- ISBN 13: 9780387297583
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- Current Mode Computational Circuits for Analog Signal Processing | Open Access Journals

Analog Circuits and Signal Processing. The Analog Circuits and Signal Processing book series, formerly known as the Kluwer International Series in Engineering and Computer Science, is a high level academic and professional series publishing research on the design and applications of analog integrated circuits and signal processing circuits and systems.

## ISBN 13: 9780387297583

Typically per year we publish between research monographs, professional books, handbooks, edited volumes and textbooks with worldwide distribution to engineers, researchers, educators, and libraries. The book series promotes and expedites the dissemination of new research results and tutorial views in the analog field. There is an exciting and large volume of research activity in the field worldwide. Researchers are striving to bridge the gap between classical analog work and recent advances in very large scale integration VLSI technologies with improved analog capabilities.

Analog VLSI has been recognized as a major technology for future information processing. Consequently, new design concepts, strategies and design tools are being unveiled. Share this. Titles in this series. Refine Search. Content Type. Release Date. The only pole of the basic current mirror is at the gate of M1 with the pole frequency given by Due to the existence of the floating gate-drain capacitor Cgd, the common source configuration is subject to Miller effect with Miller capacitances at the gate and at the drain, where and are the output impedance and transconductance of the transistor, respectively.

The pole at the input called Miller pole, is given by [ ] Where is the resistance of the source. The output pole is estimated from where is the input capacitance of the load stage. The common-gate configuration is not subject to Miller effect due to the absence of floating capacitors. The source follower is also free of Miller effect simply because its small-signal voltage gain is approximately unity. The Miller capacitances at the gate and source are given by.

For practical applications, and are often large, the dominant pole of the common-source, common-gate, and source follower amplifiers is usually at the output node. Slew Rate Figure 12 Slew rate comparison of voltage-mode and current-mode circuits a Basic current mirror; b Common-source amplifier; c Basic differential pair. The slew rate of voltage-mode and current-mode circuits is compared using the common-source configuration and the basic current mirror shown in Figure When a square waveform current is applied to the basic current mirror, because M1 is in the saturation, iDS1 is independent of vDS1 when the channel length modulation is neglected.

The rate of the change of the output current depends upon how fast is charged or equivalently how fast the gate voltage of rises. Because For voltage-mode circuits, the slew rate is usually determined by the output stage because of the large width of the transistors in the output stage and the large capacitance of the load.

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The preceding results reveal that the slew rate of common-source amplifier is set by the biasing current, the width of the transistor, and the output capacitance. It is independent of the amplitude of the input voltage. It is directly related to the swing of the signal. The above equation reveals that a small propagation delay can be achieved by either minimizing the swing of the voltage of the node or maximizing the current charging and discharging the capacitance of the node. Figure 13 Variation of nodal voltages and branch currents of current-mode circuits.

Unlike voltage-mode circuits, the information carriers of current-mode circuits are branch currents. The variation of nodal voltages can be kept small as long as the current of the branches associated with the nodes is large.

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This is one of the key advantages of current-mode circuits. Supply voltage sensitivity, defined as is a measure of the effect of the variation of the supply voltage on the response of the circuits. Figure 14 Supply voltage sensitivity analysis of voltage-mode circuits a Common-source amplifier; b Small-signal equivalent circuit. Consider the common-source amplifier shown in Figure 14 a.

M2 is biased in the saturation and behaves as a current source. The small signal equivalent circuit of the amplifier for supply voltage sensitivity analysis with junction capacitances neglected is shown in Figure 14 b.

Now let us consider the circuit shown in Figure The load is a current mirror with the source current provided by an ideal current source J. Figure 15 Supply voltage sensitivity analysis of current-mode circuits a Current mirror amplifier; b Small-signal equivalent circuit. No low-impedance paths from the input pads to the ground exist to discharge electrostatic charge accumulated at the pads, as shown in Figure On the contrary, the low-impedance characteristics of the input pads of current- mode circuits prevent the accumulation of static charge at the pads, as shown in Figure The output node of the adjoint network is node 1 and the two control nodes are nodes 2 and 3 with node 3 the voltage-control node and node 2 the current-control node.

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The voltage-control node is node 3 and the current-control node is node 2. In such a method a circuit using voltage amplifiers and passive components is converted into one that contains current amplifiers and passive components. An ideal voltage amplifier has infinite input impedance and zero output impedance, while an ideal current amplifier has zero input impedance and infinite output impedance. Consequently, direct replacement of a voltage amplifier with a current amplifier will lead to different circuit behaviour.

A voltage-mode circuit can be converted into a current-mode circuit by constructing an inter-reciprocal network by using the adjoint principle. According to this principle, a network N is replaced with an adjoint network Na, the voltage excitation is interchanged to a current response, and the voltage response is interchanged to a current excitation.

Thus, the resulting transfer functions of these two networks N and Na are identical: The networks N and Na are thus said to be inter-reciprocal to one another.

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When the networks N and Na are identical, for example in the case of passive networks, the networks are said to be reciprocal. Since all passive networks are reciprocal, all passive circuit elements have themselves as their adjoint elements i. In order to maintain identical transfer functions for both the original network N and the adjoint network Na the impedance levels in the corresponding nodes of both networks should be identical.

Therefore, the signal flow is reversed in the adjoint network and a voltage source is converted to a current sensing element as they both behave as short circuits. Figure 18 Inter-reciprocal networks N and Na. In addition, controlled sources can be converted with the same principles: the signal flow is reversed and the impedance level is kept the same. In this way, a voltage amplifier is converted to a current amplifier and a current amplifier is converted to a voltage amplifier, respectively.

