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The paper presents a new universal biquadratic filter using single universal voltage conveyor (UVC), two resistors and two capacitors. The offered structure has three inputs and one output and can realise all the five basic biquadratic filters: high-pass (HP), low-pass (LP), band-reject (BR), band-pass (BP) and all-pass (AP) from the same circuit topology. The proposed universal filter also provides following advantageous features, not available simultaneously in any UVC based universal biquadratic filter so far: (i) low active and passive sensitivities, (ii) independent control of natural frequency (ω
_{0}) and bandwidth (BW) and (iii) no requirement of any component matching condition and inversion of input signal(s) (as needed in most of the earlier reported structures). The workability of proposed structure has been presented by SPICE (Version 16.5) simulation using 0.18 μm TSMC technology.

Interest in the design of multi-input single-output (MISO) or single-input multi- output (SIMO), current-mode (CM) or voltage-mode (VM) universal filter configurations have been emerging, due to their flexibility and versatility for practical applications [

In ref. [

The Universal Voltage Conveyor is a 6-port active element with one voltage input x, two difference current inputs (y^{+}, y^{−}), two mutually inverse voltage outputs (z^{+}, z^{−}), and one auxiliary port w.

schematic symbol and ideal circuit model of UVC respectively. The relationship between port currents and voltages of a six port UVC is given in the following matrix.

( I x I w V y + V y − V z + V z − ) = ( 0 0 1 − 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 − 1 0 0 0 0 0 ) ( V x V w I y + I y − I z + I z − ) (1)

A routine circuit analysis (assuming ideal UVC) of

V o = V 2 ( s 2 ) − V 1 ( s C 2 R 2 ) + V 3 ( 1 C 1 C 2 R 1 R 2 ) s 2 + s C 2 R 2 + 1 R 1 R 2 C 1 C 2 (2)

From Equation (2), second order filter functions (LP, HP, BP, BR and AP) can be realized.

1) If V 3 = V i n , V 2 = V 1 = 0 (grounded), a low pass filter can be realized.

T ( s ) | L P = 1 C 1 C 2 R 1 R 2 D ( s )

2) If V 2 = V i n and V 3 = V 1 = 0 (grounded), a high pass filter can be realized.

T ( s ) | H P = s 2 D ( s )

3) If V 1 = V i n and V 2 = V 3 = 0 (grounded), a band pass filter can be realized.

T ( s ) | B P = − s C 2 R 2 D ( s )

4) If V 3 = V 2 = V i n and V 1 = 0 , a band reject filter can be realized.

T ( s ) | B R = s 2 + 1 R 1 R 2 C 1 C 2 D ( s )

5) If V 1 = V 2 = V 3 = V i n , a all pass filter can be realized.

T ( s ) | A P = s 2 − s C 2 R 2 + 1 R 1 R 2 C 1 C 2 D ( s )

where: D ( s ) = s 2 + s C 2 R 2 + 1 R 1 R 2 C 1 C 2

The expressions for quality factor (Q_{0}), bandwidth (BW) and natural frequency ( ω 0 ), respectively are given by:

Q 0 = R 2 C 2 R 1 C 1 , B W = 1 C 2 R 2 , ω 0 = 1 R 1 R 2 C 1 C 2 (3)

From (3), it can be observed that after adjusting BW by R_{2}, ω 0 can independently be controlled through R_{1}. Furthermore, it is seen that no inversion of input signal(s) and no component matching condition is required while realizing any of the five filter functions.

In the ideal case, the various sensitivities of ω 0 and BW with respect to R_{1}, R_{2}, C_{1}, and C_{2} are found to be:

S C 1 ω 0 = S C 2 ω 0 = S R 1 ω 0 = S R 2 ω 0 = − 1 2 (4)

S C 1 B W = 0 , S C 2 B W = − 1 , S R 1 B W = 0 , S R 2 B W = − 1 (5)

Taking into account the non-idealities of UVC, the relationship between the port voltages and currents is shown by the hybrid matrix:

( I x I w V y + V y − V z + V z − ) = ( 0 0 α 1 − α 2 0 0 0 0 0 0 0 0 0 δ 1 0 0 0 0 0 δ 2 0 0 0 0 γ 1 0 0 0 0 0 − γ 2 0 0 0 0 0 ) ( V x V w I y + I y − I z + I z − ) (6)

where α j = 1 − ε i j and δ j = 1 − ε v 1 j , γ j = 1 − ε v 2 j for j = 1 , 2 . Here ε i j ( | ε i j | ≪ 1 ) and ε v 1 j , ε v 2 j ε i j ( | ε v 1 j | , | ε v 2 j | ≪ 1 ) represent the current and voltage tracking errors of the UVC respectively. The parasitic present on the low impedance ports ( y^{+}, y^{−}, z^{+}, z^{−}) are quite low as compared to the resistances on the other ports (wand x) [

V 0 = α 1 γ 2 V 2 ( s 2 C 1 C 2 ) − γ 2 V 1 ( s C 1 R 2 ) + V 3 R 1 ( s C x + 1 R 2 + 1 R x ) s 2 ( α 1 δ 1 γ 2 C 1 C 2 + C 1 C x + C w C x ) + s ( ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) ) + ( 1 R 2 + 1 R x ) ( 1 R 1 + 1 R w ) (7)

ω 0 = ( 1 R 2 + 1 R x ) ( 1 R 1 + 1 R w ) C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 (8)

B W = ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 (9)

