Wilson Current Mirror - MOSFET Implementation

MOSFET Implementation

When the Wilson current mirror is used in CMOS circuits, it is usually in the four transistor form as in Fig. 5. If the transistor pairs M1-M2 and M3-M4 are exactly matched and the input and output potentials are approximately equal, then in principle there is no static error, the input and output currents are equal because there is no low frequency or DC current into the gate of a MOSFET. However, there are always mismatches between transistors caused by random lithographic variation in device geometry and by variations in threshold voltage between devices.

For long-channel MOSFETs operating in saturation at fixed drain-source voltage, the drain current is proportional to device sizes and to the magnitude of the difference between the gate-source voltage and the device threshold voltage as

....(8)

where is the device width, is its length and the device threshold voltage. Random lithographic variations are reflected as different values of the ratio of each transistor. Similarly threshold variations appear as small differences in the value of for each transistor. Let and . The mirror circuit of Fig. 5 forces the drain current of M1 to equal the input current and the output configuration assures that the output current equals the drain current of M2. Expanding equation (8) in a two-variable Taylor series about and truncating after the first linear term, leads to an expression for the mismatch of the drain currents of M1 and M2 as:

...(9)

The statistics of the variation in threshold voltage of matched pairs across a wafer have been studied extensively. The standard deviation of the threshold voltage variation depends on the absolute size of the devices, the minimum feature size of the manufacturing process, and the body voltage and is typically 1 to 3 millivolts. Therefore to keep the contribution of the threshold voltage term in equation (9) to a percent or less requires biasing the transistors with the gate-source voltage exceeding the threshold by several tenths of a volt. This has the subsidiary effect of lowering the contribution of the mirror transistors to the output current noise because the drain current noise density in a MOSFET is proportional to the transconductance and therefore inversely proportional to .

Similarly, careful layout is required to minimize the effect of the second, geometric term in (9) that is proportional to . One possibility is to subdivide transistors M1 and M2 into multiple devices in parallel that are arranged in a common-centric or interdigitated layout with or without dummy guard structures on the perimeter.

The output impedance of the MOSFET Wilson current mirror can be calculated in the same way as for the bipolar version. If there is no body effect in M4, the low frequency output impedance is given by . For M4 not to have a body-source potential, it must be implemented in a separate body well. However, the more common practice is for all four transistors to share a common body connection. The drain of M2 is a relatively low impedance node and this limits the body effect. The output impedance in that case is:

... (10)

As in the case of the bipolar transistor version of this circuit, the output impedance is much larger than it would be for the standard two-transistor current mirror. Since would be the same as the output impedance of the standard mirror, the ratio of the two is, which is often quite large.

The principal limitation on the use of the Wilson current mirror in MOS circuits is the high minimum voltages between the ground connection in Fig. 5 and the input and output nodes that are required for proper operation of all transistors in saturation. The voltage difference between the input node and ground is . The threshold voltage of MOS devices is usually between 0.4 and 1.0 volts with no body effect depending on the manufacturing technology. Because must exceed the threshold voltage by a few tenths of a volt to have satisfactory input-output current match, the total input to ground potential is comparable to 2.0 volts. This difference is increased when the transistors share a common body terminal and the body effect in M4 raises its threshold voltage. On the output side of the mirror, the minimum voltage to ground is . This voltage is likely to be significantly greater than 1.0 volts. Both potential differences leave insufficient headroom for the circuitry that provides the input current and uses the output current unless the power supply voltage is higher than 3 volts. Many contemporary integrated circuits are designed to use low voltage power supplies to accommodate the limitations of short-channel transistors, to meet the need for battery operated devices and to have high power efficiency in general. The result is that new designs tend to use some variant of a wide swing cascode current mirror configuration. In the case of extremely low power supply voltages of one volt or less, the use of current mirrors may be abandoned entirely.


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