Introduction
Motivation
For the realization of a mechanical flexible sensor system-in-foil all rigid
components, like crystal oscillators as frequency reference, have to be
avoided. Therefore, a direct conversion receiver for the 27 MHz ISM band is
realized, where a high-Q BPF is used for band selection to diminish
interferences. To keep the foil system simple and flexible, an integrated
on-chip BPF is desired. As inductors for lower frequencies are quite large,
and Q factors of on-chip inductors are very limited, they are replaced by
active components. Since resistors also use a large area on the chip and
no clock reference is available, neither RC filters nor switched-capacitor
circuits can be used. Therefore, the BPF is realized by a GmC circuit,
which only consists of OTAs with the transconductance Gm and capacitors
with the capacitance C, and can be well integrated in common CMOS
technologies (Wangenheim, 2008; Schaumann et al., 1990).
Filter requirements
For the band selection of the 27 MHz direct conversion receiver,
neighbouring bands at 26 and 28 MHz with possibly comparatively high
radiated power values of several hundreds of Watts, and other less powerful
transmitters in between, should be filtered out. Therefore, an attenuation
of at least 30 dB at 0.5 MHz offset and of 50 dB at 1 MHz offset, as well as
a maximum ripple of 1 dB in the pass band, are the specified filter characteristics.
A survey of different filter topologies shows that a Butterworth filter with
3 different stages gives the best compromise between circuit requirements
and filter characteristics for the mentioned specifications. For this
BPF, two stages with a respective Q factor of around 200, and one stage with
a Q factor of around 100, are chosen.
Basic GmC circuits: (a) integrator; (b) emulated
inductor; (c) negative conductance; (d) voltage amplifier.
(a) RLC resonator; (b) emulated resonator in GmC
technique and decoupling OTA; (c) same as (b) but fully differential.
GmC circuits
Basic GmC circuits
To realize a BPF, different basic functions in GmC technique are needed.
Figure 1 shows the used basic GmC circuits which
are an integrator, an emulated inductor, a negative conductance and a voltage amplifier.
The transfer function of the integration shown in Fig. 1a is derived in
Eq. (1) (Amirpour, 2015):
VoutVin=VC1V1=I1/jωC1I1/Gm1=Gm1jωC1.
Extending the integrator circuit by a feedback OTA, the behaviour of an
inductor can be emulated by two OTAs, which work as a gyrator, and a
capacitor. Since phases of currents and voltages are interchanged at
inductors and capacitors, the inductor can be emulated as a capacitor, where
voltages and currents are interchanged at the in- and output.
Figure 1b shows the respective circuit and
Eq. (2) proves the proportional behaviour of the reactance versus the
frequency and derives the value of the emulated inductor:
Zin=VinIin=VL1-IL2=VL1-VL2GmL2=1VCL1VL1GmL2=Eq.(1)jωCL1GmL1GmL2⇒L=CL1GmL1GmL2.
Figure 1c shows the negative conductance. It is
negative, since the differential input voltages are interchanged.
Figure 1d depicts the voltage amplifier, which
is described by Eq. (3). An additional load conductance GL at the output
changes the voltage amplification value.
VoutVin=-V4V3=-I4/Gm4V3=I3-I5Gm4V3=Gm3Gm4-VoutGLVinGm4⇒VoutVin1+GLGm4=Gm3Gm4⇒VoutVin=Gm3Gm4+GL
GmC bandpass filter (BPF) stage
With the basic GmC circuits, a GmC BPF stage can be realized with 4
OTAs and two capacitors. The BPF consists of an emulated lossy LC resonator
with an added negative conductance -GmQ to compensate for the sum of
the losses of the OTAs' output resistances and capacitors through the
parallel conductance GLP,OTA. The Q factor can be adjusted through the
value of GmQ. To decouple the different filter stages, another OTA is
used between the stages with the transconductance Gmd. Figure 2 shows a
conventional RLC circuit (Fig. 2a), the respective GmC equivalent with decoupling
(Fig. 2b) and the corresponding fully differential circuit (Fig. 2c). Since the resonant
circuit is tuned to resonance at the desired frequency, the load can be
described as a real conductor. The decoupling OTA and the Q factor OTA form a
voltage amplifier, with the amplification determined according Eq. (3) as
the ratio between Gmd and GmQ + GL. To minimize the dynamic
range requirements of the OTAs, the voltage gain should ideally equal one.
Therefore, the values of CCP, CLP and the transconductances should
be chosen in a way, that the voltage swing is similar at all nodes.
Additionally, the OTAs should be identical or similar, to reduce the
development effort. To realize a small GmQ, two similar transconductors
are used in parallel, which are partly cancelling each other. For a better
performance, a fully differential circuit is used. The resulting structure
can be seen in Fig. 2c.
The resulting centre frequency and Q factor of the BPF stage shown in Fig. 2
is noted in Eq. (4):
f0=12πCCPLP=Eq.(2)12πGmL1GmL2CCPCLP;Q=1GLPCCPLP=1GLP,OTA-GmQCCPGmL1GmL2CLPwithQ=f0fBW.
