GB2314475A - An operational amplifier connected to a low pass filter with complex pole pairs and having a feedback loop with a real pole to maintain good output impedance - Google Patents

Abstract

An operational amplifier filter arrangement is described, which comprises an input for receiving a input signal, an operational amplifier with a feedback loop, a passive low pass filter network and an output for providing an output signal. The passive low pass filter has a transfer characteristic given by complex pole pairs and a single real pole is incorporated into the feedback loop. This gives the same overall frequency response as a conventional filter, but the amplifier's roll-off is dominated by the real pole. Increased negative feedback at higher frequencies maintains a good output impedance. A method of operating such an operational amplifier is also described.

Description

AN OPERATIONAL AMPLIFIER FILTER ARRANGEMENT The present invention relates to filters and in particular relates to a filter operable with an operational amplifier.

Filters are frequently employed in communications systems, for example passive LC networks providing anti-alias, pole shaping or channel selection functions. They are often used together with operational amplifiers, for example in systems employing moderate to wide communication bandwidths in which baseband gain is required in conjunction with the filtering. However, an operational amplifier will have a limit to the maximum frequency at which it can be used, and when used close to the limit of its gain-bandwidth product, the performance may be badly controlled. It may vary in any specific amplifier in an unpredictable manner due to temperature variations, and from example to example as a result of manufacturing tolerances. Such variations are undesirable and may only be avoided if we limit the maximum frequency at which the operational amplifier is used.

We characteristically observe two limits to the maximum frequency at which an operational amplifier may be used in conjunction with a passive LC filter.

First of all, we must limit the maximum frequency of operation so that the open-loop gain of the amplifier at the frequency limit exceeds the closedloop gain by some small margin, in order for the amplifier to have a welldefined gain throughout its pass-band. This limit derives from the normal theory of operational amplifier circuit design.

The second limit is usually more severe. When an operational amplifier circuit drives a filter, it must also maintain a well-controlled output impedance, matching the filter's input impedance. At frequencies inside the filters pass-band, it must match the filter's input impedance in order to maintain the desired filter pass-band characteristics, and so accurately pass wanted signals inside the desired frequency range. At frequencies outside the filter's pass-band it must also maintain a good impedance match in order for the filter to adequately reject unwanted signals. This implies that the open-loop gain of the amplifier at the maximum frequency of operation must be substantially higher than the closed-loop gain in order for the output impedance to be well maintained even throughout some of the stop-band of the filter.

There is also a third consideration, common to most operational amplifiers that limits the maximum frequency at which they can be used. They need electronic compensation for their limited gain-bandwidth product in order to ensure their stability. The compensation will usually cause the gain of the operational amplifier to be reduced as frequency increases so that in its operating configuration the amplifier's gain falls below 0 dB before the phase shift through the amplifier and its feedback network reaches 360 This compensation will usually reduce the available bandwidth in a circuit using the amplifier.

Thus a trichotomy exists between offering a wide operational bandwidth, obtaining a high gain, having good stability over a broad frequency range, and maintaining an accurate filter characteristic. Usually this means that the highest frequency at which an amplifier may be used has to be curtailed if the other essential performance criteria are to be met. However, by matching the components of a filter with the feedback circuit of an operational amplifier used in conjunction with it, good filtering performance may be provided over an extended frequency range that exceeds the range obtainable with an un-matched filter-amplifier combination.

At low frequencies, operational amplifiers provide a high level output signal in response to a low level differential input signal. However as the radian frequency X of the input signal increases, a point is reached where the gain of an uncompensated operational amplifier starts to decrease due to the limitations of the amplifier's components. This frequency is referred to as the open-loop bandwidth (for the purposes of this disclosure, the upper limit will be taken to be the -3dB point). It is generally desirable for the operational amplifier to have both a high gain and a high gain-bandwidth product, so that satisfactory operation may be obtained over a wide band of frequencies.

In normal use, the gain of an operational amplifier circuit is set to a value below the open-loop gain by employing a feedback loop in which a fraction of the amplifier's output is fed back to its input. This creates an amplifier circuit in which the closed-loop gain is lower than the amplifier's open-loop gain, but which is substantially well controlled by the feedback circuit alone over a wider frequency range than the open-loop bandwidth. If the fraction of the output signal that is fed back to the input is constant over frequency, the closed-loop gain will also be substantially constant over the frequency range where the open-loop gain of the operational amplifier exceeds the closed-loop gain. This frequency range is referred to as the closed-loop bandwidth.

