ICETACS 2013

978-1-4673-5250-5/13/$31.00 ©2013 IEEE

Analog Field Programmable CMOS Operational

Transconductance Amplifier (OTA)

G. Kapur

Department of Electronics & Communication National Institute of Technology

Shillong, Meghalaya, India kapur.garima@gmail.com

S. Mittal

Department of Electrical Engineering Indian Institute of Technology

Kanpur, India

sajalmittal82@ieee.org

C.M. Markan

Department of Physics and Computer Science

Dayalbagh Educational Institute

Dayalbagh, Agra, India

cm.markan@gmail.com

V.P. Pyara

Department of Electrical Engineering

Dayalbagh Educational Institute

Dayalbagh, Agra, India

prempyara@rediffmail.com

Abstract—This paper defines a approach to design the field

programmable CMOS Operational Transconductance Amplifier

(OTA). All the MOSFETs are replaced by the floating gate MOSFETs to make the OTA design programmable. The charge

at the floating gate can be programmed after fabrication, based

on Hot-e-injection and Fowler-Nordheim tunneling techniques

which results in threshold voltage variation which in turn can

modify circuit’s specifications. The high frequency small signal analysis of the design is prepared and specifications like output

current, Transconductance, input impedance, output impedance

and offsets of the design are re-derived in terms of threshold

voltages of the MOS FETs. In order to achieve circuits AC and DC characteristics, the circuit is simulated using BSIM3 level49

MOSFET models in T-spice 0.35um CMOS process. The

simulated results shows 13 bit programming precision in

transconductance, input impedance, output impedance,

Temperature stability and dc offsets with respect to threshold

voltage of respective MOSFETs.

Index Terms—Floating Gate MOSFETs, Operational Transconductance Amplifier, Specification, Threshold Voltages,

High Frequency Small S ignal Analysis

I. INTRODUCTION

The expansion of communication and electronics

industry with high level of reliability communication requires

high level of chip integration and directed research towards

the field of high frequency applications. In the new designed

circuit topologies for high frequency signal processing

conventional methods based on voltage op-amp are no longer

adequate as op-amp has a closed-loop gain dependent

bandwidth. OTA is a transconductance type device, which

means that the input voltage controls an output current by

means of the device transconductance, labeled gm. This makes

the OTA a voltage-controlled current source (VCCS). An

OTA produces an output current that is proportional to the

voltage difference between its input terminals multiplied by

the gain which is controlled by the bias current of OTA which

is third input of operational transconductance amplifier [1].

OTA has very high input impedance and very high output

impedance. As shown in Figure1, OTA process the input

voltages with low input current over a wide common mode

input range, to produce an internal representation of the input

differential voltage and to provide a current to the output that

is relatively independent of the output voltage.

Operational transconductance amplifiers are important

building blocks for a wide range of electronic circuits. It acts

as a replacement for the conventional op-amp in both first and

second-order active filters [2]. It can use as a two-quadrant

multiplier and hence can be used for implementing voltage

controlled oscillators (VCO) and filters (VCF) for analog

music synthesizers. OTA uses a pseudo-differential input

stage and common mode feed forward which is used for

realization of high frequency continuous time filters [3].

Therefore, applications like filters, impedance inversion,

differential amplifier etc. can be easily implemented with

OTA, as it use capacitance only in place of resistance. OTA is

also being used as a programmable unit in FPAAs [4].

Programmability is required like for biologically inspired

circuits such as bionic ear processor, learning circuits and

related adaptive filters, neuromorphic and cellular computing

circuits, etc. According to the proposed design procedure and

using FGMOS in place of conventional MOSs in the circuit,

programmability is introduces. While maintaining small size

and low power consumption, conductivity of a MOS can be

corrected by altering its threshold voltage (VT) by a field user

[5, 6].

Figure 1. Block Diagram of OTA

II. PROPOSED ANALOG DESIGN CYCLE

A. Proposed Analog Design Cycle

Floating gate MOS are like conventional MOS with an

additional gate in which by modifying the charge at the

floating gate MOS characteristics (threshold) can be

Analog Field Programmable CMOS OperationalTransconductance Amplifier (OTA)

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programmed on-chip after fabrication with real time, non-

volatile, reconfigurable programming. Programmability can

easily be introduced in CMOS operational transresistance

amplifier design by following the design cycle shown in

Figure2.

Algorithm:

1. Analyze circuit with the help of block diagram to

establish desired functionality.

