GB2123631A

GB2123631A - All pass filter

Info

Publication number: GB2123631A
Application number: GB08313026A
Authority: GB
Inventors: Aldo A Martinez
Original assignee: Racal Data Communications Inc
Current assignee: Racal Data Communications Inc
Priority date: 1982-05-14
Filing date: 1983-05-11
Publication date: 1984-02-01
Also published as: DE3314468A1; FR2527025A1; JPS58219811A; GB8313026D0

Abstract

A differential amplifier (11) is fed directly via a resistance (R1) and via a potential divider comprising a resistor (R3) and a frequency-dependent impedance such as the series L-C circuit shown. A feedback resistance (R2) can be set to balance the effects of non-ideal inductor Q. The impedance arrangement shown reduces the effects of stray capacitance (C1). <IMAGE>

Description

SPECIFICATION All pass filter The subject invention relates to filters and more particularly to an all pass filter section. The filter section of the preferred embodiment finds particular use in data modems requiring all pass filter responses around 100 kilohertz.

Prior art active filters of the type under discussion have been subject to parasitic capacitance effects which limit high frequency response. Another problem which has limited performance of such filters is the departure from ideality caused by non-ideal coils (inductors) and introduced by a real pole created by operational amplifiers used in such filters. When such prior art filters are cascaded as is required in various applications, the cumulative effects of the limitations of prior art circuits can seriously degrade performance.

These and other objects and advantages are achieved according to the invention by providing a filter circuit arrangement which enables adjustment of a resistance in the feedback path of an operational amplifier to eliminate effects of coil non-ideality and which, at the same time, greatly reduces the effect of stray capacitance in the frequency band of interest.

One embodiment of the invention will now be described, by way of example, in conjunction with the drawings, in which: Fig. 1 illustrates a prior art all-pass filter section; Fig. 2 illustrates the poles and zeros of the transfer function of an ideal all-pass filter; Fig. 3 illustrates poles and zeroes of a prior allpass filter circuit subject to parasitic effects; Fig. 4 is a schematic diagram of the all-pass filter of the preferred embodiment; Fig. 5 illustrates one example of a resistance combination for modelling one of the resistors of an actual circuit according to the preferred embodiment.

A typical prior art all-pass filter circuit is shown in Fig. 1. As known in the art, the purpose of an all-pass section is to produce a prescribed phase vs. frequency response with flat amplitude characteristics. For a second order all-pass section, this is accomplished when the poles and zeros of the transfer function are the mirror images of one another, as shown in Fig. 2.

In practice, imperfections present in the elements with which the circuit is physically realized, (such as inductors with losses, amplifiers with decaying gain as frequency increases, stray capacitances, etc) introduce extraneous singularities and move the position of the ideal case poles with respect to their corresponding zeros. Fig. 3 shows the case where the poles and zeros are not in their mirror-image positions and, furthermore, an extra pole has appeared on the real axis. The actual pole-zero pattern, of course, depends on the actual circuit elements and configuration, but this case is illustrative of the problems addressed by the invention.

An analysis of the prior art circuit of Fig. 1 reveals the following: a) The all-pass condition tH(jcs)l=1 for all a) no longer holds. The real-axis pole forces the amplitude vs. frequency response to decrease toward zero as the frequency increases.

b) The mis-alignment between the poles and zeros will also yield different values for the quadratic factors in the numerator and denominator of the IH(jw)l function at any value of 9, thereby further degrading the amplitude response.

c) The phase and delay responses of the prior art circuit will deviate from the ideal case and, unless the value and effect of the undesired elements are precisely known and compensated for, there will be an error component in the desired phase and delay responses. Such precise knowledge and compensation is not available as a practical matter.

While it is a fact of life that circuit element imperfections such as energy loss in inductors and stray capacitance cannot be eliminated, the circuit arrangement to be described combines elements in such a way so as to reduce deleterious effects to acceptably low levels.

