GB2059213A - Active inductors - Google Patents

Abstract

A known active inductor of the type shown in Figure 1 can be made to have a high Q, with characteristics independent of roll-off frequency and input impedance to first order when the relationships between the resistors 2, 4 and 5 are chosen to be in the ratios 2R:R: (1 + 2ROOT 2)R respectively. Two such inductors can be connected to form a fully floating active inductor, which may be connected between two earthed inductors. <IMAGE>

Description

SPECIFICATION Active filters This invention relates to precision active filters, in particular for use in telecommunication systems.

In telecommunication systems there are requirements for high performance active filters whose performance is substantially independent of both the gain and the input impedance of the operational amplifiers used in the filter. Many designs for active filters are available from widely published handbooks.

Generally the components can readily be regarded as simple capacitors, inductors, resistors and inductive transformers.

A high performance active filter requires a high quality active inductor. One known inductor is of the type shown in Figure 1. The arrangement of Figure 1 comprises a first operational amplifier 1 to the positive input of which the input signal is applied. The output of the first amplifier 1 is coupled via a resistor 2 to the negative input of a second similar operational amplifier 3. The negative input of amplifier 1 and the positive input of amplifier 3 are connected together and are grounded through a resistor 4. The output of amplifier 1 is connected via a feedback resistor 5 to negative input of amplifier 1 and the output of amplifier 3 is connected via a feedback capacitor 6 to the negative input of amplifier 3. Finally the output of amplifier 3 is connected via a feedback resistor 7 to the positive input of amplifier 1.

According to the present invention there is provided an active inductor of the type hereinbefore referred to wherein the values of the resistors between the output of the first amplifier and the negative input of the second matching amplifier, between the output of the first amplifier and the negative input thereof, and between the negative input of the first amplifier and ground are respectively in the ratios 2R: R : (1 + V2)R, where R is given value of resistance.

The use of such values provides an inductor capable of producing a high Q, with characteristics independent of roll-off frequency and input impedance to first order, as the relationship between the passive components are suitably chosen. In this context "input impedance" refers to the active input impedance.

Clearly the input impedance of the operational amplifiers appears in parallel with the active inductor.

Embodiments of the invention will now be described with reference to the accompanying drawings, wherein: Figure 1 illustrates a high Active inductor, Figure 2 illustrates a fully floating high Q inductor, and Figure 3 illustrates an active filter incorporating a fully floating inductor.

The basic circuit of Figure 1 has already been described. To obtain optimum results the values of resistors 2,4 and 5 are 2R, Rand (1 + V2)R respectively. The inductance L is given by the formula 2(1 + V2)RTC where T is the value of resistance 7 and C is the value of capacitor 6. This circuit has optimum performance regarding sensitivity to D.C. gain and to second order effects or roll-offfrequency at particular frequencies.

The frequency for minimum sensitivity to gain is V2-1 4nRC This value also minimises the change in the inductance value due to the roll off.

The frequency for minimum second order effects of the roll off frequency is 0.306 f= 4aRC Because these frequencies are fairly close, an overall optimum will generally come at 0.36 f=~ 4nRC Thus, if a distinct resonance is desired the component values should be chosen so that the resonance tames at this frequency.

A floating inductor may be realised by taking two identical inductors according Figure 1 and connecting Giie earthed points together as shown in Figure 2.

if the values of 7 and 7' are made equal, the inductance L = 4(1 + /2)ROC. If 7 and 7' are different the arrangement of Figure 2 still looks like an inductor from both ends, but acts also as an impedance converter (this has no transformer equivalent, as power gain is involved). This can be useful where a filter requires different values on two sides of a floating inductor, and it is desired to use uniform capacitors throughout.

It may be noted that a floating inductor may readily be connected between two grounded inductors where a coupled resonator is required. Such a design is illustrated in Figure 3. It will be appreciated that the two pairs of amplifiers 1,3 and 1', 3' form the equivalent of one floating inductor, whilst amplifiers 1', 3', and 1", 3" form the equivalent of another floating inductor.

Claims (7)

1. An active inductor of the type hereinbefore referred to wherein the values of the resistors between the output of the first amplifier and the negative input of the second amplifier, between the output of the first amplifier and the negative input thereof, and between the negative input of the first amplifier and ground are respectively in the ratios 2R R: (1 + 2)R, where R is given value of resistance.

2. An active inductor arrangement including two inductors according to claim 1 connected together such that each forms a virtual ground for the other, resistors of value (1 + 0/2) Rare in series.

3. An active inductor arrangement including more than one inductor according to claim 1, wherein the resistors of value (1 + ) R are formed of parallel resistors, some of these resistors being connected to ground, and others in series with like resistors to create a network of grounded and floating inductors.

4. An active resonant circuit incorporating active inductors according to any one of claims 1-3 in which the component values are chosen so that 0.36 4aRC is approximately equal to the resonant frequency, where C is the value of the capacitive feedback around the second amplifier.

5. An active filter arrangement incorporating active inductors as claimed in any one of claim 1-4.

6. An active inductor substantially as illustrated in Figure 1 or Figure 2 of the accompanying drawings.

7. An active filter arrangement substantially as described with reference to Figure 3 of the accompanying drawings.