2. Simulate the circuit to check its functionality with

basic sizing and biasing conditions.

3. Design the equivalent small-signal model of the

circuit.

4. Derive specifications in terms of threshold voltage of

transistors.

5. Analyze sensitivity of each specification with respect

to respective thresholds.

6. Simulate the circuit to check the sensitivity of each

specification.

7. Layout creation and verification of the circuit with

basic sizing and biasing conditions.Then after testing

and extraction, fabricate the design.

8. Program the transistor’s thresholds to adjust the

desired specifications with huge accuracy

Figure 2: Flowchart of Proposed Analog IC Design Procedure

Therefore this design analogy saves design time and cost.

The tradeoff between accurate and optimize design which

analog designer has to maintain throughout the design

procedure does not remain the major issue while designing

analog circuits now. As with the proposed design flow

optimized design can be fabricated and final accurate

prototype with fine on-chip tuning can be derived.

B. Design Objectives

Before designing or introducing programmability inOTA

CMOS circuit few design objectives need to be considered.

Firstly the variation in the design specifications should be

large and continuous. Indirect, non-volatile and high precision

programming of FGMOS thresholds can produce large range

and continuous programming of specifications. Second design

objective is that the variation of each specification should be

independent of the otheri.e., each specification should be

programmed either by one or more FGMOS but should not

alter any other design specifications. However if specification

programming are not independent then either through

modifying the circuit or by compensating the affected

specification value using different set of FGMOS, should

beprepared. Thirdly, operating point of the circuit should not

alter too much during programming, i.e. current density in

each transistor should not change significantly or in other

words offset current should not vary significantly.

III. BASIC CMOS OTA CIRCUIT DESIGN

A. OTA Circuit Design

An operational Transconductance amplifier (OTA) is a

high gain voltage controlled current source amplifier (as

shown in Figure 3(a)) and consists of differential pair M1 and

M2 and according to the difference of input voltages, current

flows through it and get mirrored from M6 and M5 to M8 and

M7 through two current mirrors M3 & M5 and M4 & M6.

Hence output current through M8 is proportional to the

difference of input voltage applied to the differential amplifier.

Basic circuit [7] is considered and using its first cut design

equations deriving specifications are derived in terms of MOS

threshold voltage. While analyzing basic OTA circuit, to

obtain the desired functionality and basic characteristics,

circuit sizing and biasing conditions are adjusted.

(a)

(b)

Figure 3 (a): Circuit diagram of CMOS OTA (b): High frequency small signal equivalent circuit loop of the OT A.

B. High Frequency Small Signal Analysis

For high frequency small signal analysis of OTA, circuit

is subdivided into the smaller sub-parts like Differential

Amplifier and current mirrors. Diff-Amp produces currents in

the drains proportional to the input voltage difference. At high

frequency, effect of parasitic capacitances need to be

considered. The high frequency small signal analysis of

differential amplifier is shown in Figure 3(b) where, outputs

current get mirrored to the output terminal with the help of

current mirrors. By applying basic KVL and KCL current and

voltages in the circuit is analyzed and the expressions for ID9

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and ID10 in terms of differential voltage is derived which in

turn is used to derive the design equations for OTA. The

expression of output current depends upon the threshold

voltage of M9 and M10

(1)

Transconductance(depends upon threshold voltages of M9 and

M10)

(2)

Similarly expressions of other specifications are derived:-

(3)

(4)

(5)

So, design specifications are dependent on respective

MOSs threshold voltages. Sensitivity analysis of each

specification with respect to respective MOSs is performed

and results have been formulated. Simulation results

characterizing the basic OTA design is illustrate in next

section.

C. Characteristics of basic OTA design

The basic OTA design has been simulated and its basic

functionality with central value of specifications at specific

biasing and sizing conditions of the circuit is estimated.

Transistors aspect ratio is tabulated in Table 3.9. The biasing

current IB = 100μA. The supply voltages are ±2.5V. Thus at a

specific sizing and biasing condition of the design, frequency

response ofopen loop gain, input impedance, output

impedance and transconductance is shown in Figure 4(a), 4(b),

4(c) and 4(d) respectively.The characteristics summary is

tabulated in Table2.

Figure 4: Frequency Response of (a) Open loop gain (b) Input impedance(c)

Output impedance (d) Transconductance of OTA.

