimulation; recording site in accordance with an embodiment of the invention. 
         FIG. 17 b    illustrates measured waveforms (HP filtered from 800 Hz) during stimulation; CCIA output, a 1-kHz sinusoid was injected to represent a neural signal in accordance with an embodiment of the invention. 
         FIG. 18 a    illustrates measured waveforms (LP filtered up to 50 Hz) during stimulation; recoding site in accordance with an embodiment of the invention. 
         FIG. 18 b    illustrates measured waveforms (LP filtered up to 50 Hz) during stimulation; CCIA output, pre-recorded human neural recording were injected to emulate the neural signal in accordance with an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     Turning now to the drawings, high dynamic range, common-mode-interferer tolerant sensing front-ends for neuromodulation systems in accordance with various embodiments of the invention are illustrated. In many embodiments, the neuromodulation system uses a feed-forward common-mode cancellation (CMC) path to attenuate common-mode (CM) artifacts appearing at a voltage input, thus allowing for the simultaneous recording of neural data and stimulation of neurons. In many embodiments of the invention, the feed-forward CMC path is utilized to attenuate the common-mode swings at the input of the operational amplifier, V in,CM , which can restore the linear operation of the front-end for differential signals. 
     Since the signals of interest may occupy frequencies as low as 1 Hz, a high-pass filter may be necessary with a corner frequency less than 1 Hz. Such low corner frequencies can be difficult to implement as they usually require very-large resistors and capacitors, making it prohibitively area expensive. Accordingly, many embodiments of the invention provide a Multi-rate Duty-Cycled Resistor (MDCR) to implement high-pass filters with low corner frequencies. 
     Accordingly, in several embodiments, the neuromodulation system utilizes an anti-alias filter (AAF) that includes a duty-cycles resistor (DCR) switching at a first frequency f 1 , followed by a DCR switching at a second frequency f 2 . The AAF allows for a significantly reduced second frequency f 2  that enables the multi-rate DCR to increase the maximum realizable resistance, which is dependent upon the frequency ratio f 1 /f 2 . 
     In several embodiments, the neuromodulation system introduces chopping in the auxiliary path in order to address a feedback problem in the auxiliary path. In particular, the auxiliary-path used in the prior art charges the input capacitor C in  at the beginning of every chopping phase using aux-buffers, reducing the charge provided by the input to zero, thus boosting the input impedance Z in  of the chopper amplifier. 
     In several embodiments, storage capacitors assist the aux-buffers at the beginning of the pre-charge phase by charge-sharing with C in , and are disconnected for the remainder of the pre-charge phase. Hence, the input caps C in  may be accurately charged to V in  by the end of the pre-charge phase. Thus the settling error in the pre-charge phase may be reduced, leading to higher input impedance without increasing power consumption. 
     Systems and methods for implementing high dynamic range sensing front-ends for neuromodulation systems in accordance with various embodiments of the invention are discussed further below. 
     Bio-Signal Front-Ends 
     A neural signal recording system typically calls for a system that is small, fully implantable, consumes very low power while processing several channels, and can wirelessly transmit data to terminals such as (but not limited) to servers and/or a host computer. In addition, neuroscientists also seek the capability of recording neural data while simultaneously stimulating neurons. To preserve patient safety and compliance with FDA regulations, such systems face a unique set of design challenges. 
     Closed-loop neuromodulation with simultaneous stimulation and sensing is desired to administer therapy in patients suffering from drug-resistant neurological ailments. However, stimulation can generate large artifacts at recording sites, which can saturate traditional front-end systems used to record neural data. The common-mode (CM) artifact can be ˜500 mV, and the differential-mode (DM) artifact can be 50-100 mV. 
     In many embodiments, a neuromodulation system is utilized that includes a neural recording chopper amplifier that can tolerate 80 mV pp  DM and 650 mV pp  CM artifacts in a signal band of 1 Hz-5 kHz. In several embodiments, a linearity of 80 dB is provided to enable digitization of a 2 mV pp  neural signal to 8 bits accompanied by an 80 mV pp  DM artifact. In many embodiments, the neural recording front-ends also function within a power budget of 3-5 μW/ch, an input-referred noise range of 4-8 μV rms , and a DC input impedance range of Z in &gt;1 GΩ and have a high-pass cutoff of 1 Hz. Systems and methods for implementing high dynamic-range neural recording chopper amplifiers in accordance with various embodiments of the invention are discussed further below. 
     High Dynamic-Range Neural Recording Chopper Amplifier: 
     The susceptibility of conventional recording front-ends to common-mode interference can be appreciated by way of comparison of amplifiers implemented in accordance with various embodiments of the invention and typical chopper amplifiers, such as the conventional chopper amplifier illustrated in  FIG. 1 a   . As illustrated in  FIG. 1 a    the amplifier  1   a   100  can be implemented using capacitive feedback in the “inverting” topology. Chopping can be implemented using passive mixers  1   a   105  at the input and feedback arms of the capacitive feedback network. The demodulation mixer  1   a   110  is placed within the operational amplifier g m    1   a   115 , usually in-between the 1 st  and 2 nd  stages of a 2-stage operational amplifier. The signals appearing at the electrode inputs consist of a differential signal with amplitudes &lt;100 mV, and a common-mode signal with amplitudes up to 500 mV. Passive mixers may allow the common-mode signal to pass unaltered. The operational amplifier  1   a   115  used in the chopper amplifier  1   a   100  can be usually designed to respond only to differential signals while having high common-mode rejection. This can be accomplished by using a differential-pair with a high-impedance tail current source. Also, common-mode feedback (CMFB) loops can be used to set the bias voltages at the outputs of g m . Hence, for common-mode signals, the CMFB loops create low-impedance connections to ac-ground at the output of g m . To set the common-mode DC bias at the input of the operational amplifier  1   a   115 , large resistors (R B  in  FIG. 1 a   ) can be used. The equivalent common-mode circuit for a chopper amplifier in accordance with an embodiment of the invention is illustrated in  FIG. 1 f   . The transfer function from the common-mode input at the electrode E CM  to the operational amplifier input V in,CM  is found to be 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       
                         in 
                         , 
                         CM 
                       
