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Integrated Continuous-Time Filters forRF Applications
Narendra M.K. RaoMaxim Integrated Products
COURSE OUTLINE1. CONTINUOUS-TIME FILTERS2. SYNTHESIS TECHNIQUES 3. FILTER BUILDING BLOCKS 4. TUNING5. PRACTICAL CIRCUITS6. SUMMARY & CONCLUSIONS7. REFERENCES
1. CONTINUOUS-TIME ACTIVE FILTERS -TRADITIONAL APPLICATIONS
Continuous-Time (CT) Active Filters are traditionally used for :
1. Interface Applications –• Anti-Aliasing, and, Reconstruction – “Support” functions.
Typically the signal frequencies are relatively “low” and, “real” filtering is performed in the Digital domain to take advantage of sophisticated DSP techniques - several kHz to tens of MHz
The CT filters act transparently to permit A/D and D/A functions, without appreciably degrading the spectral contents and adding noise, distortion, etc.
2. Direct Filtering – Main filtering function• At “high” frequencies, CT filters perform all of the signal processing in the
analog domain to realize Magnitude and/or Phase (Delay) Shaping – DSP is not an option; several kHz to hundreds of MHz.
1. CONTINUOUS-TIME ACTIVE FILTERS -TRADITIONAL APPLICATIONS, contd.
1. Interface Applications
Anti-Aliasing
MainFilter
Reconstruction
MainFilter
A/D D/A
In Out
Main FilterIn
Out
Out
Sampled-Data
Digital
Continuous-Time
2. Direct Filtering
1. CONTINUOUS-TIME FILTERS -ACTIVE VS. PASSIVE
• Active filters circuits are traditionally preferred to passive circuits because of integration and programmability- a direct consequence of growth in microelectronics.
• Primary limitations of active CT filters are –additional power consumption, limited Dynamic Range (DR), tuning, noise, etc. - problem is exacerbated in RF applications.
1. CONTINUOUS-TIME ACTIVE FILTERS -RF SPECIFICS.
• In general, RF Baseband (BB) filters’ specifications are more demanding - sharper channel-selection, wider DR, lower noise. Presence of PGA and increased linearity of ADCs can mitigate some of the filter specs.
• Applications are continuously increasing – direct conversion receivers, programmable BW, switchable and reconfigurable filters – exacerbating the filter specs.
• Specifically, the biggest problem is the presence of blockers that increase filter DR specs. resulting in excessive power consumption – shifting the burden to ADCs is unacceptable !
1. CONTINUOUS-TIME ACTIVE FILTERS -RF BB FILTER SPECS.
• Frequency range : 100kHz to ~ 25 MHz; Passband ripple = 0.5 to 2dB; stopband rejection = 20 to 50dB, up to 100MHz .
• SFDR :in-band ~ 40 to 55 dB ; IIP3 ~ 0dBVout-of-band ~ 55 to 75 dB ; IIP3 ~ +20 dBV (blockers).
• Power budget : 1 to tens of mW.
References : [1] – [7]
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits.
• Given: Well defined Network Transfer Function H(s).• Problem: Realize an IC implementation.
• In theory, any real Causal H(s) can be synthesized by interconnecting a Negative Immittance Converter (NIC) and R, C elements – if only we can guarantee 0.1% tolerance elements , even for modest applications [8] !
• In practice, need low sensitivity, commercially viable realization.
nmni
isib
mi
isia
sDsNsH ≤−−−−−
∑=
∑===
1
1)()()(
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits, DF structures.
• Direct-Form structure is readily realizable with integrators, summers and amplifiers for moderate Q (<10) and for moderate applications – Q<10; m,n < 5, freq. ~ 10MHz. This is somewhat practical for limited applications.
• With increasing m,n, the DF structure becomes increasingly sensitive to co-efficients of D(s).
• In addition, active RC-circuits exhibit active sensitivity, viz., sensitivity to active elements’ parameters (Gain, Ft), that degrade via D(s), leading to instability even in modest applications.
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits, Cascaded BIQUADs.
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isibsibib
l
isiasiaia
sH ≤−−−−−−−∏=
++
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++=
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210)(
• Decompose the high order H(s) into biquadratic sections to distribute the sensitivity problem over multiple sections., making sure there is no single major contributor.• Realize each biquadratic section independently, and, • Connect all the sections in a cascade fashion, in an appropriate sequence to realize the overall transfer function.
