shows a picture of the printed circuit board (PCB) electronics. The PCB board interfaces directly with a National Instruments 6259 16-bit data acquisition card via two SHC68-68-EPM shielded cables. The data acquisition card can acquire all 24-channels simultaneously at a maximum rate of 41.6 kHz. Furthermore, the board has a trigger output so that LabView can coordinate signal detection with dispensing of reagents onto the chip, e.g. dNTPs required for DNA polymerization.
A 4-layer printed circuit board (PCB) was designed to amplify the signal from each electrode and is capable of amplifying 24 channels simultaneously. The PCB was manufactured on FR4 substrate by Advanced Circuits (Aurora, CO). Each channel consists of a transimpedance amplifier followed by a unity gain 4-pole anti-aliasing filter with a -3 dB frequency of 2 kHz. Each transimpedance section uses a thick-film 100 MΩ feedback resistor for a low-frequency current-to-voltage gain of 108. shows a schematic for one such channel.
The Analog Devices AD8627 op-amp, which has a JFET input stage, was chosen for the transimpedance stage because of its low input-referred current noise,
and voltage noise
at 1 kHz. Note that op-amp manufacturers typically specify the input-referred noise characteristics at a single frequency (typically 1 kHz). Furthermore, the AD8627 chip has a low
-noise. The input-referred noise of the op-amp ensures that the noise performance of the overall detection system will not be limited by the op-amp as discussed in Section 4.1. The Maxim MAX274, which has four 2-pole filter sections, is used to make two 4-pole anti-aliasing filters by cascading two 2-pole filters with a combined -3 dB frequency of 2 kHz. The filter also limits the noise bandwidth.
Each 2-pole filter section of the MAX274 has a maximum offset voltage of ± 300 mV, resulting in a maximum contribution of a 4-pole filter section of ± 600 mV. This dominates the maximum output offset voltage of the transimpedance stage (given by
is the maximum op-amp offset voltage,
is the maximum input bias current, and R is the 100 MΩ feedback resistor). The measured output-referred offset voltages were within ± 400 mV for all channels in our system.
shows the mean gain of the 24 amplifier channels along with gains which are 3 standard deviations above and below the mean. shows the standard deviation of the amplifier gain normalized by the mean channel gain. Below 300 Hz, the normalized standard deviation of an amplifier’s gain is less than 1.1%; below 4 kHz, the normalized standard deviation of an amplifier’s gain is less than 4%. The design uses resistors with a 1% tolerance, and these tolerances do not fully explain the gain deviation above 300 Hz. Above 300 Hz, the main contribution to the gain deviation is chip-to-chip variations in the MAX274 filter. If required, the measured channel gains could be used to correct for the deviation in gains from channel-to-channel and thus obtain a flat frequency response, over the frequencies of interest, via post-processing of the acquired data.
Fig. 3 Mean channel gain and the percent deviation from the mean. (a) Mean gain of all amplifier channels in . (b) Gain standard deviation normalized by the mean gain.
Voltage regulators (7805 for +5V, and 7905 for -5V) from ON Semiconductor are used to regulate the Agilent E3631A power supply closer to the circuitry. The 7805 and 7905 respectively add 50 and 40 μ
V RMS voltage noise over 10 Hz to 100 kHz, according to the manufacturer specifications. The regulated power-supply noise was measured to be have an RMS voltage noise of
and a flat spectrum over the same bandwidth.
4.1 Input-Referred Current Noise
The input-referred current noise of the electronics determines the limit of detection bound of the system (assuming the limit of detection is not set by the biology). Because a small limit of detection is desired and because the sensor will be used to measure small currents, it is important to have as small of an input-referred current noise as possible. A good discussion of noise can be found in [8
]. All noise sources in the system can be referred to the input and treated as contributions to a total input-referred current noise. Neglecting finite op-amp gain, the input-referred RMS current noise is given by calculating the output voltage noise spectral density and dividing by the transimpedance gain,
. The spectral density of the input-referred current noise is
is Boltzmann’s constant, T
is the temperature in Kelvin, RF
= 100 MΩ , Vf
are respectively the voltage noise of the filter and op-amp referred to their respective inputs in units of V2
/ Hz, Ioa
is the current noise of the op-amp referred to the op-amp input in units of A2
/ Hz, and Kv
is a constant which models the input-referred
contributions to the voltage noise of the op-amp, in units of V2
. Furthermore, Gps+
represent the gains from the positive and negative op-amp power supply pins to the op-amp output respectively, and Vps+
represents the voltage noise in V2
/ Hz on the positive and negative power supplies respectively. Typically, the gains Gps+
are not specified on manufacturer data sheets. However, the power supply rejection ratio — the ratio between the gain from the power supply to the output and the open-loop gain — is specified on manufacturer data sheets and could be used to estimate these gains, using the data sheet value for the open loop gain of the op-amp.
For the MAX274, the specified maximum input-referred (referred to the filter input, not the channel input) RMS voltage noise for a 2-pole section from 10 Hz to 10 kHz is 120 μ
V. Since two cascaded filter sections are used in the channel,
, assuming the filter noise is white. Because
at 1 kHz, we expect the input-referred current noise contributions of the op-amp to be dominated by the contributions from the 4-pole filter and the 100 MΩ resistor. From the AD8627 datasheet, Kv
= 3.92 × 10-13 V2
, and thus the contribution of the
-noise to the total input-referred current noise is negligible. Neglecting the noise contributions from the power supply, the maximum input-referred current noise at 300K is
Over a 2 kHz bandwidth, the total input-referred RMS current noise is 1.2 pA, excluding the power supply noise. Other potential sources of noise include
-noise in the resistor, substrate coupling, and electromagnetic interference.