Operational transconductance amplifier (OTA)
Requirements
The central part of the GmC BPF are the OTAs. To achieve a constant centre
frequency f0 and Q factor over the desired dynamic range, very linear
OTAs are required. As f0 is more critical, we first define the maximum
allowed deviation of f0 in respect to the filter bandwidth fBW as
ec,max = Δf0/fBW to determine the OTA's required
linearity. Then, Eq. (5) gives the condition for the maximum variation of
the transconductance ΔGmLx,max which depends on the Q factor (Mader, 2016):
12π1±ΔGmL1GmL11±ΔGmL2,maxGmL2,maxGmL1CCPGmL2CLP=12πGmL1GmL2CCPCLP±ec,maxf0Q⇒1±ΔGmL1,maxGmL11±ΔGmL2,maxGmL2=1±ec,maxQ.
If we assume the same relative variance of the different OTAs, we get the
result in Eq. (6):
1±ΔGmL1,2,maxGmL1,2=1±ec,maxQ⇒ΔGmL1,2,maxGmL1,2=ec,maxQ.
If we choose ec,max to 0.1, for a Q factor of around 200 a maximum
non-linearity of around 0.5 ‰ or around -66 dB is required.
The OTA should keep the linearity requirements in a dynamic range of
single-ended peak-to-peak input voltages up to 150 mVpp,se.
Circuit implementation
Like most analogue circuits, the OTA is based on a differential amplifier.
Different techniques like cross-coupled amplifiers or current feedback can
be used to linearize differential amplifiers. At cross-coupled amplifiers,
two different amplifiers are placed in parallel and designed in such a way,
that the third harmonics cancel each other, but the first harmonic is not
limited too much. This is an energy-efficient way for a linearization and
can be realized by different transistor currents and widths, but is strongly
dependent on process variations and therefore not used in the realized OTA.
Current feedback can be realized by a source degeneration resistor RDG,
and leads with a large resistance value RDG to an acceptable linearity
despite process variations. The large resistance value can be realized by
either resistors or MOSFETs. Because of the limited supply voltages and the
relatively large desired dynamic range, the transconductance Gm will be
limited in all cases.
(a) Similar basic concept and (b) schematic of the
used OTA in the BFP stage.
To achieve the desired linearity values in the developed OTA, a source
degeneration linearization technique is used together with a feedback
structure, which additionally keeps the voltage VGS more stable.
Therefore, the gm of the differential switching transistors stays also
more stable and hence the amplifier's linearity is further improved.
Figure 3 shows a similar basic principle (left panel) and
the schematic of the used OTA (right panel). For a high linearity and low process
variation dependence, the degeneration is realized by the resistor RDG
and not a MOSFET. Together with the transistors N3 and N4,
the resistor RDG forms the amplifier's core. In Fig. 3 (left panel) the input
voltage is transferred to RDG by the feedback loop. The same happens
in Fig. 3 (right panel), although the feedback amplifiers have a different input
impedance to be realized in a novel, more compact and power efficient way.
The gate-source voltage VGS and therefore the gm of the transistors
N3 and N4 are also kept more stable by the feedback loop. For
example, if Vin+ is increased, the gate potential of P1 is
decreased and the gate potential of N3 increased. Consequently, the
voltage over RDG and common source voltage of N1 and N3
increases. If it increased too much, the feedback loop would decrease it
again. Hence the feedback loop stabilizes the voltage over RDG and
VGS of N3. Since the amplifier's output resistance leads to
distortions and additionally decreases the quality factor, high output
resistances are needed. Thus, cascode current sources (P5 to P8)
and thick oxid transistors (N9 and N10) are used at the output
path. Cascode current mirrors also enhance the function of the feedback
controller (N5 to N8). Different supply voltages are needed to
keep the transistors in the proper operation region and realize the desired
dynamic range. The typical supply voltage of the used 130 nm CMOS technology
is 1.2 V. Additionally, supply voltages of VDD1 = 1.8 V and
VDD2 = 2.5 V are used. Since the voltage is split up between the
different transistors, the use of a higher voltage is not critical here.
Therefore, at no transistor a voltage of more than 1.2 V is applied. A
proper ramp up of the supply voltage prevents the destruction of the
transistors at power up.
To keep the output common mode voltage constant, a CMFB control is added,
which controls the upper output impedance by VCMFB1 and VCMFB2 of
P5 to P8. The output has a simulated standard deviation of 13.3 mV
and ensures a proper operation with global and local process variations.
Since local process variations significantly deteriorate the OTA's
linearity, an offset feedback (OSFB) control circuit is required. It
consists of a differential pair with a negative feedback via VOSFB1 and
VOSFB2 at N9 and N10. A large time constant is used in the
controller so that the influence on the RF-signal is strongly mitigated. For
the realization of a simulated standard variation of approx. 4.5 mV and
maximum deviation of approx. 12 mV, a high gain and consequently a
controller circuit with two stages is used. To tune the OTA's
transconductance to the required value after processing, a digital tuning
network is added. In it, the value of RDG can be switched in a binary
way in the required region.
