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A generic design (GD) for realizing an

The popularity attributed to the use of continuous-time filters in ever growing wireless industry is their effective handling of high-frequency real-world signals and low-power systems. But the integration of continuous-time filters and digital circuits on the same IC needs reduction in supply voltage which entails increase in the power consumption of conventional analog signal processors for conservation of same dynamic range (DR) and chip area for a given bandwidth [

The use of logarithmic and exponential functions in the development of log-domain filters permits them to operate on very low supply voltage without sacrificing the dynamic range [

The implementation of filters with multifunction feature finds applications in phase-locked loops, FM stereo demodulator, touch-tone telephone tone decoder, and crossover network used in three-way high-fidelity loudspeakers [

Based on the above facts, a simple generic

It is worth to point out here that the high-order log-domain MFF of [

The general transfer function of

Algebraic manipulations yield

The generic functional block diagram (GFBD) of the

GFBD of the proposed generic

The filter functions HP, BP, and LP being in conformity with (

Signs (Noninverting or inverting) of the filter functions (NA: Not Applicable, BP1: BP_{(n/2)}, BP2: BP_{(n+1)/2}, BP3: BP_{(n-1)/2)}.

Order | MFF1 | MFF2 [ | MFF3 | MFF4 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

LP | BP1 | BP2 | BP3 | LP | BP1 | BP2 | BP3 | LP | BP1 | BP2 | BP3 | LP | BP1 | BP2 | BP3 | |

1 | + | NA | NA | NA | + | NA | NA | NA | − | NA | NA | NA | − | NA | NA | NA |

2 | − | + | NA | NA | + | + | NA | NA | − | − | NA | NA | + | − | NA | NA |

3 | − | NA | − | + | + | NA | + | + | + | NA | − | − | − | NA | + | − |

4 | + | − | NA | NA | + | + | NA | NA | + | − | NA | NA | + | + | NA | NA |

5 | + | NA | − | − | + | NA | + | + | − | NA | + | − | − | NA | − | + |

6 | − | − | NA | NA | + | + | NA | NA | − | + | NA | NA | + | − | NA | NA |

7 | − | NA | + | + | + | NA | + | + | + | NA | + | + | − | NA | + | − |

8 | + | + | NA | NA | + | + | NA | NA | + | + | NA | NA | + | + | NA | NA |

9 | + | NA | + | − | + | NA | + | + | − | NA | − | + | − | NA | − | + |

10 | − | + | NA | NA | + | + | NA | NA | − | − | NA | NA | + | − | NA | NA |

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Mode of integrators^{* } | Type of feedback^{# } | HP transfer function | Stability status^{~} | ||
---|---|---|---|---|---|

_{1} | _{2} | F_{1} | F_{2} | ||

NI | NI | + | + | U | |

NI | I | + | − | ||

I | NI | − | − | ||

I | I | − | + | ||

NI | NI | + | − | U | |

NI | I | + | + | ||

I | NI | − | + | ||

I | I | − | − | ||

NI | NI | − | + | U | |

NI | I | − | − | ||

I | NI | + | − | ||

I | I | + | + | ||

NI | NI | − | − | S | |

NI | I | − | + | ||

I | NI | + | + | ||

I | I | + | − |

_{1}_{1}

^{#}F_{1}: Feedback from first integrator, F_{2}: Feedback from second integrator.

^{~}U: Unstable, S: Stable.

To transpose GFBD to its log-domain counterpart, an appropriate set of complementary LOG and EXP operators are required, which are, respectively, given by [_{O}

The sequence of steps to be followed in transforming a linear GFBD into log-domain one are given hereunder

Place EXP and LOG blocks in front and behind of each integrator, respectively.

Place LOG and EXP blocks at the input and output of the filter, respectively.

dc stabilize the circuit by applying the rules contained in [

Following the above steps, we obtain the transposed GFBD of the log-domain MFF filter topology depicted in Figure

Transposed topology of the filter in Figure

The building blocks for implementing log-domain integrator are exponential cells (E cells) which have been reported in [

The log-domain lossless noninverting and inverting integrator configuration is depicted in Figures _{O}

(a) Lossless DC stabilized log-domain noninverting integrator. (b) The employed symbol.

(a) Lossless DC stabilized log-domain inverting integrator. (b) The employed symbol.

The multipleinput algebraic summation blocks required for obtaining HP filter in each configuration are demonstrated in Figures

Multipleinput algebraic summation block (for even and odd order) and the employed symbol in all cases. (a) MFF1 (b) MFF2 (c) MFF3 (d) MFF4.

To verify the validity of the proposed design, 5th-order log-domain MFF of each configuration depicted, respectively, in Figures _{CC}_{EE}_{O} =_{C}

Topologies of the 5th-order generic log-domain MFF of Figure

Simulated magnitude responses of standard filter functions of MFFs of Figure

Demonstration of electronic tunability of cut-off frequency and gain of MFFs.

A comparative study of the proposed circuits was carried out on the basis of usually used parameters of nonlinear behaviour, number of components, sensitivity, and power consumption.

The nonlinear behaviour of each MFF biquad configuration for LP response was carried out employing IMD3 test. For this purpose, two closely spaced tones 3 MHz and 3.2 MHz, which fall in the passband of the LP response, were applied at the input of each of the filters. The simulated values of distortion at

Comparison of nonlinearity, component count and power dissipation of MFFs of Figure

MFF/Par. | IMD3. at | rms output | DR @ 0.3% IMD3 level (dB) | No. of components | Static power cons. (mW) | |

Tr. | C_{S} | |||||

MFF1 | −49 dB | 230 | 36.82 | 66 | 38 | 3.62 |

MFF2 | −45.9 dB | 240.1 | 35.24 | 72 | 36 | 3.76 |

MFF3 | −41 dB | 250.3 | 33.75 | 60 | 40 | 3.48 |

MFF4 | −47.8 dB | 236.4 | 35.82 | 60 | 40 | 3.43 |

Also, the simulated IMD3 responses as a function of the modulation index factor, are given in Figure

Statistical simulation results about the frequency behaviour of the LP filter functions of log-domain MFFs of Figure

MFF | Gain | Cut-off Frequency | IMD3 at | |||
---|---|---|---|---|---|---|

STD | MV | STD | MV | STD | MV | |

MFF1 | 0.0078 | 0.96 | 0.252 MHz | 9.82 MHz | 1.53 dB | −47.7 dB |

MFF2 | 0.0087 | 0.95 | 0.284 MHz | 9.8 MHz | 1.65 dB | −44.5 dB |

MFF3 | 0.0095 | 0.94 | 0.288 MHz | 9.81 MHz | 1.72 dB | −39.4 dB |

MFF4 | 0.0095 | 0.94 | 0.292 MHz | 9.78 MHz | 1.84 dB | −46.1 dB |

Linear performance of the LP filter functions of 5th order log-domain MFFs of Figure

The results of Tables

A novel generic

_{m}-C filters to DC stabilized log-domain filters