The preferred embodiment of the invention is shown in Fig. 4. It includes a differential operational amplifier 1 resistors R1, R2and R3, an inductor L and capacitor C. The resistor R2 is connected in a feedback path of the amplifier 11 between the output 1 3 and inverting input 1 5.

Resistors R1 and R3 are connected in common at one terminal 19 and to the inverting and noninverting inputs 1 5, 1 7 of the amplifier 11, respectively, at their opposite terminals. The inductor L and capacitor C are connected in series between the noninverting input 17 and ground.

The filter circuit is driven by a source Vg having a series impedance Zg connected to the common resistor terminal 19. With the circuit of the preferred embodiment, the effect of the nonideal Q of the inductor L can be compensated for by adjustment of the resistor R2. This may be shown mathematically by the expression for the transmittance:

R2 Q=Q of inductor L and K R, By setting R2 K= R, equal to Qo 1+2 QL the absolute value of the linear term in the numerator and denominator of T(s) become equal, thereby giving an all pass characteristic, which may be perfected by varying resistor R2.

Furthermore, the impedance level at the noninverting input 1 7 is very low, since R3 is of the order of a few hundred ohms. Reasonably good estimates for the value of the parasitic capacitor C1, are 10-30 picofarads (pf). For frequencies in the 50-1 00 kHz band of interest, L and C will have values in the neighborhood of 2 millihenries and 1000 pf. It can be seen that the effect of C, is minimai in the band of interest.

One additional consideration should be noted.

The circuit is typically driven by another operational amplifier represented by Vg, Z9. The impedance Zg should be as low as possible for best operation. with standard off-the-shelf amplifiers, Zg < 5Q may be realized.

In a typical 100 kHz all-pass section according to the preferred embodiment, LM 318 operational amplifiers may be used for Vg and operational amplifier 11. Resistor R, is a 1000 ohm resistor and R2 is modelled by a 500 ohm variable resistor in parallel with 124 ohms, the parallel combination in series with 953 ohms. The R2 model is illustrated in Fig. 5.

Exemplary R3 values are 113 ohms and 41 ohms for QO values of 14 and 40 respectively, with C=.001 microfarads.

The arrangement described will be seen to more precisely compensate for imperfections in prior art filter circuits used in all pass networks, and to mitigate the effect of parasitic capacitance on an all-pass filter circuit, whilst using standard operational amplifier components.

Claims

1. An all-pass filter circuit comprising: an operational amplifier; a frequency dependent impedance exhibiting a finite Q factor and connected to the noninverting input of said amplifier; a resistance connected to the inverting input of said amplifier; and means in the feedback path of said operational amplifier for substantially cancelling the nonideality in frequency response caused by the Q factor of said frequency dependent impedance.

2. The all-pass filter circuit of claim 1 wherein said frequency dependent impedance includes means for minimizing effects of stray capacitance.

3. The all-pass filter circuit of claim 1 or 2 wherein said frequency dependent impedance includes: a second resistance connected to the noninverting input of said operational amplifier and to the input of said all-pass filter-circuit; a series combination of inductance and capacitance connected between the noninverting input and ground.

4. The all-pass filter circuit of claim 3 wherein said second resistance is in the range 20 to 3000 ohms, and said capacitance is on the order of ;001 microfarads.

5. An all pass filter comprising a potential divider connected to the input of the filter, and a differential amplifier arranged to produce an output signal proportional to the difference between the output of the potential divider and a signal proportional to the input signal, one arm of the potential divider consisting of a frequency dependent impedance means having a finite Q factor, the real component of the impedance thereof being substantially frequencyindependent.

6. An all pass filter according to claim 5, in which the impedance means is a series LC tuned circuit.

7. An all pass filter according to claim 5 or 6, in which the differential amplifier is a non-inverting input connected to the output of the potential divider and an inverting input connected via a first resistance to the input of the filter and via a second resistance to the output of the amplifier.

8. An all pass filter substantially as herein described with reference to figure 4 of the accompanying drawings.