However, since transresistance and transconductance amplifiers are inter- reciprocal, networks containing only transresistance or transconductance amplifiers and passive elements differ only in signal direction and type. In this case, a bipolar transistor in a common-emitter amplifier configuration is inter-reciprocal to itself and the common-collector amplifier configuration has the common-base configuration as its adjoint.

Converting a voltage-mode bipolar transistor circuit to a current-mode MOS- transistor circuit could be beneficial as it minimises the use of source-follower stages which have poor low-voltage performance due to the bulk effect.

Bipolar transistor circuits are conventionally constructed of common-emitter and common-collector amplifier stages and the resulting MOS-transistor adjoint circuit is constructed of common-source and common-gate amplifier stages. Input voltage-to-current conversion Since signals are normally represented as voltages, a voltage-to-current conversion is required at the input of most current-mode integrated circuits. A simple example of this is presented in Figure 19 a , where a simple NMOS current-mirror is used as the input stage of an integrated circuit.

Because the DC-voltage at the current-mirror input is sensitive to process and temperature variation, a DC-decoupling capacitor C is added in series with the off-chip resistor R. Because of the simplicity of the input structure there are several non idealities present in the circuit. Since the input impedance of the NMOS current-mirror is generally approximately one kilo-ohm, a large off-chip resistance R is required for accurate voltage-to- current conversion.

The parasitic capacitance Cp, including the mirror input capacitance and parasitic capacitances deriving from the pad and wiring, amount to several Pico farads and, since this capacitance is in parallel with the input impedance of the current-mirror, the bandwidth is relatively limited.

Moreover, this capacitance additionally increases high- frequency distortion. As a consequence of the closed-loop operation, large input capacitance may cause instability. However, if this capacitance is in series with a resistance Rp of a few hundred ohms, the phase lag deriving from the parasitic capacitance Cp is significantly reduced.

This series resistance cannot be avoided since it is included in the protection devices of the input pad. The resistor Rp is normally realised as a diffusion resistor, and so is weakly non-linear and temperature dependent. However, because this resistance is significantly smaller than the input impedance of the NMOS current-mirror, its contribution to the nonlinearity and accuracy of the voltage-to-current conversion is similarly minor.

In order to reduce the effects of the input pad diffusion resistor, the circuit can be modified so that the current output Z1 is connected directly to the input pad rather than the conveyor X input, as depicted in Figure 20 a. Since the resistor Rp1 is in this case inside the feedback path, the input impedance seen at the input pad is reduced to roughly ten ohms. The parasitic capacitance Cp reduces feedback at high frequencies and thus stability problems seldom occur. It may not be possible to connect the conveyor Z-output directly to the input pad without protecting devices, so there is an additional resistance Rp2 between the input pad and the high impedance Z-output.

However, this resistance has virtually no effect on the circuit performance as it is in series with a current output. Most of the problems involved in voltage-to-current conversion at the low impedance current input can be avoided by using a voltage input for the system in conjunction with an on-chip voltage-to-current converter. Because almost all CMOS current conveyors have a relatively poor input voltage swing, high-impedance voltage inputs are not feasible in low voltage current-mode systems unless the input signal amplitudes are relatively small.

Another way to implement a voltage input with a large signal swing is to use a voltage-mode operational amplifier with rail-to-rail input and output swing. However, they are relatively complex circuits and commonly exhibit a moderate bandwidth and lengthy settling time.

Thus, the series resistance in the output pads do not degrade the performance, and the parasitic capacitances at the output do not cause stability problems to the circuitry in the integrated circuit. Furthermore, the current to voltage conversion i. Figure 21 Typical output current to voltage conversion. However, there may be some gain errors and output offset currents due to the same reason. In the case of this circuit, it is straightforward to set the DC-voltage of the output simply by setting the voltage at the operational amplifier non-inverting terminal.

Thus, the parasitic capacitance Cp deriving from pad and wiring capacitances degrades the settling behaviour, as depicted in the small-signal transfer function of the current-to-voltage converter. Therefore, the parasitic capacitance Cp degrades the phase margin of the closed-loop amplifier if the inverse of the time constant R. Cp is comparable to the gain-bandwidth product of the amplifier and thus settling times become long.

This can be avoided by reducing the resistance R or by using an overcompensated operational amplifier. The latter is difficult to realise with discrete operational amplifiers as there are currently extremely few operational amplifiers available with an option for an external compensation capacitor.

## Current Mode Computational Circuits for Analog Signal Processing | Open Access Journals

This capacitance can be as small as the capacitance Cp resulting in only slightly decreased bandwidth, while the settling becomes significantly faster. Alternatively, a current- feedback operational amplifier can be used in preference to the voltage-mode operational amplifier in the current-to-voltage converter. Since the closed loop bandwidth of the current- feedback operational amplifier is inversely proportional to the feedback resistance R, in the case of large feedback impedances the amplifier is overcompensated, and thus relatively insensitive to the extra phase lag arising from Cp.

This book deals with the analysis and design of continuous-time CMOS current-mode circuits for data communications over wire chan nels. CMOS current-mode sampled-data networks, such as switch- current circuits, and current-mode logic circuits, are excluded. The book is organized as the followings : Chapter 1 examines the distinct characteristics of ideal voltage-mode and current-mode circuits.