Whilst high open-loop gain in itself is not difficult to achieve, an operational amplifier must also maintain stability in its closed-loop operation. The stability of an operational amplifier circuit is determined from the phase margin and gain margin of the circuit. These may be determined from the magnitude of the loop transfer function and its phase versus radian frequency o. The phase margin is the difference between 3600 and the phase response of the loop transfer function at the radian frequency corresponding to 0 dB (decibels) of the loop gain response; whilst the gain margin is the difference between 0 dB and the loop gain at the critical frequency (which corresponds to 360 of the phase response). When the loop gain is greater than one (0 dB), less than 3600 of phase shift should occur through the amplifier and the feedback circuit. If this is not the case, when the output of the operational amplifier is coupled back to its input by an impedance arrangement, for example in an active filter application, the output signal could create a feedback signal in-phase with the input signal thereby permitting the operational amplifier to sustain its own operation and oscillate.

Most operational amplifiers are therefore compensated with a dominant pole inserted at a predetermined low frequency to ensure that the transfer function rolls off at a low rate and drops below 0 dB before the phase response reaches 360 . EP-A-479119 (Motorola) provides an operational amplifier which includes several compensation circuits for stabilising the characteristics of the operational amplifier. Some operational amplifiers have external ports where a capacitor can be coupled for providing the dominant pole. Operational amplifiers can be internally frequency compensated by "pole-splitting" capacitors which load the output terminal.

A negative feedback loop through the pole-splitting capacitor causes, at higher frequencies, the load change applied at output terminal to be opposed. Additional current drawn from output terminal will lower the signal level whereby the RC time constant at output terminal and increases the frequency of the output pole. Pole-splitting capacitors are known as such since they provide a low frequency dominant pole internally and a high frequency pole at the output terminal. The low frequency dominant pole is needed to roll-off the transfer function of operational amplifier such that the gain is less than 0 dB before the critical 3600 of phase shift, yet the pole at output terminal must be placed at a high frequency such that the 900 of phase shift associated therewith does not influence the phase response in the region of the unity gain frequency ea (0 dB crossing) of the gain response with an adverse effect on the overall stability.

The value of the compensating capacitor and the predetermined low frequency of the dominant pole are important in determining the performance of the operational amplifier. The frequency of the dominant pole should be made as high as possible for providing a good bandwidth, yet the higher frequency selection will extend the roll-off frequency and the unity gain frequency thereby lowering the gain and phase margin. If the frequency of the dominant pole is too high, manufacturing tolerances and temperature variation could allow the frequency of the dominant pole to drift whereby the phase response passes through 3600 before the gain response falls below 0 dB. Operational amplifiers are not perfect devices for producing high gain: at high frequencies stability cannot be guaranteed and the output impedance may exceed acceptable limits.

Double poles are employed in some designs and are inserted at the predetermined low frequency for providing an even steeper roll-off of the gain response say, 12 dB/octave, which might seem to offer a higher roll-off frequency without increasing the unity gain frequency and providing a wider bandwidth. However the double poles also causes a 180 shift, causing the phase response to approach the critical 3600 at a lower frequency as compared to a single pole response. Phase margins may reach unacceptable limits and allow the operational amplifier to oscillate, thereby defeating the purpose of the double pole. A single dominant pole is preferred for the internal frequency compensation circuit to enable sufficient guard band in the gain and phase margins to allow for variations.

The filtering of base band signals is necessary in many communication networks. The base band filtering is used for anti-alias, pole shaping and for channel selection purposes and can be effected using passive inductorcapacitor (LC) networks. Such filters are sometimes realised in networks which include a high speed operational amplifier to simultaneously provide base band gain. This base band gain has a limited bandwidth. Problems arise from the fact that the in-band roll-off of the amplifier adds unwanted features to the desired filter response and out of band the impedance of the amplifier will vary, creating filter matching problems. This frequency roll-off is not, however, fixed and will vary with temperature and manufacturing tolerances. This reduces the open loop gain at the filter band edge and the operational amplifier output impedance cannot be suitably controlled by negative feedback alone. This means that the subsequent filter sees a poor drive impedance at some frequencies giving a poor frequency response. A simple type of operational amplifier, will have a resistive feedback arrangement driving an inductor-capacitor filter network. The transfer function of the filter, F(s), can be determined from the following equation, assuming that the input and output impedances are well matched: F(s)=k/(s-co)(s-(aiii))(s-(Ifl2)) ... equation 1 Accordingly with conventional designs, the open loop gain of the amplifier at the filter cut-off frequency has to be significantly higher than the closed loop gain. Thus the maximum usable frequency of operation is limited.

Accordingly an object of the present invention is to provide an improved filter operable with an operational amplifier.

