fully differential cmos voltage amplifier
DESCRIPTION
Design Project ReportECE 511 Analog Integrated CircuitsDesign of a CMOS fully-differential operational transconductance amplifierJoel Prabhakar Periathambi Ajit Narwal North Carolina State University 5th December, 2011Honor Pledge“We, Ajit Narwal and Joel Prabhakar Periathambi, have neither given nor received any unauthorized aid on this project”1Executive summaryDesign for the fully-differential operational transconductance amplifier (OTA) was implemented using a folded cascode opTRANSCRIPT
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Design Project Report
ECE 511
Analog Integrated Circuits
Design of a CMOS fully-differential operational
transconductance amplifier
Joel Prabhakar Periathambi
Ajit Narwal
North Carolina State University
5th December, 2011
Honor Pledge
“We, Ajit Narwal and Joel Prabhakar Periathambi, have neither given nor received any unauthorized aid
on this project”
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Executive summary
Design for the fully-differential operational transconductance amplifier (OTA) was implemented using a
folded cascode operational amplifier with PMOS-differential pair input and the required gain was
achieved by employing gain-boosting operational amplifiers. The common-mode feedback (CMFB)
circuit is that of a series-shunt feedback type (topology 41). All the design specifications were
comprehensively met; however, the operational amplifier gain suffers from cross-over frequency
distortion (further elucidated in section 2.4).
1.1) Design results
Compliance table for the fully-differential operational transconductance amplifier-
Parameter Specifications Achieved values Low Frequency Gain 92 dB 104.9dB Unity gain frequency >200MHz 553.8MHz Phase margin >70 deg, for unity gain feedback,
no external load 71.3 deg
Settling time (1% of final value)
<90 nsec with 4pF cap load 87nsec with 4pf cap load
Output Swing .8 V pk-pk single-ended 1.6 V pk-pk differential
0.849V pk-pk single ended 1.624 V pk-pk differential
Input common-mode range Overlap with output range >0.5-V 0.1 to 1.05 with an overlap of 0.669 V
CMRR >60dB 135.3dB
PSRR >60dB 245.1dB
Supply Voltage 1.8V 1.8V
Power dissipation <10mW 6.695mW
Slew rate >30 V/usec 33.08 V/usec
Input-referred noise voltage <10 nV/√Hz 9.96 nV/√Hz
Table 1
1.2) Design Methodology
At the onset attempts were made to establish the circuit using a folded amplifier with gain boosting
provided by a common-source second stage; rigorous calculations were followed by circuit simulations,
however the circuit displayed severe limitations when it came to the overlap of the common-mode
input voltage range and single-ended output (to the tune of 30mV),which rendered the circuit hard to
implement for unity gain feedback even though substantial gain could be achieved through the second-
stage. The second and the final circuit that was attempted was a folded cascode design. The proposed
circuit used PMOSes for input for they provided a higher slew rate in comparison to NMOSes for the
same current. Design on paper was based on the gain-bandwidth product (GBWP). Employing the
gpdk180 design kit the nominal size of the input PMOSes was randomly decided upon to provide enough
transconductance for a given current to achieve the basic specification of GBWP. One thing to be kept in
1Dr. B Floyd, Analog Integrated Circuits Lecture Notes-21, pg. 17-18
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mind while designing folded cascades is that the current through NM5 (and NM1) shall be larger than
the tail current through PM8. This prepared the arrangement for the worst case of differential wherein
all the current is drawn to one leg of the input PMOSes which can occur when if inputs rail to one side.
To make sure that the circuit endured the situation and the CMOSes were being driven in saturation (i.e.
the circuit gain is maintained) INM5 (and INM1)>IPM8. The bottom current sources thus were designed
accordingly and a rough idea of designing the other CMOSes in the circuit was gained. Fig.a) depicts the
circuit in discussion. The design criteria also lend a valuable range of VDsats for CMOSes in the circuit.
Since output swing, single ended, was 0.8 V the overdrive ІVDsatsI could be designed ≤ 0.25V, preferably
on the lower side to ensure a safety margin.
