Unwind di Analogue Integrated Circuit Design - 2 di 5

Current Mirrors Using Integrated Circuit

A current mirror is a 3-terminal (input terminal, output terminal, and reference terminal) circuit device. Its main feature is that the output current is an integer multiple or rational multiple of the input current.

Types of Current Mirrors

There are 2 types of current mirrors, the n-type and the p-type:

Usually, regardless of the type of the Current Mirror (CM):

• N I_out i.snM

Where “N” and “M” are integers. Moreover, typically: M=1.

Small Signal Behavior

The small signal behavior of the CM (Current Mirror) is best described by a two-port network (same for n-type and p-type):

• In tout N iim dont il Vin dont

MOSFET Basic Implementation of CM

This circuit exploits the good matching between same-type devices on the same microchip. In fact, the analysis of this device is very easy if the two MOSFETs are equal. This allows the use of some hypotheses.

The hypothesis that the devices are equal allows, in particular, these assumptions:

• These assumptions mean that the two devices are equal, but the second device is “N” times larger than the first one.
• The two devices must also work in the active region (saturation).

DC Analysis of the CM

Let's have a DC analysis of the CM (currents are constant in time):

• Vos VinII NIDI µKI Vos VinIone KID NY

In the equations are indicated two different voltages “VGS1” and “VGS2” but due to the topology of the circuit, they are equal:

• Vos Vasa Vosa

Under these assumptions:

• N.IN tout

All these assumptions are true only if the devices are in the saturation region, but looking to the circuit:

• Vos iVins Vas Vas vgs.hnVasi ese

The saturation condition of the first device is automatically verified because the drain and the gate of “M1” are shorted. About “M2”:

• V_tn evo vi v.eVDs rs v_gsz iVor LIEN VisseKIN W_i L

The saturation condition is not guaranteed on the second device.

Non-Ideal Effects

Let's apply now some non-ideal effects. The first non-ideal effect is the channel modulation effect. The current equation becomes:

• I_KI Voi Vasat ourt rout 1 tout Idea t a

The goal of a good CM is to get a current “I_OUT” perfectly equal to “I_IN” so it must be considered the channel modulation effect.

From a graphical point of view:

• Triode Saturation region region Real behavior: lambda != 0 tout AIDI oui.N.IN Ideal behavior: lambda = 0 out 52 V_or V_oss Visset out Vin VosGs

As shown in the graph, with different drain-source voltages between the two devices, the currents are different by a specific quantity, that is:

• i Voi ki Vissi ID Visse 2 Nfl vaiki 7E1 IIsa NE2 oz 20

This systematic error is small if the difference between the drain-source voltages is small or if the output resistance is large.

Device Parameter Differences

Another type of non-ideality considers that the parameters of the two devices are different, for example:

• i ksi Vinse Krisa Tmr Kin I_tout Kmt Vcrs1 Vin kme a D2 i tant fin kn km 2 Cox Vin Kmt km2 µ

The factors “DeltaKn” and “DeltaVtn” are normal (Gaussian) distribution with the following variances:

• A A kmkm i A 0N Vin Vinkm km Vin W WL L km

First Order Equation Terms

Let's consider now the expansion of the equation of the current considering only the first order equation terms (the perturbations are very low in respect of the nominal one):

• 2Kin ID I Kmt Vcrs1 km Van2 e a2 Dout 2 Nov Va Kikm tant I Considering only the kmi first-order terms km2 Voi km aknvotkn fmtknvov.hn

Nominal value (expected) gm2=Kn*Vov It's called “Idnom”

• 1km IDnom ltd kkn nt. IMnom Error due to the mismatch

The output current can be seen as a normal distribution equally distributed around “Id2nom.”:

• Star out tout Inman2 ohm Qflutto e Luton

Where “Q” is the number of copies of current mirrors.

Moreover:

• iÔ Ima 0cm OIv.inkme Innovikm

To minimize the mismatch effect:

• A A kmkm W A Al Vin km km km large a a very Vin W WL L km 9mi small

Example of CM Application in DC

Let's have an example of CM application in DC:

• Vda Vda Vda Vda Ne IREF MIREE MIMgMs IRET IRET. tl Notre Ms Ma Nature 1441 µ Ns NÉ

The current “I_ref” is a so-called “gold reference current.” Usually, this type of currents is reference current that are generated with very high precision.

The parameters “N2”, “N3” and so on means that the width of the device is “N2”, “N3” and so on times the width of the principal device “M1”:

• We NAW ii WWs NL

Small Signal Analysis of the CM

Let's consider now the small signal analysis of the CM:

• iim l'out Tin dont M Ma

The ideal model of “M1”, considering the shortcut between drain contact and gate contact becomes:

The voltage-controlled current source is in parallel with the voltage that controls itself, so II_gs it’s equivalent to a resistor Gm Images whose value is: 1/gm

When the drain of a MOSFET is connected with the gate, the configuration is named “diode” configuration.

The CM becomes:

• l'out Iim Iim e'out Tin dont 1 tout lgs MrM tgs Imi 8mF Vor Kin Vor