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Reconstruct input current in grounded-impedance current sensor

18 Sep 2012  | Abhirup Lahiri

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It is possible to reconstruct the small-signal current flowing into a grounded impedance, which is part of a larger circuit. This current, such as the highpass-filter output for several current-mode biquadratic filters flowing into a capacitor—and which is a working impedance of the filter—can be the summation of multiple currents.

Reconstruction of the output current by means of individually duplicating all constituent input currents through current mirrors can be error-prone, as the following equations show: IIN=I1+I2+I3 ... +IN, and IO1I12I23I3 ... +αNIN. The current-mirroring coefficients, αi, should ideally achieve unity to reconstruct IIN accurately. All of these coefficients, however, not only deviate from their ideal values of unity but also can differ from each other because of current-mirror mismatches, including systematic mismatch due to the mirror's finite output resistance and random threshold mismatch for CMOS current mirrors. Those mismatches can cause the frequency character of the output's small-signal current—for example, a highpass response—to change. A useful technique is to sense the voltage across the impedance and then do a single-precision voltage-to-current conversion, thereby getting rid of the errors arising from multiple mirroring operations.

Figure 1 shows a small-signal current-sensing circuit that must sense the total current flowing into an impedance, Z1. The voltage-to-current conversion requires a matched load impedance, Z2, and is built around an operational current conveyor (reference 1). Any mismatch between the loads will cause the output current to be a scaled value of the input current, where the scaling factor is the ratio of impedances; hence, the frequency character of the small-signal output current will remain unchanged.

The mismatch in either of the current mirrors is also of interest: Assuming that the input current of Current Mirror 1 is IB+IIN and the input current of Current Mirror 2 is IB, then the output current is IO1IB1IIN−β2IB=(β1−β2) IB1IIN, where IB is the quiescent current of the last stage of the amplifier and β1 and β2 are current-mirror mismatches. The output current has a dc-offset current, which you can easily cancel out, and a scaled value of the input's small-signal current, IIN.

References
1. Gift, Stephan JG, "Hybrid current conveyor-operational amplifier circuit," International Journal of Electronics, Volume 88, No. 12, 2001, pg 1225.
2. Robinson, John, "New CCII Current Conveyor," Application Note 4198, Maxim Integrated Products, March 27, 2008.

About the author
Abhirup Lahiri is from New Delhi, India.

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