This method has been very successful and there is a plethora of literature available from RC-active network circuits.
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits, BIQUAD implementations.
All circuit implementations of Biquadratic (biquad) sections fall under 2 broad categories -
1. Single OPAMP (OA) based biquads [9,10]:• Uses one OA and RC elements. All of these circuits employ OAs in finite gain,
closed loop configurations and exhibit poor sensitivity performances and limited programmability.
• A sub-section of this class, called "Sallen-Key" structures, exhibit only somewhat better sensitivity. Same is true for Rauch filter [13] as well.
• Not suitable for High-frequency (HF), integrated CT filters, particularly for RF.
2. Multiple OAs based or Direct Form biquads [9,10]: • There are two methods available. The first one called the Generalized Immittance
Converter (GIC) based approach is very successful for RC-active synthesis, and is unsuitable for CT filters due to the unavailabilty of accurate, stable resistors.
• The second one is the direct form biquad realization using 2 integrators, also known as State Variable Loop or Two Integrator Loop synthesis method, and this has become the de facto standard method in integrated CT filter design.
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits,
Two Integrator Loop BIQUAD implementationThe most general form of a two integrator loop is shown below usingintegrators, summers and amplifiers.
ωo/s ωo/s
1/Q
Σ
Σ
ΙΝ OUT
+
+
+
+
__
k2
k1
k3
BPF
LPF
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits,
Two Integrator Loop BIQUAD implementation….cont’d• The above structure has been the subject of extensive research, and is realized in
many different circuit forms, depending on the application - all such circuits have potentially good sensitivity properties.
• Note that by properly combining the signals at different nodes, using co-efficients k0, k1, k2, a fully biquadratic output function is realized.
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=
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ω
ωωω
sQ
s
s
Q
ss
ssbpfH
++=
++=
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits, Ladder structures.
For applications with stringent sensitivity requirements, designers are forced to return to classical LC filters because passive LC filters, i.e., lossless LC ladder sections with resistive terminations, exhibit -
• zero sensitivity to LC elements at attenuation zeroes,• low-valued sensitivity throughout the passband,• low-sensitivity ( < 1) to resistive terminations,• high attenuation peaks in the stop-band,• low noise - thanks to noiseless L, C, and, finally• extensive literature exists in this field.
This has led to the development of CT filters (and active RC, switched and Digital filters) to simulate LC filters and preserve the low-sensitivity properties.
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits, Ladder structures, contd.
There are many ways of realizing active filters to simulate passive LC prototypes -
1. Direct simulation of inductance using active transconductors/gyrators.
2. Signal flow graph technique.3. Frequency transformation techniques using
frequency-dependent-negative resistors.Only the first two methods are directly applicable to integrated CT filters; the last one is more relevant to specific active-RC circuit synthesis.
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits, Ladder structures,
Active Inductance simulation
• Simulate and replace each inductance, in the passive prototype, by an active circuit known as a gyrator or a Positive Immittance Inverter (PII).
• A simple Gm-C based active inductor is shown below. (Note : Active Op-amp with feedback isalso
sCmGmGinV
inI 21= sLmGmG
sCinIinV
inZ ===21 21 mGmG
CL =
I = 0Gm1 Gm2
Iin
+Vin
Iin
CI = 0
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits, Ladder structures,
Active Inductance simulation…..contd.
• The circuit, excluding the capacitor, in the previous page is commonly known as a gyrator or a Positive immittanceinverter.
• Also note that the Gm1-C combination is an integrator. Other implementations of integrator include op amps, with the Capacitance in a feedback configuration (OA-C) and will be discussed later.
• Finally, a floating inductor is realized using two back-to-back gyrators [12-14].
• Very high quality active inductors are also realized using Op-amp in feedback configuration [9].
2. SYNTHESIS TECHNIQUES -Traditional RC-Active Circuits,
Cascaded Biquads vs. Ladder Structures.
• There is some confusion about the relative merits of biquads and cascaded biquadsstructures.
• In general, ladder structures are less sensitive for very high quality filters, where the pole (zero)-pair Q >10.