                     
                     
                       E 
                       CM 
                     
                   
                   = 
                   
                     
                       ω 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         C 
                         in 
                       
                       ⁢ 
                       
                         R 
                         B 
                       
                     
                     
                       1 
                       + 
                       
                         
                           ω 
                           ⁡ 
                           
                             ( 
                             
                               
                                 C 
                                 in 
                               
                               + 
                               
                                 C 
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                             ) 
                           
                         
                         ⁢ 
                         
                           R 
                           B 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     The above transfer function is plotted in  FIG. 1 g   . It is evident that V in,CM /E CM  is a 1 st  order high-pass filter, with the corner frequency set by the capacitance C in +C f  and the resistor R B . To ensure proper functioning of the chopper amplifier, this corner frequency can be usually set to &lt;10 Hz. Hence, common-mode signals beyond 10 Hz pass unattenuated to the input of the operational amplifier, which could cause the differential response of a power-optimized amplifier to show significant departures from the expected response. Consider the current-reuse differential pair illustrated in  FIG. 1 h   , which is the most common topology (due to its favorable power-noise trade-off) used for the 1 st  stage of the operational amplifier g m . To ensure sufficient headroom for the tail current sources, the gate bias V in,CM  of the input transistors M 1-4  may need to be within the following range: V 0v6 +V GS3,4 &lt;V in,CM &lt;V DD −V ov5 −V GS1,2 , where V DD  is the supply voltage, V ov5,6  are the overdrive voltages of the tail current sources and V GS1-4  are the required gate-source voltages for transistors M 1-4  to carry a bias current of I B /2. Assuming V DD =1.2V, V ov5,6 =0.1V and V GS1-4 =0.45V (typical values), the range for V in,CM  is 0.55V&lt;V in,CM &lt;0.65V. Hence the input common-mode range may be limited to less than 100 mV. This range can be significantly lower than the common-mode swings (500 mV) that are expected at the electrodes. To estimate the distortion caused by common-mode artifacts, the chopper amplifier in  FIG. 1 e    was simulated with a differential input of 80 mV pp  at 1 kHz, along with a common-mode interferer of 500 mV pp  amplitude at 900 Hz. The total harmonic distortion (THD) degraded from −74 dB to −43 dB when the common-mode interferer was enabled, thus exposing the severity of the problem. 
     A solution to the CM-interferer problem can be to use an operational amplifier with a large input common-mode range (ICMR), like a folded-cascode topology. Although the folded-cascode may consume more than twice the power as compared to the current-reuse operational amplifier (for the same noise), immunity to CM interference could be worth the power penalty. However, it must be noted that these CM interferers are not “slow” signals. Since the CM interferers have the same BW as the differential signals of interest, large CM swings at the input of operational amplifiers could lead to distortion. This can be particularly significant when the operational amplifier is designed for low-noise and low-power operation, i.e. the input devices (and possibly others) are biased in weak inversion, where they are most nonlinear. To verify this, a simulation was performed on a folded-cascode operational amplifier with an n-MOS input diff-pair, from a 1.2V supply with an ICMR of 0.7V. The following set up scenario was applied: differential input of 40 mV pp  at 1 kHz, along with a common-mode interferer of 500 mV pp  amplitude at 900 Hz. Since the CM interferer (0.5V) is smaller than the ICMR (0.7V), the linearity of the front-end could be preserved in the presence of the CM interferer. However, the total harmonic distortion (THD) degraded from −78 dB to −62 dB when the CM interferer was enabled. Thus it is evident that a simple folded-cascode with its large ICMR is insufficient. 
     Accordingly, the presence of large common-mode swings at the operational amplifier input V in,CM  can lead to distorted outputs. In many embodiments of the invention, a feed-forward common-mode cancellation (CMC) path is utilized to attenuate the common-mode swings at V in,CM,  which can restore the linear operation of the front-end for differential signals. An example of a CMC path in accordance with an embodiment of the invention is illustrated in  FIG. 1 c   . The common-mode signal at the electrodes can be sensed and amplified by the operational amplifier g ma    1   c   105  and capacitors C a  and C b . This amplified common-mode signal may then be subtracted from V in,CM  through capacitors C cm . The gain in the CMC path can be set by the capacitor ratio A cm =2 C a /C b . If C cm  is sized to be C in /A cm , then the common-mode signals at the input of the operational amplifier V in,CM  can be ideally cancelled to zero. Any mismatches in the ratio of C in /C cm  may lead to residual common-mode swings at V in,CM . However, since g m  may be immune to small common-mode swings (&lt;20 mV), a cancellation accuracy of 2% may be sufficient. This can be achieved by matching the capacitors C in  and C cm . However, the presence of the capacitors C cm  may lead to an increase in the input-referred noise of the front-end, as shown by the following equation: 
     
