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43 ELECTRONICS AND ELECTRICAL ENGINEERINGISSN 1392 – 1215 2010. No. 9(105)ELEKTRONIKA IR ELEKTROTECHNIKA ELECTRONICS T 170 ELEKTRONIKA An Analog Array Approach to Variable Topology Filters for Multi-mode Receivers D. Csipkes, G. Csipkes, S. Hintea Technical University Cluj-Napoca,Memorandumului 1, Romania, phone: +400264401463,e-mails:
[email protected],
[email protected],
[email protected] H. Fernandez-Canque Glasgow Caledonian University,Cowcaddens Road, Glasgow G4 0BA, United Kingdom, e-mail:
[email protected] Introduction Recent development of the communication industryimposes new challenges on the design of wirelessterminals. The ever increasing diversification of serviceshas led to more and more complicated equipments,supporting extended functionality. The digital section of wireless terminals greatly benefits of the advantagesoffered by the rapid advancement of semiconductortechnologies. Miniaturization allowed an increasingcomplexity and higher operating frequencies, leading tobetter performance and more integrated functionality of digital circuits. Therefore, digital processors and theirdriving software can relatively easily cope with thedemands of modern multi-mode wireless technologies [1]. Traditionally the bottleneck in the development of mixed signal IC-s has been the analog interface. Alongwith the increasing digital functionality, analog circuitsmust support extensive reconfiguration, not only to adaptto the processed signal characteristics, but also to deal withvarious environmental effects, variable supply voltages,fabrication tolerances and a wide range of operatingtemperatures specific to portable equipments [2, 3].Among the multitude of multi-mode wireless frontend architectures proposed in the literature two really standout: the zero-IF or direct conversion and the low-IFarchitectures. Direct conversion front ends have beentypically used for fixed frequency systems due to theirpredictable, well known behavior and low componentcount. This architecture is flawed by DC offset that may bedifficult to compensate when narrow bandwidth signals areprocessed. The low-IF architecture emerged as analternative to zero-IF, eliminating the DC offset issues byconverting the signal to some low intermediate frequencyinstead of the base band. However, channel or bandselection has become more tedious due to the demand tosuppress image signals. Reconfigurability exacerbatesthese problems through variable carrier frequencies anddifferent signal dynamics, specific to each supportedcommunication standard.A possible solution supporting wide band reconfi-gurability would be to combine the two architectures andemphasize the advantages depending on the characteristicsof the processed signals. The block diagram of a low-IF-zero-IF multi-mode front end is shown in Fig.1. Fig. 1. Block diagram of a reconfigurable low-IF/zero-IF analogfront end The variable LO allows the conversion to variousintermediate frequencies, including the base band. Thechannel or band select filter may be switched from a lowpass to a polyphase band pass type of frequency responsein order to accommodate the changes of the architectureand the target center frequency. Sampling may occur at theIF or in the base band. The reconfigurable filter is one of the key components in this architecture, being directlyresponsible for the receiver selectivity. The remainder of this paper describes an analog array approach to variabletopology filters, suitable for multi-mode wireless applica-tions. CCII filter implementation techniques With the continuous reduction of supply voltages, 44conventional voltage mode design techniques show theirinherent limitations, being more and more often replacedby current mode signal processing. In many applicationscurrent mode circuits offer a reasonable trade-off betweensignal amplitude, bandwidth, linearity, complexity andcurrent consumption. Two of the most widely used funda-mental building blocks in current mode signal processingare the operational transconductance amplifier (OTA) andthe second generation current conveyor (CCII). The latteris often preferred for its versatility in operation. The CCIIcell typically has one high impedance voltage input (Y),one low impedance current input (X) and one or more highimpedance current outputs. The operation can be brieflydescribed by (1): ⋅±=== .,,0 XZ YX Y IIVVI α (1)where α is a current scaling factor.CCII based current mode filters can be synthesizedeither by using the voltage-current duality principle, or bydirectly implementing the functional equations defined bythe imposed attenuation characteristics. Two main synthe-sis methods are widely used in practice, fulfilling mostdemands, architecturally and performance wise. The first method employs a cascade of elementarysecond order sections to build higher order filters. Thesebiquads can be obtained by applying the duality principleto classical opamp-RC filters. Typical, double output CCII(DOCCII) based implementations of the Tow-Thomas(TT) and the Kervin-Huelsman-Newcomb (KHN) biquadsare illustrated in Fig. 2. Fig. 2. The DOCCII based TT and KHN second order filters Both biquads share the same transfer function, givenin (2) ( ) 21222212 111 CCRsRCsCCRsH ++= . (2)Biquads are mostly used in modular designs withmoderate filter orders. However, the implementation of arbitrary transmission zeros can be tedious and thesensitivity performance of the filters decreases with thefilter order. The second synthesis method, based on thefunctional simulation of a low pass ladder prototype, leadsto a filter architecture that can easily support transmissionzeros and inherits the sensitivity of doubly matched LCladder filters. The modular implementation of a currentmode leap-frog filter starts with the passive prototype andits associated signal flow graph, in which all state variableshave been written as currents. The generalized odd orderladder prototype with transmission zeros is given in Fig. 3. The even order ladder is very similar, but the impedance Z 2n+1 and the capacitance C z2n are missing. Fig. 3. The generalized, odd order passive ladder prototype The functional equations may be written as shown in(3), where R is the characteristic resistance of the network,while the currents I ˆ have been obtained from node volta-ges through resistive scaling. ( ) [ ] ( ) ( ) ( ) [ ] ( ) ( ) [ ] −+−⋅= −⋅=−−−+−⋅= −⋅=−+−⋅= +−+++− .