The sensitivity is an important performance criterion of any circuit structure. The sensitivity of Natural Frequency (ω_{0}) with respect to circuit parameters, say A is given as:

S A ω 0 = A ω 0 ∂ ω 0 ∂ A (10)

Using above definition, the various active and passive sensitivities of Natural Frequency (ω_{0}) and Bandwidth (BW), for the biquadratic filter, with respect to C 1 , C 2 , C x , C w , R 1 , R 2 , R x , R w , α 1 , δ 1 and γ 2 are found to be:

S C 1 ω 0 = − 1 2 ( C 1 C x + α 1 δ 1 γ 2 C 1 C 2 C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 ) , S C x ω 0 = − 1 2 ( C 1 C x + C w C x C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 ) (11)

S C 2 ω 0 = − 1 2 ( α 1 δ 1 γ 2 C 1 C 2 C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 ) = S α 1 ω 0 = S δ 1 ω 0 = S γ 2 ω 0 (12)

S C w ω 0 = − 1 2 ( C w C x C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 ) , S R 2 ω 0 = − 1 2 ( 1 1 + R 2 R x ) , S R x ω 0 = − 1 2 ( 1 1 + R x R 2 ) (13)

S R w ω 0 = − 1 2 ( 1 1 + R w R 1 ) , S R 1 ω 0 = − 1 2 ( 1 1 + R 1 R w ) (14)

S C 1 B W = − C 1 ( C x 2 ( 1 R 1 + 1 R w ) + α 1 δ 1 γ 2 C 2 ( C 1 ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) ) ) ( ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) ) ( C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 ) (15)

S C w B W = − C w ( C x 2 ( 1 R 1 + 1 R w ) + α 1 δ 1 γ 2 C 2 C 1 ( 1 R 2 + 1 R x ) ) ( ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) ) ( C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 ) (16)

S C x B W = − C x ( ( C 1 + C w ) 2 ( 1 R 2 + 1 R x ) + α 1 δ 1 γ 2 C 2 C 1 ( 1 R 1 + 1 R w ) ) ( ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) ) ( C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 ) (17)

S C 2 B W = − α 1 δ 1 γ 2 C 1 C 2 C 1 C x + C w C x + α 1 δ 1 γ 2 C 1 C 2 = S α 1 B W = S δ 1 B W = S γ 2 B W (18)

S R 1 B W = − C x R 1 ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) , S R w B W = − C x R w ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) (19)

S R 2 B W = − ( C 1 + C w ) R 2 ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) , S R x B W = − ( C 1 + C w ) R x ( C 1 + C w ) ( 1 R 2 + 1 R x ) + C x ( 1 R 1 + 1 R w ) (20)

Considering the typical values of various parasitic [

To confirm the feasibility of the presented biquadratic filter, the circuit was simulated using SPICE. The voltage and current values selected for CMOS implementation of UVC are ±1.9 V and 100 µA, respectively. The passive elements were chosen as C 1 = C 2 = 10 pF , R 1 = R 2 = 100 k Ω . The natural frequency ( ω 0 ) and BW of the proposed filter for the selected passive elements are 87.498 kHz and 151.266 kHz respectively. CMOS implementation of universal voltage conveyor is shown in

PMOS transistors | W (µm)/L (µm) |
---|---|

M5-M8, M10, M15-M18, M20 | 14.0/0.7 |

M3, M4 | 28/0.7 |

M25, M26, M34, M35 | 4.0/0.5 |

M27, M36 | 10.0/0.5 |

M32, M33 | 2.1/1.0 |

NMOS transistors MI, M2 | W (µm)/L (µm) |

M1, M2 | 14.0/0.7 |

M9, M11-M14, M19, M21-M24 | 28/0.7 |

M28, M29, M37, M38 | 0.8/05 |

M30, M31, M39, M40 | 10/0.5 |

A comparison with other previously known MISO-type biquads using different active building blocks has been shown in

Reference | No. of active building blocks | External resistors used | Is realization free from matching condition(s)? | Number of standard filter realized |
---|---|---|---|---|

[ | 1 | 3 | NO | 5 |

[ | 1 | 4 | NO | 5 |

[ | 1 | 3 | NO | 5 |

[ | 1 | 2 | NO | 5 |

[ | 1 | 3 | NO | 5 |

[ | 3 | 5 | YES | 3 (LP, HP, BP) |

[ | 3 | 5 | YES | 3 (LP, HP, BP) |

2 | 3 | YES | 4 (LP, HP, BP, AP) | |

1 | 2 | YES | 4 (LP, HP, BP, AP) | |

[ | 1 | 2 | NO | 5 |

Proposed | 1 | 2 | YES | 5 |

A new second order voltage-mode MISO-type universal biquadratic filter using single UVC has been presented. The proposed filter offers following advantages: i) employment of single active component; ii) ability to realize all the basic second order filters without altering the circuit configuration; iii) low active and passive sensitivities; iv) free from component matching conditions; v) independent control of natural frequency and bandwidth. On the basis of above mentioned features of the proposed biquadratic filter, it can be used for various low voltage applications. The workability of the presented circuit configuration has been established by SPICE simulation using 0.18 μm TSMC CMOS technology.

Pushkar, K.L., Gupta, K. and Vivek, P. (2017) A New Voltage-Mode Universal Biquadratic Filter Using Single UVC. Circuits and Systems, 8, 275-284. https://doi.org/10.4236/cs.2017.812020