T ABLE1: T RANSISTOR ASPECT RATIO OF THE CIRCUIT IN FIGURE 3(B)

M1,M2,M5,M6 2.1um(W)/0.7um(L)

M3,M4 2.1um(W)/10.5um(L)

M7-M10 2.1um(W)/0.7um(L)

T ABLE2: MAIN CHARACTERISTICS OF OTA DESIGN AT BIAS CURRENT, IB

=100µA AND BIASING VOLTAGES= ±2.5V

Design parameters Value

DC open loop gain 0.2

Gain bandwidth product 300MHz

Input resistance 22.139ohm

Output resistance 12Kohm

Input current dynamic range -20uA to 20uA

Offset current 0.15uA

Power dissipation 3.96mW

IV. DESIGN OF PROGRAMMABLE OTA

A. Programming Technique

From simulation results of basic OTA circuit it is

observed that the OTA circuit is justifying its characteristics.

To introduce programmability in basic OTA circuit, all

MOSFETs are replaced by floating gate MOSFETs. Floating-

gate MOSFETs are conventional MOSFETs wherein memory

is stored in the form of charge trapped on floating-gate,

affecting its threshold voltage. Two antagonistic quantum

mechanical transfer processes, viz. hot e- injection and Fowler

Nordheim tunneling, alter the trapped charge on a floating

gate. It leads additional attributes to the FGMOS transistors

such as nonvolatile analog memory storage on floating-gate,

locally computed bidirectional memory updates and memory

modification during normal transistor operation. It is

represented by symbol showing injection and tunneling nodes,

attached at the common floating gate in Figure 5(a).

(a) (b)

Figure 5 (a): Symbol of a normal MOS with indirectly programmable floating

gate using injection and tunneling (b)Output Characteristics of a FGMOSFET

1) Tunneling

Charge is added to the floating gate by removing electron

from it by means of Fowler-Nordheim tunneling across oxide

capacitor. This shifts the curve (Figure 5(b)) to the right or in

other words threshold voltage of the transistor increases.

2) Injection

Charge is removed from the floating-gate by adding

electron on it by impact-ionized hot electron injection from the

channel to the floating gate across the thin gate oxide. This

shifts the curve (Figure 5(b)) to the left or in other words

threshold voltage of the transistor decreases.

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Figure 6: Circuit Diagram of proposed modified OT A design whose

specifications are programmable by field user to any desired value

Hence the modified OTA circuit consists of floating gate

MOSFETs, introduces programming ability of its design

specifications and the circuit is represented in Figure 6.

Design characteristics of OTA can be expressed in terms of

threshold voltages, by replacing gm of the respective

transistors with their threshold voltages. Therefore basic

characteristics of the design can be adjusted to desired value

after fabrication using transistors with programmable

threshold. Hence it save several simulation steps as accurate

prototype of OTA circuit can be developed using only first cut

equations, as well as, it makes the circuit reconfigurable.

Equations expressing sensitivity of each specification with

respect to respective FGMOSs have been derived and verified

using simulation results.

B. Sensitivity Analysis of Specifications

Output Current:-Sensitivity of output currentIout has been

evaluated using equation (1) which shows dependence on

threshold of FGMOSs M9 and M10. Thus the sensitivity of Iout

with respect to FGMOSFET M9 and M10 is calculated using

partial differentiation of Iout w.r.t Vt9and Vt10considering rest

thresholds constant, is given by:

(6)

(7)

Transconductance: - Sensitivity of transconductance gm has

been evaluated using equation (2) which shows dependence on

threshold of FGMOSs M9 and M10. Thus the sensitivity of gm

with respect to FGMOS M9 and M10 is calculated using

partial differentiation of gm w.r.t Vt9and Vt10considering rest

thresholds constant, is given by:

(8)

(9)

Input impedance: - Similarly sensitivity of input resistance

Zin has been evaluated using equation (3) which shows

dependence on threshold of FGMOSs M9 and M10. Thus the

sensitivity of Zinwith respect to Vt9 and Vt10considering rest

thresholds constant, is given by:

(10)

(11)

Output Impedance: -Sensitivity of output impedance Zout of

OTA expressed by equation (4) depends on threshold voltages

FGMOSs M6 and M7. Thus sensitivity of Zout with respect to

Vt6 and Vt7 is given by:

(12)

(13)

Offset Current: - However sensitivity of offset current of

OTA is calculated with respect to respective FGMOSs M3 and

M6 is given by:

(14)

(15)

The sensitivity of offset current can also be calculated w.r.t

the other threshold voltages of FGMOS.

