Current Mirror

Analog (Integrated) Circuit Design

6 Current Mirror

Current Mirror

Figure 28: A current mirror with two output branches.

In this section we will look into a fundamental building block which is often used in integrated circuit design, the current mirror (Widlar 1965). A diagram is shown in Figure 28 with a MOSFET diode converting the incoming bias current into a voltage \(V_\mathrm{GS}= f(I_\mathrm{D1}) = f(I_\mathrm{bias})\), and two output MOSFETs working as current sources, which are biased from the diode. By properly selecting all \(W\) and \(L\) the input current can be scaled, and multiple copies can be created at once. Shown in the figure are two output currents \(I_\mathrm{out1}\) and \(I_\mathrm{out2}\), but any number of parallel branches can be realized (note that this is true for MOSFETs as no gate current flows; for the case of BJTs, the base current flowing into the various transistors is subtracted from \(I_\mathrm{bias}\), so usually a compensation circuit is added).

Current Mirror

Neglecting the impact of \(g_\mathrm{ds1}\) and \(g_\mathrm{ds2}\), the output current \(I_\mathrm{out1}\) is then given by \[ I_\mathrm{out1} \approx I_\mathrm{bias} \frac{W_2}{L_2} \frac{L_1}{W_1} \] and the output current \(I_\mathrm{out2}\) is given by \[ I_\mathrm{out2} \approx I_\mathrm{bias} \frac{W_3}{L_3} \frac{L_1}{W_1}. \]

Current Mirror: Key Points

Output current set by the size ratio: \(I_\mathrm{out} \approx I_\mathrm{bias} \cdot \frac{W_2/L_2}{W_1/L_1}\)
Any number of output branches (no gate current in MOSFETs)
Build \(W\) and \(L\) from identical unit elements for good matching
Main flaw: \(V_\mathrm{DS}\) of the diode (\(V_\mathrm{DS}= V_\mathrm{GS}\)) differs from the outputs
Long \(L\) and low \(g_\mathrm{m}/I_\mathrm{D}\) give a flatter output current

Current Mirror

Exercise: Current Mirror

Please construct a current mirror based on the MOSFET-diode which we sized in Section 4. The input current \(I_\mathrm{bias} = 20\,\mu\text{A}\), and we want three output currents of size \(10\,\mu\text{A}\), \(20\,\mu\text{A}\), and \(40\,\mu\text{A}\).

Sweep the output voltage of all three current branches and see over which voltage range an acceptable current is created. For which output voltage range is the current departing from its ideal value, and why?

For good matching, care has to be taken that the MOSFET widths and lengths are constructed out of unit elements of identical size, where an appropriate number of these single units are then arranged in series or parallel configuration to arrive at the target \(W\) and \(L\) (remember MOSFET parameters ng and m, see Important 1).

As we know from earlier investigations of the MOSFET performance in Section 3 the drain current of a MOSFET is a function of \(V_\mathrm{GS}\) and \(V_\mathrm{DS}\). As long as the MOSFET stays in saturation (i.e., \(V_\mathrm{DS}> V_\mathrm{ds,sat}\)) the drain current is just a mild function of \(V_\mathrm{DS}\) (essentially the effect of \(g_\mathrm{ds}\), which is the output conductance of the MOSFET). A fundamental flaw/limitation of the basic current mirror shown in Figure 28 is the mismatch of the \(V_\mathrm{DS}\) of the MOSFETs. The input-side diode has \(V_\mathrm{GS}= V_\mathrm{DS1}\), whereas the output current sources have a \(V_\mathrm{DS2,3}\) depending on the connected circuitry. Improved current mirrors exist (fixing this flaw); however, when a current mirror is required with mediocre performance requirements, this structure can be used for its simplicity.

Current Mirror

Exercise: Current Mirror

You see that the slope of the output current is poor, as \(g_\mathrm{ds}\) is too large. We can improve this by changing the length to \(L = 5\,\mu\text{m}\) (for motivation, please look at the graphs in Section 3). In addition, for a current mirror we are not interested in a high \(g_\mathrm{m}/I_\mathrm{D}\) value, so we can use \(g_\mathrm{m}/I_\mathrm{D}= 5\) in this case. Please size the current mirror MOSFETs accordingly (please round the \(W\) to half micron, to keep sizes a bit more practical).

Current Mirror

Exercise: Current Mirror

Compare this result to the previous one. What changed?

In case you get stuck, here are Xschem schematics for the original and the improved current mirrors.

References

Widlar, R. 1965. “Some Circuit Design Techniques for Linear Integrated Circuits.” IEEE Transactions on Circuit Theory 12 (4): 586–90. https://doi.org/10.1109/tct.1965.1082512.