• For Q<3, there is no appreciable difference between the two structures from sensitivity considerations, and Biquads are preferred because of their direct, modular structure, and ease of design and debugging.
3. CT Filter Building Blocks• Fundamental building blocks for CT filters
include transconductors (Gm), integrators summers and amplifiers.
• In general, an Integrator is the most critical fundamental block, and is the bottleneck in practical circuits [15,16]. Good integrators make good systems.
• Gms are equally critical in blocks that implement integrators in non-feedback configuration (see Gm-C integrator in inductance simulation).
3. CT Filter Building Blocks –Integrators
• The Integrator is by far the most vital building element in active filter design.Ideal Transfer function is :
For real frequencies, ωo is the unity cut-off frequency.• Magnitude |H(jω)| varies as 1/ω, and,• Phase < H(jω) is a constant -90o .• These two requirements are fundamental and need to be
satisfied over the entire frequency range of interest.• The important integrator characteristics are – infinite dc-gain
(Ao) , phase error (Θε) and dynamic range (DR) [16,17] .
ssH 0)(ω
=
3. CT Filter Building Blocks –Practical Integrators ….limitations
Practical integrators exhibit the following transfer function :
1. Finite DC gain = Ao (~ ωo/ωl ), which can range from 20dB to >100 dB.
2. Phase error , or departure from 900 , at frequencies well below and above the integrator unity frequency. For RF systems, the response needs to be close to ideal up even in stopbands due to the presence of blockers. The phase response affects the group delaydirectly. Note that the phase error is more important than the magnitude BW, because this degrades the Q-factor, and Group Delay (τ) directly [18].
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3. CT Filter Building Blocks –Integrators Mag-Phase plot.
3. CT Filter Building Blocks –Integrator Gain-Magnitude Error
Gain-magnitude error of integrator :• Finite gain of an integrator, Ao, contributes to a positive
phase error (phase lead) which is 900 at dc, and reduces progressively as the gain starts falling at -20 dB/decade. Usually this phase lead shows up at low frequencies only and is not a major problem, except where low-frequency group delay is important, such as in zero-IF circuits.
• At high frequencies, the parasitic poles cause magnitude error, positive or negative, that affect the frequency selectivity properties. This is similar to frequency tuning error and is less offensive than passive R,C accuracy.
3. CT Filter Building Blocks –Integrator Phase Error Θε
Integrator Phase Error Θε is the single most seriousoffender that decides the frequency selective properties ofthe integrator and the filter.Sources of phase error are :1. Finite DC gain of Active element , Ao, that contributes to
a phase lead, and is dominant at low frequencies.as we noted.
2. Parasitic poles due to the finite BW that introduce a phase lag (LPF) – worse with increasing frequency.
3. RHS zeroes due to the active elements and the parasitics, and are similar to that due to parasitic poles (actually worse as magnitude increases with frequency).
3. CT Filter Building Blocks –Phase Error Θε and Biquad Q-factor
• The significance of the phase error Θε can be appreciated by defining an effective Q for the integrator, Qinteg, equal to the inverse of the phase error (in radians)
` Qinteg = 1/Θε ; 1 degree of phase error gives Qinteg = 57;Since two integrators make up a biquad, the inherent natural Q of the biquad isQn=[Qinteg /2] ~ 30.
• Qn distorts the ideal design value of the biquad Q, Qb, to yield Qactual =1/(1/Qn + 1/Qb).
• In the present situation, for Qb=1.5, Qn causes a 5% distortion.• Depending on the application, the ΔQ/Q error places a minimum bound on |Qn|, or a
maximum bound on | Θε |.• Example : ωo =2π x 5 MHz, Qb= 2.5,
For, |ΔQ/Q| < 10% | Qn | > 25 , and, Qinteg = 2x25 = 50 | Θε | < 0.02 radians =1.14o,
ωp > 2π x 50 x 5 MHz = 2π x 250 MHz Ft of active element is 250 MHz !!• Note that a -ve Θε (phase lag) increases the effective biquad Q-factor while a +ve
Θε (phase lead) decreases (dampens) Q.