ˆ,ˆˆ,ˆ,ˆˆ,||ˆ 121222 12121212 2253431242 3331223122 11 nnnzoutn nnnnnnzzzinS VVsCII RZIIIZRIVVsCVVsCII RZIIIZRIVVsCII RZRI (3) The recursive equations show that the terms sC z2k Δ V correspond to currents extracted or injected into adjacentcircuit nodes. Since these terms already represent statevariable currents, there is no need to scale them with thecharacteristic impedance of the network. The correspon-ding signal flow graph of the generalized filter is illustratedin Fig. 4.For filtering in multi-mode wireless front ends onlylow pass transfer functions are of interest. In this case, oddorder impedances are capacitors and even orderimpedances are inductors. From (3) results that in the finalfilter structure inductive impedances will be inverted (e.g. R / Z 2 ). As a consequence, all the reactive elements in theactive current mode filter will be capacitances and noelectronic emulation of inductances is required. Fig. 5shows the DOCCII based implementation of the odd ordercurrent mode leap-frog filter. The even order version canbe easily obtained by eliminating the final DOCCII and theattached C z2n - C 2n+1 capacitors. Furthermore, I 2n becomesthe output current. 45Classical band pass filters can be implemented bymeans of a bilinear frequency transformation performed ona normalized low pass prototype. The transformationtranslates the low pass frequency response into a doubleside band characteristic that passes the wanted signal alongwith its mirror image at both positive and negativefrequencies. Therefore, these filters are not suitable forlow-IF front end architectures where the suppression of theimage signals is usually compulsory. Fig. 4. The signal flow graph of the generalized state variable filter Fig. 5. Current conveyor based implementation of the generalized leap-frog filter A single sideband response can be obtained by per-forming a linear frequency transformation according to (4)where ω C is the desired center frequency. The bandwidthof the filter is calculated by doubling the srcinal low passcut-off frequency [11]. C j js js ω ω ω ±=→= * . (4)It can be seen that the transformation is performed onthe frequency variable ω and it only affects the capacitorsin the low pass prototype. Each capacitor will be connectedin parallel with a complex impedance according to (5). C jC jC j C ω ω ω ±→ . (5) The complex impedance jωC can be readily imple-mented if quadrature signal paths are available. This isusually the case in low-IF receivers. The block diagram of the linear frequency shifting circuit is shown in Fig.6. Notethat a proper frequency transformation also shifts the lon-gitudinal capacitors if arbitrary transmission zeros arepresent in the filter transfer function [10]. Fig. 6. Frequency shifted (a) grounded and (b) floating capacitor In both cases the complex input impedance of thequadrature network and the value of the conductance G f aregiven by (6). CGC jC j jGC j Z Cf Cf ω ω ω ω =⇒±=±= 11 . (6)Fig. 7 shows the implementation of the block dia-grams from Fig. 6 with CCII cells. Fig. 7. DOCCII based linear frequency shift network for groun-ded and floating capacitors The following paragraph describes an analog arraybased on DOCCII-s that support the implementation of allthe filter types presented above [8, 9]. The DOCCII based FPAA Traditional FPAA architectures have been based oncrossbar type signal routing [4]. In this concept, theconfigurable analog blocks (CABs) are considered thenodes of a regular matrix and can be freely interconnectedthrough horizontal and vertical signal paths. The routingbetween these paths is implemented with omnidirectionalswitch arrays. Many of these applications have been built 46for rapid prototyping of analog functions. Therefore, awide variaty of basic operations, such as amplification,filtering and multiplication is supported by each CAB [5]. The FPAA proposed in this paper has been developedspecifically for filtering applications. The architecture of the system and of each individual CAB has been derivedby observing peculiarities common to typical, fixed topo-logy filter design techniques and synthesis methods. Theresulting FPAA is based on CABs connected in a reconfi-gurable cascade. A programmable signal bus, used as ademultiplexer, allows the injection of the current modeinput signal into various nodes of the circuit, depending onthe desired filter order [6, 7]. The chain of CABs, together with the input signalbus, support the implementation of a low pass filter basedeither on a cascade of second order sections, or on a leap-frog state variable topology. The latter is particularlyuseful for implementing filters with arbitrary transmissionzeros and enhanced sensitivities at higher filter orders. Thelow pass filter order can be reconfigured to any valuebetween 2 and 8 according to the imposed