In accordance with the invention, there is provided an operational amplifier arrangement including a passive filter network wherein a pole from the filter network is incorporated in the operational amplifier feedback circuitry.

In accordance with another aspect of the invention there is provided an operational amplifier arrangement having an input for receiving an input signal, a feedback loop, a passive low pass filter network and an output for providing an output signal, wherein the passive low pass filter network has a transfer characteristic given by complex pole pairs and wherein a single real pole is incorporated into the feedback loop. This gives the same overall frequency response as a conventional filter and amplifier, but the amplifier's low frequency roll-off is now dominated by the real pole.

Increased negative feedback at higher frequencies maintains a good output impedance.

The single real pole can be incorporated into the feedback by the incorporation of a capacitive element in parallel with an impedance.

In another aspect of the present invention, there is provided is a method of operating an operational amplifier, comprising the steps of: receiving an input signal, amplifying the input signal with an operational amplifier with a feedback loop, feeding back a signal from the output of the amplifier back through the feedback circuit which has a capacitor in parallel with an impedance circuit and provides a real pole, and passing an output signal to a filter having complex pole pairs, whereby the roll-off of the amplifier increases the negative feedback at higher frequencies whereby a output impedance is maintained.

A simple yet stable design for a high performance operational amplifier operable in a great variety of situations is thereby provided. Applications for this design include modems, cellular telephone handsets to name but a few.

In order to aid understanding of the invention, reference will now be made to the figures as shown on the accompanying drawing sheets.

FIG. 1 shows a conventional arrangement of an operational amplifier and a passive filter network; and FIG. 2 shows an amplifier and filter arrangement incorporating an embodiment of the present invention.

Referring now to Figure 1, there is shown an operational amplifier arrangement having a feedback circuit including a resistive element and a low pass filter network. The filter network is shown as a passive filter circuit. Any conventional filter characteristic can be described by the positions of the poles as given by the factorised transfer function. This factorised transfer function can be derived either directly from a generating formula or from a reference table of low pass filter prototypes. For oddorder filters, there will be a number of complex conjugate pairs of poles (n/2 - 1) and a single real pole, where n is the order of the filter.

Referring now to figure 2, there is shown one embodiment of the invention wherein the low pass filter is synthesised whereby the transfer characteristic is given by complex pole pairs only and a single real pole is incorporated into the operational amplifier's feedback loop. This transfer in position of the real pole is enabled by the provision of a capacitive element in the feedback circuit in conjunction with resistive elements. The capacitive element can be provided in the feedback circuit in parallel arrangement with resistive elements. A similar overall frequency response to the circuit of figure 1 can be obtained, but the amplifier's roll-off is now dominated by the real pole and the increased negative feedback at higher frequencies maintains a good output impedance. With reference to equation (1), the transfer function, F(s), can now be shown to be the product of Fi(s) and F2(s), where: F1(s)=ki /(s-ao) equation 2 F2(s)=k2/(s-(#1##1))(s-(#2##2)) .. equation 3 withkl.k2=kands=j(o.

It has previously been seen that a method for stabilising an operational amplifier comprises the use of a dominant pole within the amplifier circuit in order to ensure that adequate gain and phase margins are achieved. The pole that was transferred from the LC filter to the operational amplifier's feed back circuit now achieves this stabilisation function, as well as being part of the filter's transfer characteristic. Because of the dual role played by the pole in the amplifier's feed back circuit, the open-loop gain of the amplifier remains higher than otherwise possible and so its output impedance remains well controlled over a wider frequency range. Because of this the circuit may be used over a wider bandwidth than a conventional combination of operational amplifier and filter, without degradation to the filter's transfer characteristic.

Claims (4)

1. An operational amplifier arrangement including a passive filter network wherein a real pole from the filter network is incorporated in the operational amplifier feedback circuitry.

2. An arrangement according to claim 1 wherein the operational amplifier has an input for receiving an input signal, a feedback loop, a passive low pass filter network and an output for providing an output signal, wherein the passive low pass filter network has a transfer characteristic given by complex pole pairs and wherein a single real pole is incorporated into the feedback loop.

3. An arrangement according to any one of claims 1 or 2, wherein the single real pole is incorporated into the feedback loop by the incorporation of a capacitive element in parallel with an impedance.

4. A method of operating an operational amplifier comprising the steps of receiving an input signal, amplifying the input signal with an operational amplifier with a feedback loop, feeding back a signal from the output of the amplifier back through the feedback circuit which has a capacitor in parallel with an impedance circuit and provides a real pole, and passing an output signal to a filter having complex pole pairs, whereby the roll-off of the amplifier increases the negative feedback at higher frequencies, whereby a output impedance is maintained.