3. CT Filter Building Blocks –Effect of Integrator errors on Biquad-Q
Effect of Ao and Θε on Biquad Q-factor :• It can be shown that for a biquad, (two-integrator loop),
a finite Ao causes an error in ΔQ as given by ΔQ/Q ~ -2Q/Ao , almost independently of frequency.
• Therefore the problem worsens in high Q filters. • Note that Ao always reduces Q.• The effect of Θε due to " ωp " causes a ΔQ as given by
ΔQ/Q ~ - 2Q.(Θε . ω /ωo ) around ω = ωo.• The problem worsens with increasing Q , and more importantly with
increasing frequency, because | Θε | due to " ωp " increases.• In general, at low frequencies, a finite Ao reduces Q, while,
at high frequencies, a -ve Θε , due to " ωp " , increases Q.
3. CT Filter Building Blocks –Reducing Integrator errors
• Improving integrator performance - Ao and Θε :• While it may appear that by predistorting Q, the effects of
finite Ao and Θε can be compensated, the problem lies in that both Ao and Θε normally vary significantly with process, temperature etc.
• Therefore, the design goals are :• a large Ao,• a small |Θε | or a large " ωp ". • Integrator (Gm) dc-gain and phase error improvment/
compensation have been the topics of extensive research.
3. Filter Building BlocksDynamic range & Noise.
Dynamic Range (DR) and noise are important performance criteria as the industry moves towards system on a chip, lower supplies and higher bandwidths – RF !
• In general, Dynamic Range (DR) is defined as the ratio of the maximum to the minimum signal [13, 16, 17].
• The maximum signal is always associated with distortion – THD and/or IIP3 are needed to specify this meaningfully.
• The minimum signal level means the smallest detectable signal, which may or may not be below the noise level.
• For RF systems, SFDR (Spurious-Free Dynamic Range) is one convenient measure of DR, and is defined as the signal-to-noise ratio where the third-order intermodulation products’ power equals the noise power.
• SFDR and IIP3, and Ni (input-referred noise power) are related as : SFDR = (2/3)*(IIP3 – Ni) , where all quantities are in dB/dBm [15].
3. Filter Building BlocksIntegrator DR
• Filter DR depends on the transfer function synthesis technique (Q) and DR of an integrator.
• For an integrator, a simplified analysis can be used to arrive at the upper limit to For the simple case of thermal noise, the maximumsignal is VDD/2, and limited by the supply voltage.
• An integrator of any type, RC, Gm-C, MOSFET-C, has at least a input referred thermal noise source vin given by,
mGkT
finv
kTR4
24 ==
Δ
3. Filter Building BlocksIntegrator DR… cont’d
• Total output integrated noise is,
where,
ω0 is the integrator unity-gain frequency, • Rp is the leakage resistor of the capacitor, and, • Q is the corresponding quality factor at ω0 .
CkTQ
onv 22 =
Gm1 = 1/R
C4kTR
+Vext. --
+Vout--
pRmGpRCQ ...0 ==ωCmG
=0ω
mGkT
finv
kTR4
24 ==
Δ
3. Filter Building BlocksIntegrator DR… cont’d
• For the integrator, the theoretical maximum DR can be calculated as DRmax. = 10 log10 [( V2DD /2 ).C/(2kTQ) ] = 10 log10 [ V2DD .C/(4kTQ) ]
• Example:• C = 2 pF, Q = 5, VDD = 3 V DRmax. = 83 dB.• The above calculation for DRmax. is very simplified and optimistic, and
does not consider noise sources due to the active element, bias current sources, 1/f noise etc.
• Nevertheless, this value of DRmax. offers an upper benchmark.• A practical integrator can be modeled as having a noise source = F.(v2
in /Δf), where F is a noise factor for a given integrator, F > 1, and (v2
in /Δf), = 4kT/Gm .
• This approach provides more insight because the filter circuit noise is calculated more easily if each integrator is associated with just one noise source F.(v2
in /Δf), Associating an integrator with all of the noise sources due to passive and active devices is very tedious, although more accurate.
3. Filter Building BlocksIntegrator DR & Biquad Noise
Example: Using the above approach, the total noise output v2
on for a bandpass filter (bpf), realized by a generic two-integrator loop, is given below [19].
• for convenience, each integrator is assumed to have the same noise source F.(v2
in /Δf), and (v2in /Δf), = 4kT/Gm ,
• the biquad Q-factor is now labeled as Qb, and,τ is the group delay at dc, and , t = 1/(ω0.Qb).
