Unwind di Analogue Integrated Circuit Design - 5 di 5

Static error evaluation of the feedback amplifier

Let’s evaluate now the static error of the feedback amplifier to a step input of 100mV:

Ideal vs realistic case

In an ideal scenario: Vs = Vs = 400mV

However, in reality: Vs = Vs = 393mV

The difference between the ideal and the realistic case is the so-called static error. A more general parameter is the relative static error, defined as follows: la ddireH H IE ToP P 1O 0 iId dµ ToTo0 itP To 1

In this case: ETo 1.7 Padma Toi tE 31.7

Impedance nodes identification

Let’s identify the low and high impedance nodes, but firstly let’s identify all the nodes:

• The low-impedance nodes are: i ii teN N Naf ff
• The nodes 1-3 are all nodes in which are connected the gate and drain of a device, so there is a diode configuration that presents a low impedance, equal to 1/gm.
• The high impedance node is the node O:0 120 7010708

Channel length modulation effects

As long as the effect of mismatch and channel length modulation are neglected, the behavior is completely ideal:

N IIss REFIsi IsIdee 8e L'REFID µIda lID L'REFIN µ

The effect of the channel length modulation on the core of the differential pair (devices M1, M2, M3, and M4) is:

InvasiKinVasi itDi kg VipVos VissiXpID i tµMap

In an ideal situation, the two currents are equal because this term is negligible (equal to 1). In real circuits, it can happen that the drain-source voltage must be adjusted in a way that the device can go outside of the saturation region.

In the ideal situation:

Io Iss VoiVs Voi VodVasVorUstinov

If lambda_n is equal to lambda_p (this condition is never true in reality) then:

Vs VoiVon VdaVa Voust

In real circuits, the following must be considered:

• Mismatch effects;
• Channel length modulation effects (with different lambdas between P and N devices) also on current mirrors;

Channel length modulation on current mirrors

Let’s consider channel length modulation on current mirrors:

N IREFIdg NVan Iss AIDSIDsIREFNb Msi

This term is related to mismatches and channel length modulation. The channel length modulation doesn’t introduce differences only if the two devices have the same lambda and the same drain-source voltage.

For the device M7:

Vos ID IDG Ist IIsIdf Ire et7 7Iss FREEIsa Io In µIREF IDI di 2 1 IaafId Idi 7IDsIdat REFNz146 Ma Ms

Core of the differential pair

Focusing on the core of the differential pair:

ID IDsVas IdaIda eMs MaINIDID Ida HaMi

The plot of the currents becomes:

iIa Iss VoiVs Vs Voi VasVor Vosstrovi

In this case, a larger effect of the channel length modulation on the device M3 has been considered. As shown in the plot, the output voltage is much more near to Vdd and near to the boundary of the saturation of the device M3.

Compensating differential and common mode components

In general:

f vàvoi Và VorVaVoi fVorVoiVos 0

This means that if no differential signal is applied, the differential output voltage component is not 0 and must be compensated. In order to compensate, it must be applied an offset (differential) voltage at the input of the OTA, such that:

Vos Vod1dm

Where Vod is related to the mismatch of the devices and channel length modulation. The common mode component must be compensated too. In general, it’s not applied the same approach because the common mode gain is very low. In a very general way, due to the fact that the common-mode gain is low, it cannot be compensated for the output common mode voltage just by adjusting the common mode at the input.

The solution is to apply the feedback to adjust the common mode output voltage to the desired value Voc*:

This circuit generates the common-mode output voltage voi (average of the 2 output voltages), it does an operation of common-mode sensing. This circuit makes a comparison between the common mode output voltage and a desired value and generates a regulation for the bias current of the OTA. This error is used to control the bias current in a Voituoi way such that the common mode output voltage becomes 0.