       
         
           
             
               
                 
                   
                     v 
                     
                       n 
                       , 
                       in 
                     
                   
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                       v 
                       n 
                     
                     ⁡ 
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             
                               C 
                               in 
                             
                             + 
                             
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                   2 
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     Here, v n  is the input-referred noise of the operational amplifier g m    1   c   110 . To minimize the increase in the input-referred noise, C cm  can be sized smaller than C in  to provide a larger gain A cm  in the CMC path. However, increasing A cm  may result in larger signal swings at the output of g ma    1   c   105 , which may cause saturation due to limited headroom at the output of g ma . This may prevent the CMC path from cancelling the common-mode swings at V in,CM . To increase the headroom at the output of g ma    1   c   105 , many embodiments integrate a 50%-efficient charge-pump on-chip to generate a local 1.8V supply for g ma  from the available 1.2V supply. Thus, with the CMC gain A cm =2, common-mode signals as large as 650 mV pp  can be easily cancelled at V in,CM , while the noise contribution of g m  is kept low. To achieve accurate cancellation, the bandwidth of the CMC path may need to be well beyond the expected bandwidth of the common-mode artifacts. Since it is expected that common-mode artifacts occupy the entire neural signal band up to 5 kHz, the CMC-path bandwidth is set to 30 kHz. This sets the requirement of g ma  as follows: 
     
       
         
           
             
               
                 
                   
                     
                       
                         g 
                         ma 
                       
                       ⁡ 
                       
                         ( 
                         
                           
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                     30 
                     ⁢ 
                     
                         
                     
