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CMOS Current Mirrors

Sunday, January 19, 2020

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CMOS current mirrors are a fundamental component of any practical analog integrated circuits. A generic current mirror is shown in Fig. 1. An input current is buffered and mirrored to an output circuit. In this article, common current mirror topologies are examined are evaluated.
FIG:
In order to evaluated the different current mirror topologies, certain metrics need to be defined. The first metric is the current mirror output resistance. High output resistance is desirable to provide a constant current for a wide output voltage range, as shown in Fig. 2.
FIG:
Other metrics include:

• Noise: Noise can be either expressed as a noise density metric (A²/Hz) or a current noise (A) when integrated over a noise bandwidth. It is assumed in the noise analysis to follow that the noise due to the input stage of the current mirror (buffer) can be filtered out by means of a passive RC filter.
• Voltage headroom: In order to implement the current mirror a certain number of cascaded devices are necessary at both the input and output components of the current mirror. This defines a minimum input and output voltage headroom required.

1. Simple Current Mirror
   A simple current mirror is shown in Fig. 3. For equally sized devices M1 and M2, the input current is equal to the output current. Both devices, M1 and M2, are required to be in saturation for good matching between the devices. This output resistance of the current mirror is output resistance of MOSFET device, which is given as
   $$i_n^2=\frac{4\mathrm{kT}\gamma }{g_m}$$
   Equation (1)
   where L is the transistor length, ID is the saturation current through the device, and lambda is device parameter known as the early effect [1].
   FIG:
   The output current noise density of the simple current mirror is the noise of a MOSFET device, which is given as
   $$r_o=g_{\mathrm{m3}}\cdot r_{\mathrm{ds3}}\cdot r_{\mathrm{ds2}}$$
   Equation (2)
   
2. Cascode Current Mirror
   A cascode current mirror is shown in Fig. 4. The main advantage of a cascode current mirror is significantly increased output resistance, which is given as
   FIG:
   
3. Regulated Cascode Mirror
   A further improvement in output resistance can be achieved by the regulated cascode current mirror, shown in Fig. 5 [2]. An additional operational amplifiers (opamp) is used in feedback around the cascode device to boost the output resistance, which is given as
   $$r_o=A(s)\cdot g_{\mathrm{m3}}\cdot r_{\mathrm{ds3}}\cdot r_{\mathrm{ds2}}$$
   Equation (3)
   where A(s) is the frequency depending gain of the opamp.
   FIG:
   The gain of the opamp, generally has a low-pass filter response, with the highest gain at DC. This means that the full benefit in output resistance offered by this topology is only realized up to the bandwidth of the opamp. Fig. 6 shows a typical frequency response expected from a regulated cascode current mirror. The first reduction in the output resistance is due to the finite bandwidth of the opamp, eventually reducing the output resistance to that of a cascode current mirror. When the impedance of the parasitic capacitance of the internal node of the cascode current mirror, the output resistance further reduces to that of the output resistance of a single MOSFET device, which was given by (1).
   FIG:
   
4. High-Compliance Cascode Mirror
   A current mismatch between input and output currents in a regulated cascode current mirror can still exist due to the imbalance in impedances between input and output stages. Namely, the input resistance is a diode connected MOSFET with output resistance of 1/gm, whereas the output resistance is given by (4). In order to reduce this mismatch in impedances, a high-compliance cascode current mirror can be used as shown in Fig. 7 [3].
   FIG:
   One advantage of this topology is its low mirroring offset error. As the output voltage lowers, transistor M2 will eventually enter the triode region of operation. Due to the feedback action of the opamp, this will force M1 to also enter the triode region maintaining good matching between input and output currents. The main disadvantage of this topology is its increased noise performance. The output current noise is given as
   $$i_n^2=8\mathrm{kT}{r}_{\mathrm{M1}}+v_{\mathrm{opamp}}^2\cdot r_{\mathrm{M1}}$$
   Equation (4)
   
5. Regulated Input Current Mirror
   Another topology that attempts to improve the noise performance of the current mirror is a regulated input current mirror, shown in Fig. 8 [4]. In this topology, the opamp is connected to the cascode device (M4) of the input segment of the current buffer. The output resistance, however, is lower than that of the high-compliance cascode mirror and is given as
   $$r_o=A\cdot r_{\mathrm{ds2}}$$
   Equation (5)
   FIG:
   
Summary
A summary of the various current mirror topologies is given in Table 1 below. The noise expressions assume that the noise due to the input buffer devices can be sufficiently filtered by means of an RC filter. The output resistance expressions are the low-frequency output resistances (parasitic capacitances are not included). The term 'A' refers to the opamp gain. The expressions for minimum voltage headroom do not take into account the voltage headroom required for the opamp to operate correctly.

Table 1. Comparison of I/Q mismatch calculation methods


Case	Example 1	Example 2
Equation (4)	41.12dB	46dB
Equation (5)	41.19dB	46dB





References

[1]   A. Sedra and K. Smith, Microelectronic Circuits, International Sixth Edition, Oxford University Press: New York, 2011.
[2]   R. Barrett et. al., "Current mirror and self-starting reference current generator," U.S. Patent 5612614, March 1997.
[3]   O. Charlon and W. Redman-White, "Ultra High-Compliance CMOS current Mirrors for Low Voltage Charge Pumps and References," IEEE European Solid-State Circuits Conference (ESCIRC), pp. 227-230, 2004.
[4]   T. Serrano et. al., "The active-input regulated-cascode current mirror," IEEE TCAS, vol. 41, pp. 464-466, June 1994.

Keywords: current mirrors, cascode mirrors, output resistance

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