Results
Results of DC and PSS simulations of the OTA, all done with the simulator
spectre of the design environment cadence, are shown in Fig. 4. In Fig. 4
(left panel), the OTA's differential Gm at DC over the input voltage at an
operating point of 1.2 V can be seen. As mentioned earlier, the linear
region increases with decreasing transconductance and increasing resistance
RDG. In the used OTA, a standard value of around 100 µS is used.
Figure 4 (right panel) shows the amplitude spectrum of the periodic differential
output voltage with a capacitive load equivalent to the filter circuit with
a 27 MHz input voltage of around 300 mVpp,diff. The respective SFDR is
approx. 85 dBc. It can be seen, that the linearity in the respective input
voltage range is higher than required, which further improves the filter stage behaviour.
Comparison of the developed OTA.
Publication
CSI 2008
JSSC 2009
APCCAS 2012
This work
Reference
Calvo et al. (2008)
Lo et al. (2009)
Kuo et al. (2012)
Process (µm)
0.35
0.18
0.18
0.13
Supply voltage (V)
1.8
1.2
1.2
2.5
THD
-58 dB
-54 dB
-74 dB
-80 dB
0.66 Vpp
0.6 Vpp
0.6 Vpp
0.3 Vpp
@ 10 MHz
@ 20 MHz
@ 20 MHz
@ 27 MHz
Linear input range (V)
1
1
1
1
Gm (µS)
630–1310
2–110
1–155
50–150
Power (mW)
1.1
1.58
1.9
0.3
Type
measurement
measurement
measurement
simulation with local and global process
variation and layout consideration
(a) DC simulation with Gm vs. the input voltage Vin
for different resistor values RDG (Mader, 2016); (b) differential
output amplitude spectrum at nominal corners for a 27 MHz input with
approx. 300 mVpp,diff, determined with a PSS simulation (Reiter, 2016).
The current consumption of one complete OTA is around 119 µA, whereof
90 µA are consumed by the OTA itself, 20 µA by the CMFB and
around 9 µA by the OSFB.
Table 1 gives a comparison between different OTAs and this work. It can be
seen, that the OTA in this work has a high linearity and a much lower power
consumption. The high linearity is critical for the given application.
Filter stage results
To determine the performance of the whole filter stage circuit considering
global and local process variations in a widespread parameter range, corner
simulations of the main devices and Monte Carlo (MC) simulations with
200 runs and latin-hybercube option for all devices are performed. In Fig. 5
(left panel) the time domain signal of the input and output voltages can be seen.
Since the voltages are in-phase, the filter stage is tuned to 27 MHz. In
Fig. 5 (middle panel), the magnitudes of the filter stage's transfer function are
shown for corner simulations of the mainly used transistors with correction
of the tuning network. In Fig. 5 (right panel), the same is depicted for the
largest deviations of the 200 latin hybercube MC runs without and with
correction. The corrected transfer functions almost equal the nominal one.
The remaining deviations in maximum magnitude, centre frequency and Q factor
can be tolerated, as they are not critical to the filter stage's behaviour.
(a) In-phase differential input and output voltages Vin,
Vout of the filter with 27 MHz (PSS simulation) (Mader, 2016);
(b) magnitude of PSS simulated transfer function for corners of mainly used
devices (corrected by tuning network); (c) magnitude of PSS simulated
transfer function of the filter for largest deviations from the 200 MC latin
hybercube simulations without (solid, ∧, *) and with tuning (dotted, smaller
∧, *) (Reiter, 2016).
Simulations with extracted RCC parasitics from the OTA's mask layout show, that
there is hardly any effect on behaviour at the desired frequency. Since the
filter consists of many interconnected OTAs with capacitive loads of more
than 500 fF at each port, the value of additional capacitive parasitics
arising from the filter wiring can simply be subtracted from the capacitor
values. Therefore, layout parasitics have hardly any effect on the filter
behaviour at the desired frequency. The current consumption of one filter stage
which consists of five OTAs, each including a CMFB and OSFB, is less than 600 µA.
Conclusion
For a direct conversion receiver of a sensor system-in-foil, a fully
integrated, active BPF filter stage with a Q factor of more than 200 is
developed. It is simulated as a fully differential GmC design in a
130 nm CMOS technology. Therefore an OTA with a novel feedback concept and a
resulting SFDR of more than 82 dB over an input range of 300 mVpp,diff
is developed, in order to keep centre frequency and quality factor constant
despite varying input levels. To maintain the functionality despite local and
global process variations, a CMFB, OSFB and a digital Gm tuning network
are used. The results are validated by MC PSS simulations with latin
hybercube and 200 runs and corner simulations of the main devices. Resulting
from simulations with the OTA's extracted parasitics, no significant chance
is expected for the filter behaviour after layout. The current consumption of
the whole filter stage is less than 600 µA. In comparison with other
OTAs, the developed one has a superior linearity and lower power consumption.