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                     kHz 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Hence, for C a =C b =1 pF and C cm =0.5 pF, g ma  should be larger than 1.13 μA/V. Although  FIG. 1 c    illustrates a particular common-mode cancellation paths to attenuate common-mode swings at V in,CM , any of a variety of CMC paths may be utilized as appropriate to the requirements of specific applications in accordance with embodiments of the invention. A schematic of an operational amplifier used to realize g ma  in accordance with an embodiment of the invention is illustrated in  FIG. 1 j   . A current of 120 nA can be sufficient to achieve the required g ma , which is a small fraction of the overall power budget. Hence a relatively low efficiency (50%) charge-pump design was chosen for simplicity and reducing design time, since the power overhead is negligible. 
     Although the CMC path attenuates common-mode swings at V in,cm , mismatches in C cm  could degrade CMRR. However, since C cm  is large (0.5 pF), good matching (&lt;0.1%) between C cm  can be achieved by using common-centroid layout techniques. Any residual mismatches in C cm  would indeed convert a common-mode signal at the electrode into a differential signal flowing out of the CMC path. However, note that there is no chopping at the output of the CMC path. Hence, the CM-to-DM signal at the CMC output remains at baseband, as compared to the up-modulated differential signal of the electrode. Thus, the CM-to-DM component remains separate (in frequency) from the desired differential signal, which ensures negligible impact to CMRR. 
     The neural signals at the electrodes (&lt;1 mV) may be accompanied by electrode offsets as large as 50 mV. Hence any amplification may need to be applied only to the neural signals while attenuating the offset to prevent saturation. Since the signals of interest occupy frequencies as low as 1 Hz, a high-pass filter may be necessary with a corner frequency less than 1 Hz. Such low corner frequencies can be difficult to implement as they usually require very-large resistors and capacitors, making it prohibitively area expensive. Conventional capacitive-feedback amplifiers have been reported before that use “pseudo-resistors” as large resistors to realize sub-Hz high-pass corners. However, pseudo-resistors are unreliable due to its nonlinearity and sensitivity to process and temperature variations. 
     In chopper amplifiers, a DC-Servo loop can be used to realize the required high-pass corner frequency. The DC servo-loop consists of a low-bandwidth integrator that is placed in a negative feedback loop around the chopper amplifier, as illustrated in  FIG. 1 m   . The high loop-gain of the servo-loop attenuates low-frequency signals at the output V out , thus realizing the required high-pass corner. For frequencies beyond the unity-gain bandwidth of the servo-loop, the servo-loop is effectively broken. Hence, since the signal-band of interest lies beyond the servo-loop unity-gain bandwidth, the output noise of the servo-loop in the signal band will be amplified by C 3 /C 2  and appear at V out , as illustrated in  FIG. 1   m.    
     However, to achieve a sub-Hz high-pass corner frequency, a very-low bandwidth integrator may be necessary in the servo-loop. Prior implementations have used duty-cycled resistors (DCR) to realize such low-bandwidth integrators as illustrated in for example  FIG. 1 i   . The DCR consists of a passive resistor R in series with a switch. When the switch is driven by a clock with a duty-cycle factor of D, the average resistance is amplified by 1/D. This amplified resistance can be used to realize the required low-bandwidth integrator for the servo-loop. The in-band noise contribution (when referred to the electrodes) of the DCR in the servo-loop can be reduced by realizing larger equivalent resistances R/D. Accordingly, the in-band noise of the DCR R B  ( FIG. 1 e   ) can be reduced by realizing larger equivalent resistances. However, the maximum resistance of the DCR may be limited by the parasitic capacitance that appears in-between the passive resistor R and the switch as illustrated in  FIG. 1 b   . This parasitic capacitance results in an equivalent switched-cap resistor R p  that appears in parallel across the amplified resistance R/D, thus limiting the maximum equivalent resistance to R p . The value of R p  is given by 1/(f 1 C p ), where C p  is the value of the parasitic capacitance and f 1  is the switching frequency of the DCR. As an example, for C p =5 fF and f 1 =25 kHz (both being typical values), R p  is set to 8 GΩ. To increase R p , either f 1  or C p  can be reduced. However, C p  may be limited by the substrate capacitance of the resistance R, while f 1  may need to be greater than twice the signal bandwidth to avoid aliasing. Thus it would seem that the maximum resistance is limited to 8 GΩ. Accordingly, many embodiments of the invention provide a Multi-rate Duty-Cycled Resistor (MDCR) to solve this problem. An example of an MDCR in accordance with an embodiment of the invention is illustrated in  FIG. 1 d   . The following is based on an assumption of needing to realize a 0.2 Hz low-pass filter. Since such a low corner frequency may require an exceptionally large resistance (much larger than R p  from  FIG. 1 b   ), many embodiments instead first realize a low-pass filter with a moderately low corner frequency of 10 Hz. This low-pass filter, termed the anti-alias filter (AAF)  1   d   105  in  FIG. 1 d   , can be realized by the DCR formed by R 1  switching at f 1 , and the capacitor C 1 . The AAF  1   d   105  can be followed by a second low-pass filter formed by the DCR R 2  switching at f 2 , and the capacitor C 2 . The AAF may allow for a significantly reduced switching frequency f 2 , as the AAF reduces the bandwidth of the signal flowing into the second low-pass filter. The lower limit on the switching frequency f 2  can be determined by the bandwidth f aaf  of the AAF and the required attenuation of the aliased components. For this work, it was chosen to have f 2 /f aaf  to be greater than 64, which provides sufficient attenuation to the aliased components. Hence, in the second low-pass filter, the limitation of the minimum required switching frequency was circumvented by using the AAF, thus increasing the maximum realizable resistance of the DCR (formed by R 2  switching at f 2 ) by a factor of f 1 /f 2 . Although  FIG. 1 d    illustrates a particular Multi-rate Duty-Cycled Resistor (MDCR) configuration, any of a variety of MDCR configurations may be utilized as appropriate to the requirements of specific applications in accordance with embodiments of the invention. An equivalent circuit of this composite low-pass filter in accordance with an embodiment of the invention is illustrated in  FIG. 1 k   . The ON duration of the switches T ON  is 5 ns, and f 1  was set to 23.44 kHz. This results in a duty-cycle factor D of 1/8530 for the DCR formed by R 1  switching at f 1 . R 1  and R 2  were set to 350 kΩ, which leads to the equivalent resistance R 1,eq =R 1 /D=3 GΩ. Thus, R 1,eq  along with C 1 =6 pF leads to an anti-alias corner frequency f aaf  of 10 Hz. In the second low-pass filter, f 2  is set to be f 1 /32=732.5 Hz. This leads to the equivalent resistance R 2,eq =(R 2 /D)*32=90 GΩ. Hence, R 2,eq  along with C 2 =12 pF leads to the required low-pass corner frequency of 0.15 Hz. Thus by using the MDCR, a 350 kΩ resistance has been amplified to 90 GΩ. 
     Though the above example is a passive low-pass filter, an MDCR can also be used as a large resistor to realize low-bandwidth integrators. An example of an MDCR used as a large resistor in accordance with an embodiment of the invention is illustrated in  FIG. 1 l   . The transfer function and noise analysis of the conventional DCR have already been discussed in H. Chandrakumar, D. Marković, “A High Dynamic-Range Neural Recording Chopper Amplifier for Simultaneous Neural Recording and Stimulation,” in IEEE Journal of Solid-State Circuits, vol. 52, no. 3, pp. 645-656, March 2017, the entirety of which is herein incorporated by reference, and the results directly translate to the MDCR. Hence, the noise contribution of the MDCR is nearly identical to the noise contributed by the equivalent amplified resistance. By using the MDCR, a much larger resistance can be realized than what was possible using the conventional DCR, leading to lower noise in the front-end. Also, the MDCR can be realized in a small chip area, and there&#39;s no penalty on linearity unlike the pseudo-resistor. 
     Since an MDCR can be equivalent to a cascade of two low-pass filters such as the two-pass filter illustrated in  FIG. 1 k   , it could cause instability when used in a feedback-loop since it introduces two poles. The servo-loop unity-gain bandwidth sets the high-pass corner f HP  of the signal transfer function as illustrated in  FIG. 1 m   . Let the servo-loop integrator have a unity-gain bandwidth of f ugb,dsl . Hence, from  FIG. 1 m   , f HP =f ugb,dsl (C 3 /C 2 ). To ensure stability, the AAF corner may need to be chosen to be much larger than f HP , discussed further below. 
     Auxiliary-Path for Boosting Input-Impedance: 
     The auxiliary-path to boost the input impedance Z in  of a chopper amplifier is discussed in H. Chandrakumar, D. Marković, “A High Dynamic-Range Neural Recording Chopper Amplifier for Simultaneous Neural Recording and Stimulation,” in IEEE Journal of Solid-State Circuits, vol. 52, no. 3, pp. 645-656, March 2017, the entirety of which is herein incorporated by reference. The input arm of the chopper amplifier, consisting of capacitors C in  and the passive mixer in accordance with an embodiment of the invention is illustrated  FIG. 10 a   . The charge provided by V el  may be limited to a narrow time window (Δt in  FIG. 10 b   ) at the beginning of every chopping phase. If an alternate reservoir of charge (as opposed to the electrodes) could provide the charge required by C in , then Z in  can be increased. An auxiliary path technique in accordance with an embodiment of the invention is illustrated in  FIG. 10 c   . An advantage of this technique is that the auxiliary path can be used simultaneously with the servo-loop, unlike the positive-feedback loop which is rendered inoperative by the servo-loop at low frequencies. The auxiliary path may also be immune to parasitic capacitance, which limits the maximum impedance that can be achieved by the positive feedback loop. However, this technique can have two limitations. First, it provided insufficient boost to Z in , as described by H. Chandrakumar, D. Marković, “A High Dynamic-Range Neural Recording Chopper Amplifier for Simultaneous Neural Recording and Stimulation,” in IEEE Journal of Solid-State Circuits, vol. 52, no. 3, pp. 645-656, March 2017 which reported a boosted Z in  of 300 MΩ while many embodiment of the invention may need Z in  larger than 1 GΩ. The second limitation is that this technique forms a positive feedback loop around the auxiliary path since the electrode is not an ideal voltage source. It can be shown that this positive feedback may cause the DC offset and flicker noise of the auxiliary-path buffers to be amplified and appear at the electrodes. Thus, the amplified offset could cause saturation, and the amplified flicker noise may degrade the performance of the front-end since it adds directly at the input of the front-end. The positive feedback in the auxiliary path is analyzed below. The differential half-circuit of the auxiliary path along with the input arm of the chopper amplifier in accordance with an embodiment of the invention is illustrated in  FIG. 2 c   . The offset and flicker noise of the buffer can be modeled as a voltage source V off , while the electrode impedance can be modeled by the impedance R el ∥C el . For simplicity, it is assumed that R el  is infinite. In the pre-charge phase, the buffer charges the capacitor C in  to V el +V off . At the end of the pre-charge phase, C in  is re-connected back to V el , and the electrode voltage is given by 
     