• Keep F (integrator noise factor) small, and τ large for low noise !
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sbQ
s
s
bQ
ss
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3. Filter Building BlocksMaximizing DR -
Maximizing DR :• It has been shown [20] that there is a fundamental relationship among DR, power dissipation, total
circuit capacitance, signal swing, circuit Q, order of filter and frequency of operation. • Factors affecting DR • Large Ctotal• - Higher Gm or lower impedance level.• Higher power dissipation.• Gms/OAs need to drive higher loads.• Large chip area.• Large signal swing • - Large VDD (industry trend is towards lower VDD).• Linearity of Gms at large swings is difficult (distortion may negate this factor).• Higher Q means more noise and less DR.• Higher BW means more noise and less DR.• Higher order filter (more integrators) means more noise and less DR.• Higher temperature means more noise and less DR.• Large tuning range affects signal swings, and in general, reduces DR at some settings.• Large noise factor for integrator means more noise and less DR.
3. Filter Building Blocks –Practical Integrators
Attributes of high performance integrators:• Unity gain frequency ωo should be stable and well controlled over
process, supply and temperature accurate tunability and trackingover VT.
• Large signal handling capability, at both input and output terminals, along with low distortion, and low noise.. This is very important for RF systems as noted earlier.
• Good high frequency characteristics for both magnitude and phaseresponses.
• Availability of fully differential and balanced structures.• Programmable ωo over a wide frequency range.All integrators exhibit problems, such as, finite PSRR, CMRR, and in extreme cases, start-up and latch-up issues. Invariably power consumption is the challenging spec. in most cases.
3. Filter Building Blocks –Practical Integrators… cont’d
• The 3 basic implementations for integrated CT filters : Gm-C, Opamp-RC, and MOSFET-C integrators.
• Of these, Gm-C is normally the open-loop integrator employin the active Gm, and the other two employ op-amps in feedback configuration.
• High DR demands a highly linear Gm, and highly linear input stages in the op-amps. There is a myriad of highly linearized circuits available in literature [13, 20].
• Both Gm and Op-amps need to have high “dc gain” and wide bandwidth because they directly affect the magnitude and phase response of the integrators. As a rule of thumb, the BW of the active element BW should be at least 20*Q*ωo.
3. Filter Building Blocks –A Basic Gm Cell
3. Filter Building Blocks –Gm with source degeneration
3. Filter Building Blocks –Cross-Coupled Gm cell
3. Filter Building Blocks –Extended linear Gm cell.
3. Filter Building Blocks –MOSFET-C Integrator
3. Filter Building Blocks –Gm-opamp-C Integrator.
3. Filter Building Blocks –Comparison of practical integrators
Some general comments regarding the 3 types of integrators :
• Gm-C integrators are the simplest to design, have the highest bandwidth, are most sensitive to parasitic capacitors and ro, exhibit low to medium linearity (6 bits), and are not easily programmable.
• Opamp-RC integrators have medium to high bandwidth, have low sensitivity to parasitics, are easily programmable, and exhibit medium to high linearity (6-9 bits).
• MOSFET-C structures are very useful for low to medium frequencies, are least sensitive to parasitics, exhibit high linearity, are easily programmable and are best suited for VLSI realization. Also, the MOSFET in triode has no 1/f noise [4].
• It is worthwhile mentioning that in addition to the above 3 main types of structures, programmable active RC filters have been realized with MOS switches, passive /MOSFET Rs, double poly capacitor based amplifiers, for special purpose, very high linearity, low frequency applications [13].
4. Tuning• Why is Tuning Necessary [13] :• The basic CT filter components, Gm (active, MOSFET-R or passive
integrated R) and capacitor C (passive or bias-dependent) exhibit large absolute variations due to process, temperature and aging.
• The raw time constant t = (Gm/C)-1 , or co-efficients, ais and bis, in transfer functions, can vary almost + 50% which implies a 3:1 (!!) spread for the cut-off frequencies.
• Clearly this is unacceptable and some form of frequency controllability is essential. Achieving frequency accuracy and reliability (tracking) is referred to as frequency tuning - to control t or the integrator unity-gain frequency.
