Analog Integrated Circuits and Signal Processing, 41, 85–87, 2004 c 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
A NIC with Impedance Scaling Properties Using Unity Gain Cells ¨ ALI UMIT KESKIN1 AND ALI TOKER2 2
1 Department of Electrical Engineering, Yeditepe University 34755 , Kays¸dagı Istanbul, Turkey Department of Electronics and Communication Engineering, Faculty of Electrical and Electronics Engineering, Istanbul Technical University, 34469, Maslak, Istanbul, Turkey E-mail:
[email protected]
Received December 18, 2003; Accepted February 13, 2004
Abstract. A novel negative impedance converter (NIC) is proposed. This configuration is based on unity gain cells (a cascade of current and voltage followers with unity gains). The proposed circuit has wide band impedance scaling property, and it is suitable for practical implementation of realizing high-negative-valued passive components. Key Words: negative impedance converters, unity gain cells, impedance scaling
Introduction The problem of integrating high-valued positive or negative passive components is still one of the challenging issues in IC manufacturing industry. Impedance scaling circuits can be helpful to realize such components [1, 2]. Recently, a very attractive topology for implementing continuous time voltage mode (VM) circuits has been introduced, which is based on cascading unity gain cells (UGCs), i.e., current (CF) and voltage followers (VF) with the appropriate choice of admittances. Such a configuration can easily be transformed to accomodate for current inputs, enabling it to operate in the current mode (CM) [3]. On the other hand, negative impedance converters (NICs) are among indispensible building blocks used in signal processing. They are used to cancel unwanted loads for impedance matching, improving the quality factor of an inductor or a resonant circuit or to adjust poles of a circuit to help set up the oscillatory conditions in an oscillator [4]. Op-amp based traditional NIC circuit provides impedance scaling only in a limited frequency band (due to its voltage feedback nature), while conventional CM NIC circuits can not provide impedance scaling due to their simple structures [5]. Wheras there exists variety of techniques for NIC circuit design in literature, there has been no attempt made to systematic design of NICs based on UGCs. Hence, it is the aim of this paper to present a new NIC
circuit based on UGCs, which is (a) very suitable for practical implementation, and (b) offering wide band impedance scaling possibility.
Circuit Description A current follower (CF) is a two terminal building block shown symbolically in Fig. 1(a) and is characterized by I o = Ii ,
Vi = 0
(1)
A voltage follower (VF) building block is shown in Fig. 1(b). Its characteristic equations are Vo = Vi ,
Ii = 0
(2)
The NIC proposed in the paper is shown in Fig. 2 and consists of two unity gain cells, i.e, a CF and a VF in cascade. Construction of the proposed NIC can be better explained by inspection of its sub-circuits, as shown in Fig. 3. In sub-circuit 1, two cascaded CFs with two impedances are shown. The first CF in this circuit is placed after an impedance Z1 and the output of the second CF is fed back through an impedance Z2 to signal input junction. The voltage observed at the output of sub-circuit 1 is Vo1 = (1 + Z 2 /Z 1 ) · Vi . Subcircuit 2, consists of a VF and a feedback impedance Z3 , through which the current Iin2 = −(Vo − Vi2 )/Z 3 is injected into the signal input junction. Combining
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Non-ideal analysis:
Fig. 1. (a) Current follower symbolic representation and (b) Voltage follower symbolic representation.
Fig. 2.
The proposed NIC employing unity gain cells (CFs and VF).
The non-ideal equations for the CF and VF can be described as I o = α Ii
(4)
Vo = γ Vi
(5)
respectively. Here, α = 1 − εi , γ = 1 − εv , where εi is the current tracking error and εv is the voltage tracking error of the relevant active component, and their absolute values are much less than unity. Including those non-idealities in the subcircuits and solving for Z in will result Z in =
Z1 Z3 − α1 α2 γ Z 2 + (1 − γ )Z 1 + (1 − α1 α2 )Z 3
(6)
Therefore, for the UGC-based NIC circuit, the condition Z2 > (a)
(1 − α1 α2 )Z 3 + (1 − γ )Z 1 α1 α2 γ
(7)
must be satisfied. For example, assuming that all impedances are resistive, i.e., R1 = R3 = R, and tracking errors are all 2%, NIC condition is realized if R2 > 0.063R. Experimental (b) Fig. 3. Subcircuits of the NIC illustrated in Fig. 1: (a) The first sub-circuit and (b) second sub-circuit (V02 = γ V01 ).
these equations and solving for the input impedance yields Z in = −Z 1 ·
Z3 Z2
(3)
When all passive components are resistors, a scaled negative resistor is obtained. Choosing Z 1 or Z 3 as a capacitor and other components as resistors, yields a scaled negative capacitor, with a capacitance value calculated depending upon the component assignment as Ceq = −(R2 /R3 )C1 or Ceq = −(R2 /R1 )C3 . Finally, choosing Z 2 as a capacitor and other components as resistors yields a simulated negative inductor having the inductance of L eq = −R1 R3 C2 .
A CF can be obtained by using a second generation positive current conveyor (CCII+) if the y terminal is grounded [6] and the output obtained from the z terminal. In the experiments, we have implemented a commercially available current feedback amplifier, AD 844 [7], (Analog Devices, Inc., Norwood, MA), and used its external compensation pin as the output terminal of the CF. This IC readily includes a voltage buffer, as well. Figure 4 displays an oscillator realized in the laboratory. Characteristic equation of this oscillator can be obtained from 1 − Yin = 0 Ri
(8)
where Z in = 1/Yin , as given by (3). Equation (8) yields 1 1 1 Ri 2 s + + + − =0 R3 C 3 R2 C 2 R1 R3 C 2 R2 C 2 R3 C 3 (9)
NIC with Impedance Scaling Properties Using Unity Gain Cells
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it is suitable for practical implementation. The theory of operation for the new configuration, and experimental results that confirm theoretical predictions are presented. The proposed circuit is believed to be useful especially in the realization of high valued negative passive component simulations. Fig. 4. Oscillator circuit based on NIC employing unity gain cells. With Ri = R1 = R3 = 10 k, R2 = 20 k, C3 = 20 nF, C2 = 10 nF, and the power supply is Vcc = − Vdd = 12 Vdc, the frequency of sinusoidal oscillation is measured to be 808 Hz, at 19.5 Vp-p amplitude.
When Ri = R1 , the condition of oscillation is R2 = 2R3 , C2 = C3 /2. The frequency of oscillation is (with R = R3 , C = C 3 ) fo =
1 2π RC
(10)
The amplitude of oscillations can be independently controlled by Ri = R1 . Conclusion A new NIC circuit is proposed. This UGC-based NIC provides wide band impedance scaling property, and
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