C. Simulation Results demonstrating programming steps

used to program circuit specifications

The circuit diagram of Figure 6 representing modified

OTA design is simulated using BSIM3 level 49 MOSFET

models using T-Spice 0.35µm CMOS process . Voltage gain of

OTA is programmable independently using Vt4 i.e. using

FGMOS M4, as shown in Figure 7. Gain can be programmed

within range from 0.05 to 2 values using a FGMOS M4. The

transconductance can be programmed using FGMOS M7 in

range from 0.28mho to 1.2mho as shown in figure 8.

Moreover at particular sizing and biasing condition of the

proposed OTA circuit, the range of transconductance

magnitude programming in decibels is from 6 dB to 12dB

(0.28mho to 1.2mho) while change in output impedance and

gain need to be compensated using Vt6 & Vt4, respectively.

Similar input impedance of the design can be dominantly

programmed using Vt9 within programming range from

0.8mΩ to 1.2mΩ however, variation in gain with Vt9 need to

be compensated using Vt4. And output impedance is

programmed using FGMOS M6, Vt6 within range from 350Ω

to 125KΩ while variation in gain & transconductance need to

be compensated using Vt4 &Vt7 respectively. Hence with

modified OTA design, gain, transconductance, input and

output impedance can be programmed moreover, offset output

voltage/current of the circuit can also be programmed using a

FGMOS M8, i.e., programming Vt8 can adjust the offset of

the circuit. With iterative simulations and parametric analysis

of each specification, programming steps which would be used

to program design specification of OTA after fabrication, are

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tabulated in Table 3. Therefore the modified OTA design

provides on-chip programming of its specifications as well as

offset correction.

Figure7. Plot of Programmable Gain with the threshold voltage of FGMOS M4

Figure8. Plot of Programmable Transconductance with the threshold voltage

of FGMOS M7

Therefore, the final modified circuit consists of four

FGMOS which can program gain, transconductance, input

impedance, output impedance and offset current to any desired

value within the defined range with very high precision.(about

13 bit programming resolution is observed. Thus the final

circuit consists of four FGMOSs and its layout is shown in

Figure 9.

T ABLE3:- PROGRAMMING STEPS TO PROGRAM SPECIFICATIONS ALONG WITH

THEIR RANGE OF VARIATION

D. Final OTA circuit with required Floating gate transistors

and its Programming Steps:

The final modified programmable OTA circuit using

only four floating gate transistors M4, M6, M7 and M9, is

simulated using BSIM3 level 49 MOSFETs model along

indirectly programmable FGMOS’s simulation model using

Virtuoso, 0.35 um CMOS process. The design is also being

developed for fabrication and the layout is demonstrated in

Figure 9. The chip area occupied by the circuit is 65µm ×

54µm. Thus circuit specifications of modified high frequency

operational transresistance amplifier after fabrication to

desired value in the specific range using respective floating

gate transistors as expressed in form of programming steps in

Table 3. Moreover, the specifications can be programmed with

13bit programming precision. Hence, circuit specifications can

also be programmed continuously.

V. CONCLUSION

The proposed programmable modified OTA design are

simulated and results claimed that the circuit specifications

like Gain, transconductance, input impedance and output

impedance can be programmed along with offset voltage

compensation, using number of programming steps which can

be executed with the help of five floating gate transistor M4,

M6, M7, M8 and M9. All three design objectives, variation in

the specifications should be large and continuous, variation of

each specification should be independent of the other and

operating point of the circuit should not alter too much during

programming, i.e. offset current should not vary significantly

have been justified from our results. Therefore, we would like

to conclude by proposing OTA in which gain,

transconductance, input impedance and output impedance can

be programmable after fabrication. It finds applications in high

frequency systems where field programmable voltage control

current source is required and justifies a systematic approach

to develop programming ability in basic analog building

blocks using non-volatile, indirect field-programming ability

feature of floating gate transistors. Hence it can be used in RF

programmable current-mode systems which require low

power, thermally stable yet compact and simple hardware such

as universal filters, voltage controlled oscillators and various

other non-linear applications.

Figure 9: Layout of final OTA circuit in which gain, transconductance, input output impedance and offset current can be programmed independently using

FGMOSs (M4, M6, M9 and M7 respectively)

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