• In addition, the pole-zero Q-factors are sensitive to active elements' dc gain and phase errors, and matching accuracies of Rs and Cs. By careful design and layout, the ratios of similar elements canmatch to better than 1%, while the effects of phase errors, in particular, are horrifying in high frequency and/or medium to high Q filters. Hence there is a need for Q tuning ( not for RF-BB filters).
4. TUNING :Tuning Methods
• In general, tuning is not solved easily or inexpensively.• The common practice is to do a one time initial trim. This
is a partial solution only because of aging and variations during operation.
• Also, manual tuning is not an option. A closed-loop, continuous monitoring and correcting mechanism is desired .
• Broadly speaking, automatic tuning is implemented in two ways.
• Master-Slave or Indirect tuning - used for majority of applications.
• On-line or Direct tuning - for very critical applications.
4. TUNING :Master-Slave Frequency Tuning
• Master-Slave (M/S) Frequency Tuning [13]:• While VLSI is the cause for the need for automatic tuning, tight
matching of similar components is the redeeming feature of VLSI that makes M/S tuning possible.
• As the name suggests, the actual filter, referred to as the slave (S), is indirectly tuned via a model or a Master (M) section. The latter is calibrated or tuned directly using a standard reference that is absolute, stable and accurate.
• The degree of success depends on the accuracy of reference, the calibration method, how closely the M section copies the S section, as well as the matching of M and S sections.
• Some examples of standards are :• Accurate voltage (external reference or internal band-gap) and an
external precision resistor.• Accurate frequency - Clock reference or a fundamental frequency.
4. TUNING :Q- Tuning
Automatic Q-Tuning :• The causes for Q-factor errors of an integrated Biquad are -• Mis-match among similar Gms or Cs.• Phase errors in a two-integrator loop. This is the limiting factor for high Q-circuits and for high
frequency applications. • Q-tuning should always be performed after frequency has been tuned, and without affecting
frequency-tuning.• Basic Q-tuning is achieved by a magnitude locked loop (MLL) using the VCF approach [10].• Consider the bandpass function Hbpf(s) at resonance. • In principle, a closed loop system that tunes a master section to a correct output at resonance will
provide Q-tuning.
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5. Practical CircuitsA.Yoshizawa, Y. Tsividis
A Channel-Select Filter with Agile Blocker Detection and Adaptive Power Dissipation, A.Yoshizawa, and Y.Tsividis, JSSC, vol.42, No.5, May 2007, pp. 1090-1098. [4]
• Trades linearity with power depending on the presence or absenceof blockers.
• Employs blocker fast detection circuitry (~3us settling time) to detect out-of-band blockers. Two detection circuit blocks are used in the front end of the filter.
• Dynamically adjusts bias to optimize IIP3 and power consumption . depending on the presence or absence of blockers.
• A dynamic bias scheme is used; an elaborate frequency compensation scheme is used for a nested Miller class AB stage in the early stages; class A stage is used for later ones where theeffect of blockers is insignificant. …cont’d
5. Practical CircuitsA.Yoshizawa, Y. Tsividis .. cont;’d
• Filter is based on a ladder structure and is of the opamp-RC type.
• Fifth order Butterworth opamp-RC LPF at, 1.92MHz is implemented in 0.18um.
• SFDR=48dB, -5dBV IIp3, 1.2mA current• SFDR=68 dB , 20dBV IIP3, 2.7mA current.• Detector current consumption = 60uA.
5. Practical Circuits..cont’d
A Broad-band Tunable CMOS Channel-Slect Filter for a Low-IF WirelessReceiver., F Behbahani et al, JSSC, VO.35, No.4, April 2000, pp.476-489. [1]
• Sharp channel select filters are used to alleviate A/D requirements.• Uses a novel semi-scaling technique to remove large interferers – as
opposed to conventional full equal-amplitude scaling.• Tunable Band-pass filter (BPF) with selectable passbands – 625kHz,
2.5MHz, 10MHz , centered over a 10MHz center frequency; • Passband ripple is 2.5 dB and stopband attenuation is over 50 dB
exceeding 100MHz.• BPF realized as a cascade of HPF and LPF- less power compared to a true
BPF that requires higher Q, and not easily programmable for low and high frequencies.