Fig.a OTA design circuit
Simulations were run for single ended circuit lending a gain of 57dB.
1.3) Gain-boosting amplifiers
The Δ(required gain) =92-57dB was the basis for the design of the gain-boosting amplifiers. The design
parameters for NMOS operational amplifier is as under. It was made sure that the differential amplifier
inputs were
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Fig.b Gain-boosting amplifier design
NMOSes if providing negative feedback to a PMOS. These operational amplifiers drive the gate of the
CMOS to ensure that there is the source of PM4 is set to a set voltage, and which if set properly can
allow only a Vdsat drop across PM6 and NM1 lending an output of the circuit a swing of 2×Vdsat within
each rail. Also voltage drop across PM6 becomes less dependent on Vout.
Fig b) is an NMOS gain-booster. Another PMOS booster was designed as well. A circuit of this type
comes with a few caveats. Firstly make sure that the feedback of the circuit is indeed negative or else
positive feedback shall lead to oscillations. Secondly the input common mode range for booster
amplifiers shall be within the range of the parent operational amplifier.
This circuit lends the capacitor between gate and source of PM4 Miller effect and Cgs becomes
effectively Cgs (1+A), ‘A’ being the gain of the internal operational amplifier. This leads to reduction in
frequency of the secondary pole which deteriorates the phase margin of the circuit2. This needs to be
countered and hence these boosters need compensation. This shall be discussed under the section-
Compensation, section 1.4.
2Jiang, Xin, Sanghyun Seo, and Yumin Lu. “CMOS Single Stage Fully Differential Operational amplifier
with 120 dB DC Gain” (2003): 1-2. Print.
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Fig.c Operating points for the main circuit, with the gain-boosting operational amplifiers inserted
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Fig.d Operating points for NMOS booster amplifier circuit
1.4) Common-mode feedback (CMFB) circuit
Common mode feedback is required in all fully-differential amplifiers having active loads. Here a
topology was used which senses the output voltages in terms of current flowing through PM0. This can
be classified as a sensor for the output voltage.
Fig.e Common mode feedback circuit
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Gate of PM0 drives the gates of PM5 and PM6 until the common-mode output voltage is set to the
desired point. The feedback is negative and the phase margin of the loop thus obtained has to be taken
care of to ensure stability of the circuit.
Fig.f Common-mode feedback operating point
1.5) Compensation
Every circuit which includes feedback needs to be checked for stability and hence compensated for
adequate phase-margin for operation over variations of process, voltage and temperature. As discussed
in 1.4 the gain-boosting amplifiers induced a Miller effect on Cgs of PM4 and reduced the secondary pole
frequency wp2 which deteriorated the phase margin of the loop, hence a capacitor was connected at the
high impedance node (gain-boosting operational amplifier output) to ensure that the loop gain dropped
to a low value at wp2. The unity-gain frequency of the gain-boosting operational amplifiers must lie
between the 3-dB bandwidth of the original circuit and its unity-gain frequency ensuring a high gain
during the bandwidth of the original circuit and such that at higher frequency the pole of the gain-
boosters doesn’t affect the stability of the system.
Likewise the CMFB circuit also needed compensation which was provided by the compensation
capacitor of the main operational amplifier.
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1.6) Supply independent biasing
While the initial stages of circuit design involved extensive use of ideal energy sources, these were
finally replaced with circuits which require a trigger circuit and the regular Vdd supply=1.8V.
These circuits were replaced by a current reference (Vgs based) biasing circuit. Here the produced
current is independent of Vdd. One can notice two feedback loops in the biasing circuit, one positive
and the other negative, here the negative feedback dominates the circuit and ensures circuit
stability. The necessary bias voltages were obtained by the usage of a MOS transistor and its
complementary in diode connection.
Fig.g Supply-independent biasing circuit design
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Fig.h Biasing circuit operating-points
Circuit simulation results
Fig.i Frequency response of OTA
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As seen from the response above the low frequency gain obtained was about 105dB with a healthy
phase margin of 71o. The gain-bandwidth product was 554 MHz and the 3dB bandwidth of the circuit
was 4KHz. These values not only meet but exceed the required specifications by a healthy margin.