The input-referred current noise for a particular channel is obtained by disconnecting the input from any sources (while the power is still applied) and measuring the output noise voltage spectral density using a spectrum analyzer. Dividing the output voltage noise spectral density (units of V2/ Hz) by the square of the channel gain (units of Ohms2) yields the input-referred current noise spectral density (units of A2/ Hz). A Stanford Research Systems SR780D spectrum analyzer was used to make the measurements. Measurements were made by averaging over 16 data sets. Note that the input-referred current noise will vary between channels because there is variation in the channel gains () and also in the noise contributions (e.g. the input-referred current and voltage noise will not be the same for each AD8627 op-amp).
shows the measured mean input-referred current noise spectral density for all 24 channels (the system was shielded by a Faraday cage to eliminate electromagnetic interference). Note that the input-referred current noise is an order of magnitude worse than given by Equation 2
. Over a 2 kHz bandwidth, the measured mean input-referred current noise is 8.47 pA.
Fig. 4 The measured input-referred current noise at room temperature averaged over all 24 channels. Lowering the input-referred current noise corresponds to lowering the limit of detection. Lowering the input-referred current noise below a point will eventually (more ...)
The excess noise compared to theory likely reflects noise coupled from the supply rails. The required gain from each power supply terminal to the output of the op-amp to account for the excess noise is given by
is the noise on the power supply and the factor of 2 arises because there is both a positive and negative power supply terminal. Gains of this magnitude are not unreasonable given that open-loop op-amp gains are in excess of 120 dB ( 123 dB from the data sheet) and the AD8627 power supply rejection ratio is typically 104 dB with a minimum of 80 dB. Thus, the gain from each
power supply pin to the output could be anywhere between 22dB (i.e. 12.6) and 46 dB (i.e. 200). To test the hypothesis that the excess noise originates from that on the power supply, we measured the input-referred current noise with a power supply that had a 1000 times more noise than our Agilent E3631A supply, and as a result the input-referred current noise increased by the same order of magnitude. As a possible remedy, we replaced the Agilent power supply with 9 V batteries, but did not see any reduction in the noise; either the Agilent supply and the 9 V batteries have the same noise or the voltage regulators contribute the dominant noise to the power supply pins of the integrated circuits.
In any multi-channel amplifier system, minimizing signal crosstalk between channels is an important concern. In our system, signal coupling between channels may lead one to conclude that a target DNA sequence is present at an incorrect concentration. If a current I1
flows into the input of channel 1, then the crosstalk on channel 2 induced by channel 1 is defined as
, the ratio of the output voltage on channel 2 to the output voltage on channel 1. Different channels are electrically connected through the PC board and microchip substrates via the substrate resistance, RL
, and through the capacitance between adjacent channels, CL
. shows a circuit model for the crosstalk between channels. A discussion of crosstalk in integrated circuit microarrays which sense currents is discussed in more detail in [1
Fig. 5 A model for the crosstalk and a layout technique to reduce capacitively-coupled crosstalk. (a) Crosstalk circuit model. (b) Guarding the input signal to reduce capacitive coupling. The black regions represent conducting planes surrounding the signal trace (more ...)
In , we assume that the input current all flows into channel 1, a good approximation if the impedance looking into channel 1,
, is much smaller than the impedance of the substrate resistance and capacitance, that is if
is the finite op-amp gain and
. The crosstalk arises because the finite op-amp gain causes the potential at the inverting node of channel 1 to vary, which is then amplified by a standard inverting op-amp configuration to the output of channel 2. The op-amp holds the inverting input of channel 1 at the potential
. The crosstalk voltage on channel 2 is
where the approximation holds for frequencies that satisfy
. shows the measured crosstalk versus frequency for several of the channels, illustrating the crosstalk follows the shape of Equation 5
when preventative measures are not taken. Because the substrate resistance is large, the coupling impedance generally appears capacitive for frequencies as low as 60 Hz. Equation 5
shows that crosstalk increases both with the channel gain, i.e. RF
, and frequency. The increasing crosstalk with frequency arises from a standard differentiator circuit involving the coupling capacitance CL
and the feedback resistance RF
on channel 2. Thus, there is a tradeoff between channel gain and crosstalk for a fixed substrate resistance, RL
, and capacitance, CL
. As the channel gain, RF
, increases (or equivalently as the limit of detection decreases) then the crosstalk also increases, and vice versa. In fact, for RF
= 500 M
Ω, the crosstalk between channels is 7% at 1kHz for our system. Note that the effects of the anti-aliasing filter will have approximately the same effect on two different channels and to first-order does not affect the crosstalk. Also, note that below their unity-gain frequency, op-amps generally exhibit single-pole dynamics. For frequencies above this dominant single-pole and below the unity-gain frequency, the crosstalk will increase as ω2
because for these frequencies the amplifier gain
Fig. 6 Crosstalk between guarded and unguarded channels. Note that the crosstalk between unguarded channels follows Equation 5. (a) Crosstalk between guarded channels. (b) Crosstalk between unguarded channels.
In order to reduce the capacitive coupling of Equation 5
, the PC board was designed using the guarding technique wherein the input trace is surrounded as much as possible by conductors (not physically connected to the other channel traces) held at the same potential as shown in . Due to the arrangement of the pins at the microchip socket, it was not physically possible to put a guard between every pair of adjacent traces right up to the microchip socket. shows the mean coupling between pairs of adjacent channels from a sample of 19 measurements. shows the capacitive crosstalk as modeled in Equation 5
between the channels for the 7 cases in which complete guarding was not possible as mentioned above. For guarded channels, the mean crosstalk from 0 - 2 kHz is less than 0.1%. For those 7 cases without complete guarding, the crosstalk is still less than 1.4% over the bandwidth 0 - 2 kHz.