attenuationtemplate.In many cases target applications, such as the analogfront ends in wireless receivers, impose a band pass filtercapable of selectively supressing image signals at positiveor negative frequencies. These circuits are typically imple-mented as complex polyphase filters that require thereplication of the low pass prototype on the quadraturesignal path and a linear shift of the low-pass frequencyresponse. The proposed FPAA supports the implementa-tion of complex filters, derived from any prototype realizedby the low pass chain of CABs. The frequency transforma-tion is based on the circuits in Fig. 7. The resulting architecture of the FPAA is illustratedin Fig. 8. Fig. 8. General architecture of the proposed current mode FPAA The switch network supports the mapping of indivi-dual filters on the array according to Table 1. This tableshows the switch position for the leap-frog topology of different orders. Since second order sections require onlylocal feedback and a single connection to the followingCAB, all switches corresponding to the " down " signal pathare in OFF state if this synthesis technique is considered. The other switches will be configured identically, while theoutput signal is always taken from I o-even or I o-odd . Table 1. Switch states depending on filter type and orderOrder 2 3 4 5 6 7 8 K in2 ON K in34 ON ON K in56 ON ON K in78 ON ON K 34up ON ON ON ON ON ON K 34dw ON ON ON ON ON ON K 56up ON ON ON ON K 56dw ON ON ON ON K 78up ON ON K 78dw ON ON The linear frequency shift network is connectedbetween the two low pass replicas only if a band passtransfer function is required. The internal structure of a CAB has been defined inorder to support the implementation of any biquad fromFig. 2 and a complete up-down section of the leap-frog fil-ter in Fig. 5. The schematic of the CAB is given in Fig. 9. Fig. 9. Structure of a single CAB within the FPAA The switches K R2k-1 and K R2k serve the realization of termination resistors in leap-frog filters when CABs arefirst or last in the chain, or of the resistors required by thebiquads of Fig. 2 and a lossy integrator. The switch K fb isused to connect the local feedback path around the firstDOCCII in KHN biquads, while K C2k inserts a transmissionzero in the filter transfer function. Table 2 show theposition of specific switches within the CAB for differentbasic configurations. Table 2. Switch states within the CAB according to the filter typeSynthesis K R2k-1 K R2k K fb Output TT biquad ON I o-up KHN biquad ON I o-up lossy integrator ON I o-dw leap frog (LF) I o-up +I o-dw LF input ON I o-u +I o-dw LF output (even) ON I o-up LF output (odd) ON I o-dw Simulation results The operation of the FPAA for various filter configu-rations and approximations has been validated through 47simulations performed in the Eldo simulator provided byMentor Graphics. The DOCCIIs have been modeled withcontrolled sources. The models include first order non-idealities, such as a frequency dependent transfer function,finite output resistance and non-zero input resistance at theconveyor X terminals. The first filter example shown in this section is a 5 th order low pass filter with inverse Chebyshev approxima-tion built upon the leap-frog topology. The filter has beendesigned for a 2MHz cutoff frequency and a stopband ratioequal to 2. The input current is injected to the CAB2, whilethe output signal is taken from I o-dw of the CAB4. Theresistor R 2k-1 in CAB2 implements the source resistanceand R 2k-1 in CAB4 the termination of the ladder. Theswitch positions in each CAB are summarized in Table 3. The overall configuration of the switches in the FPAA canbe taken from Table 1 for a 5 th order filter. Table 3. CAB switch configuration for the first filter example K C2k K R2k-1 K R2k K fb OutputCAB1CAB2 ON ONCAB3 ONCAB4 ON I o-dw The simulated magnitude response of the filter andthe measure -3dB cutoff frequency are illustrated in Fig.10. Fig. 10. The simulated low pass magnitude response of the FPAAfor an inverse Chebyshev approximation The second example is a 4 th order complex band passfilter with Butterworth approximation. The filter has beenbuilt with a cascade of two Tow-Thomas second ordersections. The required bandwidth was 4MHz, while themagnitude response was centerd on 10MHz. The configu-rations of the switches within each CAB and the entireFPAA can be determined from Table 1 and Table 4,similarly as for the previous example. Additionally, thefrequency shift network performs the linear low pass toband pass transformation for each of the four capacitorsconnected into the circuit.Fig. 11 illustrates the simulated band pass magnituderesponse of the filter. The measurements show the imposed10MHz center frequency and 4MHz bandwidth. Table 4. CAB switch configuration for the second filter example K C2k K R2k-1 K R2k K fb OutputCAB1CAB2CAB3 ONCAB4 ON I o-up The third example is a complex band pass filterwhose low pass prototype has been presented in the firstexample. The inverse Chebyshev low pass transferfunction has been shifted to a 10MHz center frequencywhile the 2MHz cutoff frequency yields a 4MHz band-width. The switch configurations are identical with the lowpass prototype but the frequency shift network is alsoconnected between I and Q signal paths. Fig. 12 shows thesimulated magnitude response of the filter and themeasured frequency parameters. Fig. 11. The simulated band pass magnitude response of theFPAA for a Butterworth approximation Fig. 12. The simulated band pass magnitude response of theFPAA for an inverse Chebyshev approximation Conclusions This paper investigated the system level aspects of