Fig.j Frequency response of Common-mode feedback circuit
Low frequency gain=96.7dB, phase margin=70o
2.2) Step response and settling time
Settling time for this circuit is the time required for the output to settle within a band of 1% of the final
value after being subjected to a step input with a load of 4pF capacitor. PMOS inputs for the OTA
ensured a high slew rate and hence a low settling time. As can be seen from Fig.k) the settling time
achieved with this design was around 87.5 ns and the slew rate was around 33 V/µs.
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Fig.k Slew rate and settling time
2.3) Input common-mode range
The common-mode input range was measured by sweeping the common mode voltage and plotting the
frequency response of the design. The range of voltages for which the gain of the amplifier lies within +-
6dB of the peak gain was found to be from 0 V to 1.05 V.
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Fig.l Input common mode range
2.4) Output Swing
The differential output swing is the output that can be obtained from the OTA whilst a healthy gain is
maintained. The range achieved with this design was from -797.6 mV to 826.794 mV (Fig. m) amounting
to a peak-to-peak differential voltage of 1.624 V. The single ended output swing had a peak-to-peak
differential swing greater than 0.8 V (Fig. n) for both the positive and negative outputs. The circuit,
however, suffered from cross-over frequency distortion wherein NM0 (and NM1) (refer fig. e)) were
pushed out of saturation when the single ended output of the circuit was low. The gain henceforth was
truncated and a dip is observed at point M (refer fig. m)). This is evidently a limitation of the employed
CMFB topology; however, the problem could be worked out by appropriately sizing the CMOS sizes in
the CMFB circuit to ensure a Vout+ and Vout- were maintained at halfway through the input rails. The
output swing was limited to values around 1.3 V when attempts were made to do away with the
distortion.
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Fig.m Differential Output Swing
Fig.n Single Ended Output Swings
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2.5) CMRR & PSRR
The CMRR or the common-mode rejection ratio is an estimation of sensitivity of the circuit. The common-mode
gain was determined by providing a 1 V alternating supply to the common mode input and plotting the
response of the common mode output. Ideally operational amplifiers must have a very low common mode gain
so that the differential gain is unaffected by changes in the common-mode input. The common mode rejection
ratio was obtained by plotting the response of the common mode gain and the differential mode gain and then
subtracting the latter from the former over a wide frequency range. One thing that was kept in mind while
performing the above test was that gains for both differential and common-mode were obtained using two
samples of the same OTA to avoid signal mixing and crossing-over.
Fig.o) Common-mode Rejection Ratio
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The power supply rejection ratio or PSRR is a measure of circuit robustness against supply variations, both in
Vdd and ground. The PSRR was calculated by plotting the differential gain while applying only a common mode
input to the differential pairs of the OTA and adding a 1V AC to the power supply, versus the differential mode
gain.
Fig.p) Power Supply Rejection Ratio
In both the scenarios it can be observed that the transconductance amplifier exhibits a high common mode
rejection ratio and power supply rejection ratio.
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2.6) Noise
The design exhibited a noise, referred to the input, less than 10 nV/√Hz. The main culprit devices were the
current sourcing NMOS transistors in the cascade circuit (namely NM5 and NM1, refer fig. a)) followed by the
input differential pairs.
Fig.q Equivalent input-referred noise response
Project learnings
The endeavor leading to the project provided invaluable insight to the circuit operation from a design
perspective. Among many a thing the behavior of CMOS devices under different operating conditions was
noticed and various trade-offs were dealt-with through various iterations that went into the design. In the
nascent stages of circuit simulations it was realized the CMOSes required to be sized and biased appropriately
to obtain an evenly distributed Vds among circuit elements. This lesson could save substantial time in the analog
circuit design. The voltages for common-mode to be set by the feedback loop provide important information
about the voltages to be selected for biasing. Also valuable confidence was gained in understanding and
working on the tool CADENCE. The design can be further improved by using further sizing the CMOS members
of the CMFB circuit to ensure a healthy gain throughout the input range. A rail-to-rail input operational
amplifier could be used to achieve input common-mode range between any values between the input rails.