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A universal biquadratic filter using single universal voltage conveyor (UVC), two resistors and two capacitors is presented in this paper. The proposed structure has three inputs and one output and can realize all the five standard biquadratic filters: low-pass (LP), high-pass (HP), band-pass (BP), band-reject (BR) and all-pass (AP) from the same circuit configuration. The presented universal filter offers low active and passive sensitivities. SPICE (Version 16.5) simulation results using 0.18 μm TSMC technology have been included.

There is a growing interest in the design of single-input multi-output (SIMO) or multi-input single-output (MISO) voltage-mode (VM) or current-mode (CM) universal filter configurations, due to their flexibility and versatility for practical applications [

Filter structures presented in references [

The symbolic representation and equivalent circuit model of the UVC are shown in ^{+}, y^{−}), two mutually inverse voltage outputs (z^{+}, z^{−}), and one auxiliary port w. Using standard notations, the relationship between port currents and voltages of a six port UVC is given by the following equations.

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

A routine circuit analysis (assuming ideal UVC) of

ing expression for the output voltage in terms of input voltages:

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

From Equation (2), all standard filter functions (LP, HP, BP, BR and AP) can be realized (for R 1 = R 2 = R and C 1 = C 2 = C ):

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

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

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

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

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

T ( s ) | B P = − s ( 1 R C ) D ( s )

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

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

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

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

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

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

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

From Equation (3), it can be observed that after adjusting BW by R_{1}, ω 0 can independently be controlled through R_{2}. Furthermore, it is seen that no inversion of the input signal(s) is required in any of the five filter realizations.

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

Model of UVC including parasitic elements is shown in the

Taking into account, the non-idealities of UVC, the relationship of the terminal voltages and currents in Equation (1) can be rewritten as:

I x = α 1 I y + − α 2 I y − , V y + = δ 1 V w , V y − = δ 2 V w , V z + = γ 1 V x , V z − = γ 2 V x , I w = 0 (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 Math_39# represent the current and voltage tracking errors of the UVC, respectively. The parasitic present on the low impedance ports (y^{+}, y^{−}, z^{+}, z^{−}) is quite low as compared to the resistances on the other ports (w and x) [

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

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

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

Its active and passive sensitivities can be found as:

S C 1 ω 0 = − 1 2 ( 1 1 + C 2 C x α 1 γ 1 C 1 C 2 + C 1 C x ) , S C 2 ω 0 = − 1 2 ( 1 1 + C 1 C x α 1 γ 1 C 1 C 2 + C 2 C x ) (10)

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

S C 1 B W = − C 1 ( ( α 1 γ 1 C 2 2 ) ( 1 R x + 1 R 1 ) + α 1 γ 1 C 2 C x R 2 + C x 2 R 2 ) ( ( C 1 + C 2 ) ( 1 R x + 1 R 1 ) + C x R 2 ) ( α 1 γ 1 C 1 C 2 + C 1 C x + C 2 C x ) (12)

S C 2 B W = − C 2 ( ( α 1 γ 1 C 1 2 ) ( 1 R x + 1 R 1 ) + α 1 γ 1 C 1 C x R 2 + C x 2 R 2 ) ( ( C 1 + C 2 ) ( 1 R x + 1 R 1 ) + C x R 2 ) ( α 1 γ 1 C 1 C 2 + C 1 C x + C 2 C x ) (13)

S C x B W = − C x 2 ( C 1 C x R 2 + α 1 γ 1 C 1 C 2 R 2 − C 2 ( C 1 + C 2 ) ( 1 R x + 1 R 1 ) ) ( ( C 1 + C 2 ) ( 1 R x + 1 R 1 ) + C x R 2 ) ( α 1 γ 1 C 1 C 2 + C 1 C x + C 2 C x ) (14)

#Math_50# (15)

S R x B W = − 1 1 + ( ( C 1 + C 2 ) R 2 + C x R 1 ) R x ( C 1 + C 2 ) R 2 R 1 (16)

Considering the typical values of various parasitic capacitance C x = 17.41 pF and parasitic resistance R x = 378.73 k Ω , α 1 = α 2 = δ 1 = δ 2 = γ 1 = − γ 2 = 1 [

To validate its theoretical analysis, the presented biquadratic filter is verified by SPICE simulations. The voltage and current selected for CMOS implementation of UVC are ±1.9 V and 100 μA, respectively. CMOS implementation of universal voltage conveyor 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 |

in

A New voltage-mode MISO-type universal biquadratic filter configuration is

Reference | No. of active components | No. of passive components | Requirement of matching condition(s) | Number of standard filters realized | |
---|---|---|---|---|---|

Capacitors | Resistors | ||||

[ | 1 (CDTA) | 2 | 3 | Yes | Five |

[ | 1 (CDBA) | 4 | 4 | Yes | Five |

[ | 1 (CDBA) | 2 | 4 | Yes | Five |

[ | 1 (MCFOA) | 2 | 3 | Yes | Five |

[ | 1 (CFA) | 2 | 2 | Yes | Five |

[ | 1 (CFA) | 2 | 3 | Yes | Five |

[ | 1(VDVTA) | 1 | 2 | No | Four |

[ | 3 (UVC) | 2 | 5 | No | Three (LP, HP, BP) |

[ | 3 (UVC) | 2 | 5 | No | Three (LP, HP, BP) |

2 (UVC) | 2 | 3 | No | Four (LP, HP, BP, AP) | |

1 (UVC) | 2 | 2 | No | Four (LP, HP, BP, AP) | |

Proposed | 1 (UVC) | 2 | 2 | YES | Five |

proposed. The presented filter circuit employs single UVC with a minimum number of passive components, two capacitors, and two resistors. By proper selection of input voltages, all the basic second order filters can be realized, which are LP, HP, BP, BR, and AP without altering the circuit structure. Simulation results using 0.18 μm TSMC CMOS technology have been presented to confirm the workability of the proposed new universal biquadratic filter. Limitations of the proposed structure are: i) matching of passive components and ii) reduced gain of band pass filter. For future scope matching conditions could be removed, further unity gain of the band pass filter can be achieved.

Pushkar, K.L. and Gupta, K. (2017) MISO-Type Voltage-Mode Universal Biquadratic Filter Using Single Universal Voltage Conveyor. Circuits and Systems, 8, 227-236. https://doi.org/10.4236/cs.2017.89015