       
         
           
             
               
                 
                   
                     
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     From the above equation, it is evident that the transfer function from V off  to V el  is identical to that of an ideal first-order integrator. Hence for a non-zero DC value of V off , V el  will go to infinity. To get a more accurate description of the positive feedback, the effect of a finite R el  is considered next. From  FIG. 2 c   , the capacitance C in  can be periodically switched between the buffer output and the electrode. Hence, this switching capacitance forms an equivalent resistance, as illustrated in  FIG. 2 d   , with a value of R a =T c /(2 C in ), where T c  is the chopping period. Thus the buffer output V a =V el +V off , and V el =V a ·Z el /(Z el +R a ). Using these 2 equations, the transfer function V el /V off  is determined to be 
     
       
         
           
             
               
                 
                   
                     
                       
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     The above transfer function is shown in  FIG. 2 a   . The DC gain is given by 2 R el C in /T c . Assuming R el =200 MΩ, C in =1 pF, C el =1 nF and T c =40 μs (all typical values), the DC gain from V off  to V el  is 10. Hence, a 5 mV auxiliary-buffer offset is amplified to a 50 mV DC voltage by the positive feedback in the auxiliary path, and this voltage appears at the electrodes. Also, from the transfer function in  FIG. 2 a   , it reveals that low-frequency components of V off , for example the flicker noise of the auxiliary-buffers, may also be amplified and appear at the electrodes, thus degrading the low-frequency noise performance of the front-end. 
     A solution to this problem can be determined by taking a closer look at the transfer function in  FIG. 2 a   . The unity-gain bandwidth (UGB) of this transfer function is given by αf c /π, where a is the ratio given by C in /C el . For the above-chosen typical values of C in  and C el , the UGB of V el /V off  is approximately given by f c /3000. Thus, if V off  can be up-modulated to a frequency that is much larger than f c /3000, then V off  will appear as tiny ripples at the electrode instead of a large DC voltage. This is realized by introducing passive mixers M 1,2  in the auxiliary path as illustrated in  FIG. 11 . The frequency of the ripple at the electrodes will be equal to the clock frequency f aux  used in the mixers M 1,2 . To ensure that these ripples remain outside the frequency band of interest, f aux  should be larger than 5 kHz. The amplitude of the ripples can be determined to be 
     