• 3rd order Chebychev HPF; 5th order elliptic LPF. Qmax.=6.9 …cont’d
5. Practical CircuitsBehbahani et al…. cont’d.
• Filter based on Ladder structure.• Uses Gm-C implementation using simulated inductors with gyrators.• Gm uses a resistively degenerated MOS triode (tunable Gate
voltage).• High dc-gain is achieved by using negative conductance to
compensate for low output resistance.• Both Gm and C are varied to cover the wide band-pass frequencies.• Differential topology used common-mode feedback at input and
output.• Employs both frequency and Q tuning loops.• 22.5dBm out-of-band IIP3, 18.5 dBm in-band. • 0.6um CMOS ; 14 mA with 3.3V supply.
6. Summary & Conclusions• Need for continuous time filters are increasing –
thanks to the exploding RF world.• Reconfigurable and Software Defined Radios
are demanding unprecedented specifications and programming flexibility.
• Advancement in technology is delivering higher performance CMOS and SiGe transistors to mitigate the stringent filter specs.
• Tremendous opportunity for extensive research & development is visioned for a long long time.
6. Summary & ConclusionsSome tips.
• Direct Form realizations suffer from large component sensitivity.• Classical Ladder structures offer the best sensitivity properties.• For low Q (<3) circuits, Biquad structures have sensitivity comparable to Ladder structures.• Dynamic Range (DR) of filters depends on supply voltage, capacitance, noise and Q-factor.• From a power/DR/linearity viewpoint, the most-efficient integrator is the passive-R, Miller-C
Integrator. Differential structures have the same DR as single-ended structures.• Active Element : Any of the four controlled sources with n large ( infinite) transfer parameter
can be used in place of the conventional OP-Amp.• The active element can be wide-band and does not have to be dominant-pole compensated to
realize an integrator because the integrating capacitance provides the dominant pole.• If passive R is unavailable, MOSFET-C Integrators can be used with slight degradation in THD
and frequency. • Active-Gms add power, non-linearity , but have the largest BW.• Ensure that the Gm dominates from a noise and linearity viewpoint for the best DR; the active
element contribution should be minimal.• The tuning method is closely coupled to filter implementation.• Floating inductors and active elements add power and complexity (instability).
Moral : Build the best integrator and you have the best filter.•
7. References1. F. Behbahani et al, A Broad-band Tunable CMOS Channel-Slect Filter for a Low-IF WirelessReceiver., JSSC,
VO.35, No.4, April 2000, pp.476-489. 2. D.Chamla et al, JSSC , July 2007. pp1513-1521.3. A. Yoshizawa, & Y. Tsividis, JSSC, May 2007, pp.1090-10994. A. Yoshizawa, & Y. Tsividis, JSSC, March 2002, pp.357-3645. A Vasilopouloset al, JSSC, Sept. 206, pp.1997-2008.6. Vito Giannini et al, JSSC , July 2007, pp.1501-1512.7. D.Chamla et al, JSSC, July 2005, pp.1443-1450.8. Linvill, see Ref.9.9. L.T. Bruton, RC-Active Circuits, Prentice-Hall, 1980.10. K. Laker & W. Sansen, Design of Aalog Integrated Circuits & Systems, McGraw-Hill, 1994.11. J. Kardontchik, Kluwer Publishers12. Sanchez paper in TCAS- Tutorial, 1999.13. Y.P.Tsividis & J.O.Voorman, “integrated Continuous-Time filters”, New York, 1993.14. R.Schaumann, Continuous –time Integarted filters., see Ref.13, p.3-14.15. T.H.Lee – The design of Radio CMOS Radio-frequency Integrated Circuits, Second edition.16. Derek Shaeffer et al, “A 115mW , 0.5um, CMOS GPS Receiver”, JSSC, Dec.1998, pp.2219-2231.17. G Groenewald, “The Design of High Dynamic Range Continuous Time Integrable Filters”, IEEE TCAS,
Aug.1991, pp.838-852.18. N.Rao et al, “A 150 MHzContinuous time seventh order equiripple filter”, ISCAS, June, 1999, pp.664-667 19. John Khoury –private communication20. Johns & Martin – Analog Integrataed Circuit Design , John Wiley,, 1997.