       
         
           
             
               
                 
                   
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     Although introducing mixers M 1,2  can mitigate the amplification of V off , it will reduce the input impedance of the front-end. This is because the gate capacitance of the auxiliary-path buffers along with the mixer M 1  will appear as a switched-cap resistance Z in,aux  at the input of the front-end. Hence the input impedance of the front-end is now given by Z in,boost ∥Z in,aux , where Z in,boost  is the boosted input impedance achieved by the auxiliary path, as illustrated in  FIG. 11 . To achieve the required 1 GΩ DC input impedance, Z in,aux  may need to be significantly larger than 1 GΩ. Z in,aux  is given by 1/(2 C auxbuf f aux ), where C auxbuf  is the gate capacitance of each auxiliary-path buffer. Since f aux  has a minimum value of 5 kHz, C auxbuf  may need to be reduced to achieve the required value of Z in,aux . However, reducing C auxbuf  can be achieved by reducing the area of the input transistors of the auxiliary buffers, which may lead to a larger value of V off  due to increased mismatch. This may cause larger ripples at the electrode (from equation 6) which is undesirable. Hence while sizing the input transistors of the auxiliary-buffers, the trade-offs for the input impedance and the ripple amplitudes at the electrode may need to be considered together. V off  is proportional to 1/√C auxbuf  and the ripple amplitude can be proportional to V off /f aux . Thus, accounting for all trade-offs, the ripple amplitude V ripple  can be proportional to Z in,aux ·√C auxbuf . Hence for a given Z in,aux , C auxbuf  may need to be minimized to reduce ripple amplitudes at the electrodes. This corresponds to using minimum-sized devices for the input transistors of the auxiliary-buffers. C auxbuf  may ultimately be limited by routing capacitance. Hence a practical solution may be to reduce the gate capacitance of the input devices of the auxiliary buffers to match the routing capacitance between the gate and the mixer M 1 . The mixers M 1,2  can be driven with a clock frequency of f c /4, where f c =23.44 kHz is the chopping frequency of the chopper amplifier. The input transistors of the auxiliary buffers can be sized such that C auxbuf  (including routing capacitance) is about 15 fF, which sets Z in,aux  to be about 6 GΩ. Hence Z in,aux  is sufficiently large to achieve the required input impedance of the front-end. 
     As discussed before, a limitation of the auxiliary path was the limited boost to Z in . This limitation was due to the limited bandwidth of the auxiliary-buffers, which caused a non-zero settling error in the pre-charge phase. The finite gain of an operational amplifier used in the auxiliary-buffers may also lead to a non-zero settling error in the pre-charge phase. This is illustrated in  FIG. 2 e    (with reference to  FIG. 10 c   ). The input-impedance at DC was derived in H. Chandrakumar, D. Marković, “A High Dynamic-Range Neural Recording Chopper Amplifier for Simultaneous Neural Recording and Stimulation,” in IEEE Journal of Solid-State Circuits, vol. 52, no. 3, pp. 645-656, March 2017, and is restated here for completeness: 
     
       
         
           
             
               
                 
                   
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     In the above equation, τ −1  rad/sec is the bandwidth of the auxiliary buffer, and A DC  is the open-loop DC gain of the buffer, which is usually around 40 dB. This implies that the maximum achievable boost to Z in  may be limited to a factor of 100. To ensure getting the most of this impedance boost, the settling error due to the finite bandwidth of the auxiliary-buffer may need to be minimized. This can be done by increasing the transconductance of the auxiliary-buffers, which would increase power consumption. An alternative is to use storage capacitors C aux , as illustrated in  FIG. 2 b   , to assist the auxiliary-buffers. At the beginning of the pre-charge phase (as shown in the timing diagram in  FIG. 2 b   ), C aux  is allowed to charge-share with C in . If C aux  is sized to be significantly larger than C in , then most of the pre-charging of C in  (labeled as ΔV assist  in  FIG. 2 e   ) is complete in this charge-sharing phase. Hence the auxiliary-buffers now may only need to complete the remainder of the pre-charging of C in . This may reduce the settling error in the pre-charge phase, leading to a larger Z in  without increasing power consumption. C aux  may be set to 8·Cin, and the DC current in the auxiliary-buffers may be 150 nA. This may be sufficient to provide an impedance boost by 2.5×, as described in detail below. From  FIG. 2 b   , when φ 1,2 =0, the auxiliary-buffer bias currents may be reduced to 25 nA to save power while ensuring that C aux  tracks V el  till the next pre-charge phase. 
     A chopper amplifier in accordance with an embodiment of the invention is illustrated in  FIG. 3 a   , and the schematics for g m1  and g m2  are shown in  FIG. 3 b   . In particular,  FIG. 3 a    illustrates a chopper amplifier for spike and local field potential (LFP) recording in accordance with an embodiment of the invention. In many embodiments, the chopping frequency f c  is 23.44 kHz. The mid-band gain may be set by C in /C f =20, and DC-blocking caps C r  may be used to avoid chopper ripple at V out . In several embodiments, the servo-loop uses multi-rate duty-cycled resistors with a 10 Hz anti-alias filter, T on =5 ns, f 1 =23.44 kHz and f 2 =732.5 Hz, which boosts a 350 kΩ poly-resistor to R int =90 GΩ. Since C int =12 pF, the servo-loop integrator BW is 0.15 Hz. In many embodiments, the chopper amplifier is fabricated in a 40 nm CMOS technology. Although any of a variety of semiconductor processes can be utilized to implement a chopper amplifier as appropriate to the requirements of a given application in accordance with various embodiments of the invention. Although  FIG. 3 a    illustrates a particular chopper amplifier configuration, any of a variety of processes and configurations may be utilized for chopper amplifiers as appropriate to the requirements of specific applications in accordance with certain embodiments of the invention. 
     In several embodiments, an amplifier can be implemented in a 40-nm CMOS technology.  FIG. 7 a    and  FIG. 7 b    show a chip micrograph and the measurement setup with provisions to emulate the electrode impedance in accordance with an embodiment of the invention. The amplifier occupies an area of 0.069 mm 2 /ch and the total power consumed from a 1.2V supply is 2.8 μW. The transconductances g m1  and g m2  consume 1.2 and 0.25 μW respectively. The servo-loop, aux-path buffers and the CMC path consume 0.36, 0.2 and 0.3 μW respectively. Biasing and control-signal generation consumes 0.45 μW. 
     The measured signal transfer function is shown in  FIG. 4 a   . The mid-band gain can be 25.7 dB and the low-pass corner can be 5 kHz. The servo-loop unity-gain bandwidth sets the high-pass corner of the signal transfer function. From  FIG. 3 a   , it is evident that f HP =2 f ugb,dsl . The high-pass corner f HP  can be programmable from 0.12 Hz to 0.3 Hz by varying the duty-cycle factor in the MDCR. The AAF corner frequency in the MDCR can be chosen to be 10 Hz (Section IV-B). Hence, the pole associated with the AAF may be a non-dominant pole since it is far away from the unity-gain frequency f HP  of the servo-loop, and the phase margin of the servo-loop may be close to 90° ensuring stability. 
     The measured input impedance of the front-end is shown in  FIG. 4 c   . When the auxiliary path is disabled, Z in  may be 21 MΩ. When the auxiliary path is enabled, Z in  can be boosted to 600Ω, which can further increase to 1.6 GΩ when the auxiliary-buffer assistance is enabled. Hence Z in  can be boosted by a factor of 76.2, with the storage capacitors C aux  providing a 2.6× boost. 
     The linearity measurements of a chopper amplifier in accordance with an embodiment of the invention are shown in  FIG. 5 a   . For a differential input sinusoid of 40 mV p  (or 80 mV pp ) at 1 kHz with no common-mode interferer, the measured THD was −76 dB. To measure the front-end performance in the presence of common-mode interference, two-tone tests can be performed. Realistic stimulation artifacts have significant power at multiple harmonics of the stimulation frequency due to their pulse-like nature. Hence, immunity to common-mode interference may need to be measured for frequencies up to several harmonics of the stimulation frequency. Stimulation is usually performed at frequencies below 150 Hz. Hence, performance should be measured with CM interference up to 900 Hz. A two-tone test can be conducted as follows. The differential input to the front-end can consist of the sum of a 40 mV p  sinusoid at 900 Hz and a 1 mV p  sinusoid at 1 kHz. A common-mode interferer of 650 mV pp  can also be applied at 900 Hz. The 900 Hz tones represent the stimulation artifacts, while the 1 kHz tone represents the neural signal of interest.  FIG. 5 b    shows measured results of two-tone tests in accordance with an embodiment of the invention. When the CMC path is disabled, it illustrates significant distortion components at the output. The Signal-to-Interferer ratio (SIR) can be defined as the power of the desired signal (in this case, at 1 kHz) divided by the power of the harmonics created by distortion. The SIR can be only 7 dB when the CMC path is disabled. However, when the CMC path is enabled, there is significant suppression of the distortion components and the SIR improves to 38 dB. When the CM interferer is disabled, the SIR can be 44 dB. Hence for a CM interferer of 650 mV pp , the SIR degrades from 44 dB to 38 dB with the CMC enabled, a 6 dB drop which is assumed to be an acceptable degradation. Thus, in many embodiments, the front-end can tolerate CM interferers up to 650 mV pp . When the frequency of the stimulation tones is lowered to 110 Hz, as illustrated in  FIG. 5 c   , the SIR improves from 19.3 dB to 40.5 dB when the CMC path is enabled. These measurements show the efficacy of the CMC path in maintaining linearity in the presence of large CM interferers. The CMRR and PSRR can also be measured, and the results are shown in  FIG. 12 . The CMRR and PSRR are better than −78 dB and −76 dB respectively in the signal band (1 Hz-5 kHz). 
     The input-referred noise was measured to be 1.8 μV rms  in the LFP band (1 Hz-200 Hz), and 5.3 μV rms  in the AP band (200 Hz-5 kHz), as shown in  FIG. 4 b   . To show the benefits of chopping in the auxiliary path, the offset appearing at the electrode was measured. When chopping in the auxiliary path, as illustrated by mixers M 1,2  in  FIG. 11 , was disabled, large offsets were observed at the electrode, as illustrated in  FIG. 9 a   , and the worst-case offset was 45 mV. When the auxiliary-path chopping was enabled, the 45 mV offset reduced to zero and a 5.4 μV ripple was observed at 5.86 kHz, as illustrated in  FIG. 9 b   . This is expected from the discussions above. The input-referred noise in the 1 Hz-200 Hz band also reduced from 4.5 μV rms  to 1.8 μV rms  when the auxiliary-path chopping was enabled, as illustrated in  FIG. 9   c.    
     In-vitro measurements were performed using a front-end to record signals from electrodes dipped in phosphate-buffered saline (PBS).  FIG. 13  shows a measurement setup in accordance with an embodiment of the invention. A pair of electrodes (Stim 1  and Stim 2 ) can be used to deliver stimulation into the PBS solution, while another pair of electrodes (V in,p  and V in,n ) can be used as sensing electrodes connected to the front-end. A separate electrode can be used to inject neural signals into the PBS solution. Although  FIG. 13  illustrates a particular in-vitro measurement setup, any of a variety of in-vitro measurement setups may be utilized as appropriate to the requirements of specific applications in accordance with embodiments of the invention. 
       FIG. 8  shows a measured output of a CCIA when pre-recorded human neural signals were injected while stimulation was disabled. To assess the magnitude of differential and common-mode artifacts due to stimulation, stimulation waveforms, as illustrated in  FIG. 14 , were injected into the PBS solution without neural signals, and the measured waveforms are shown in  FIG. 15 a    through  FIG. 15 c   . The common-mode artifact at the recording site is 342 mV pp , as illustrated in  FIG. 15 a   , while the differential artifact is 8.6 mV pp , as illustrated in  FIG. 15 b   . The measured output of the CCIA matches the differential artifact at the recording site as expected, as illustrated in  FIG. 15 c   . Next, a 25 Hz sinusoid (representing a neural signal) was injected into the PBS solution along with the stimulation waveforms. The measured output of the CCIA, after LP filtering up to 50 Hz, shows a 25 Hz signal, as illustrated in  FIG. 16 . The injected sinusoid frequency was changed to 1 kHz, and the corresponding measurements, after HP filtering from 800 Hz, are shown in  FIG. 17 a    and  FIG. 17 b   . The differential signal at the recording site, as illustrated in  FIG. 17 a   , matches the output of the CCIA illustrated in  FIG. 17 b   . Since the stimulation waveform has power at the harmonics of 110 Hz, the HP-filtered outputs show residual stimulation artifacts, as illustrated by  FIGS. 17 a  and 17 b   . Finally, the injected sinusoid is replaced with a pre-recorded human neural signal, and stimulation remains enabled. The measured waveforms (LP filtered up to 50 Hz) are shown in  FIG. 18 a    and  FIG. 18 b   . The differential signal at the recording site, as illustrated in  FIG. 18 a   , matches the CCIA output illustrated in  FIG. 18 b   . Hence, the proposed front-end of many embodiments is capable of recording neural signals in the presence of stimulation artifacts. 
       FIG. 6  compares an embodiment of the invention with the current state-of-the-art. As illustrated, may embodiments of the invention improves Z in  by 5.3× for chopped front-ends, the linear-input range by 2×, the maximum resistance of DCRs by 32× and introduces tolerance to 650 mV pp  common-mode interferers, while maintaining comparable power and noise performance. 
     Accordingly, many embodiments provide a chopper amplifier capable of closed-loop neural recording in the presence of large differential and common-mode stimulation artifacts. The assisted auxiliary path technique can enable the front-end to achieve a DC input impedance of 1.6 GΩ, and may remove a need for off-chip ac-coupling capacitors, making this front-end implantable. The linear input range can be increased to 80 mV pp  (with THD of −76 dB) and the CMC path can introduce tolerance to 650 mV pp  common-mode interferers. Many embodiments further introduce a Multi-rate Duty-Cycled Resistor (MDCR), which may enable realization of a much larger equivalent resistance (90 GΩ) as compared to a conventional DCR, allowing it to maintain low noise and low area. Finally, a positive feedback problem in the auxiliary path can be addressed by introducing chopping in the auxiliary path. These improvements can be made while ensuring that the front-end achieves comparable power and noise performance to the state-of-the-art. Although discussing in the context of bio-signals and/or neural signals and their respective amplifiers, the proposed systems and methods can be utilized with a variety of signals requiring amplification and thus are not limited to bio-signals, neural signals or any particular recording system. 
     Furthermore, although specific implementations for a high dynamic range sensing front-end are discussed above, any of a variety of implementations utilizing the above discussed techniques can be utilized for a high dynamic range sensing front-end in accordance with embodiments of the invention. While the above description contains many specific embodiments of the invention, these should not be construed as limitations on the scope of the invention, but rather as an example of one embodiment thereof. It is therefore to be understood that the present invention may be practiced otherwise than specifically described, without departing from the scope and spirit of the present invention. Thus, embodiments of the present invention should be considered in all respects as illustrative and not restrictive.