Analog Circuits Cookbook

Ian Hickman

• Publisher: Newnes
• Year: 1999
• Print ISBN: 9780750642347
• eBook ISBN: 9780080499086
• Edition: 2
• Topic: Tecnologia e ingegneria
• Subtopic: Design industriale

Analog Circuits Cookbook is a collection of tried and tested recipes form the masterchef of analog and RF design. Based on articles from Electronics World, this book provides a diet of high quality design techniques and applications, and proven ciruit designs, all concerned with the analog, RF and interface fields of electronics. Ian Hickman uses illustrations and examples rather than tough mathematical theory to present a wealth of ideas and tips based on his own workbench experience. This second edition includes 10 of Hickman's latest articles, alongside 20 of his most popular classics. The new material includes articles on power supplies, filters using negative resistance, phase noise and video surveillance systems. - Essential reading for all circuit design professionals and advanced hobbyists - Contains 10 of Ian Hickman's latest articles, alongside 20 of his most popular classics

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Advanced circuit techniques, components and concepts

Negative approach to positive thinking

Negative components

Negative components may not be called for every day, but can be extremely useful in certain circumstances. They can be easily simulated with passive components plus opamps and one should be aware of the possibilities they offer.

There is often felt to be something odd about negative components, such as negative resistance or inductance, an arcane aura setting them apart from the real world of practical circuit design. The circuit designer in the development labs of a large firm can go along to stores and draw a dozen 100 kΩ resistors or half a dozen 10 μF tantalums for example, but however handy it would be, it is not possible to go and draw a −4.7 kΩ resistor. Yet negative resistors would be so useful in a number of applications; for example when using mismatch pads to bridge the interfaces between two systems with different characteristic impedances. Even when the difference is not very great, for example testing a 75 Ω bandpass filter using a 50 Ω network analyser, the loss associated with each pad is round 6 dB, immediately cutting 12 dB off how far down you can measure in the stopband. With a few negative resistors in the junk box, you could make a pair of mismatch pads with 0 dB insertion loss each.

But in circuit design, negative component values do turn up from time to time and the experienced designer knows when to accommodate them, and when to redesign in order to avoid them. For example, in a filter design it may turn out that a −3 pF capacitor, say, must be added between nodes X and Y. Provided that an earlier stage of the computation has resulted in a capacitance of more than this value appearing between those nodes, there is no problem; it is simply reduced by 3 pF to give the Final value. In the case where the final value is still negative, it may be necessary to redesign to avoid the problem, particularly at UHF and above. At lower frequencies, there is always the option of using a ‘real’ negative capacitator (or something that behaves exactly like one); this is easily implemented with an ‘ordinary’ (positive) capacitor and an opamp or two, as are negative resistors and inductors. However, before looking at negative components using active devices, note that they can be implemented in entirely passive circuits if you know how (Roddam, 1959). Figure 1.1(a) shows a parallel tuned circuit placed in series with a signal path, to act as a trap, notch or rejector circuit. Clearly it only works well if the load resistance R_l is low compared with the tuned circuit’s dynamic impedance R_d. If R_l is near infinite, the trap makes no difference, so R_d should be much greater than R_l; indeed, ideally we would make R_d infinite by using an inductor (and capacitor) with infinite Q. An equally effective ploy would be to connect a resistance of −R_d in parallel with the capacitor, cancelling out the coil’s loss exactly and effectively raising Q to infinity. This is quite easily done, as in Figure 1.1(b), where the capacitor has been split in two, and the tuned circuit’s dynamic resistance R_d (R_d = QωL, assuming the capacitor is perfect) replaced by an equivalent series loss component r associated with the coil (r = ωL/Q). From the junction of the two capacitors, a resistor R has been connected to ground. This forms a star network with the two capacitors, and the next step is to transform it to a delta network, using the star-delta equivalence formulae. The result is as in Figure 1.1(c) and the circuit can now provide a deep notch even R_l is infinite, owing to the presence of the shunt impedance Z_p across the output, if the right value for R is chosen. So, let R′ = –r, making the resistive component of Z_s (in parallel form) equal to –R_d. Now R′ turns out to be −1/(4ω²C²R) and equating this to –r gives R = R_d/4.

Figure 1.1 (a) A parallel tuned circuit used as a rejector. The notch depth is set by the ratio of the tuned circuit’s dynamic resistance R_dand the load resistance R_I. At F₀ the tuned circuit is equivalent to a resistance R_d = QωL (Q of capacitor assumed much larger). F₀ = 1/2π√(LC). (b) The circuit modified to provide a deep notch, tuned frequency unchanged. Coil series losses r = ωL/Q = R_d/Q²(c) As (b) but with the star network transformed to the equivalent delta network. Z_s = (–j/ωC) −1/(4ω²C²R). So C′ = C and R′ = −1/(4ω²C²R) and if R′ = −r = −R_d/Q²then R = R_d/4, Z_p = (j/2ωC) + (R_d/2)

Negative inductor

Now for a negative inductor, and all entirely passive – not an opamp in sight. Figure 1.2(a) shows a section of constant-K lowpass filter acting as a lumped passive delay line. It provides a group delay dB/dω of √(LC) seconds per section. Figure 1.2(b) at dc and low frequencies, maintained fairly constant over much of the passband of the filter. A constant group delay (also known as envelope delay) means that all frequency components passing through the delay line (or through a filter of any sort) emerge at the same time as each other at the far end, implying that the phase delay B = ω √(LC) radians per section is proportional to frequency. (Thus a complex waveform such as an AM signal with 100% modulation will emerge unscathed, with its envelope delayed but otherwise preserved unchanged. Similarly, a squarewave will be undistorted provided all the significant harmonics lie within the range of frequencies for which a filter exhibits a constant group delay. Constant group delay is thus particularly important for an IF bandpass filter handling phase modulated signals.) If you connect an inductance L′ (of suitable value) in series with each of the shunt capacitors, the line becomes an ‘m-derived’ lowpass filter instead of a constant-K filter, with the result that the increase of attenuation beyond the cut-off frequency is much more rapid. However, that is no great benefit in this application, a delay line is desired above all to provide a constant group delay over a given bandwidth and the variation in group delay of an m-derived filter is much worse even than that of a constant-K type. Note that L′ may not be a separate physical component at all, but due to mutual coupling between adjacent sections of series inductance, often wound one after the other, between tapping points on a cylindrical former in one long continuous winding. If the presence of shunt inductive components L′ makes matters worse than the constant-K case, the addition of negative L′ improves matters. This is easily arranged (Figure 1.2(c)) by winding each series section of inductance in the opposite sense to the previous one.

Figure 1.2 (a) Basic delay line – (b) providing a delay of √(LC) seconds per section at dc and low frequencies. (c) Connection of negative inductance in the shunt arms to linearise the group delay over a larger proportion of the filter’s passband. Not a physical component, it is implemented by negative mutual inductance (bucking coupling) between sections of series inductance

Real pictures

Now for some negative components that may, in a sense, seem more real, implemented using active circuitry. Imagine connecting the output of an adjustable power supply to a 1 Ω resistor whose other end, like that of the supply’s return lead, is connected to ground. Then for every volt positive (or negative) that you apply to the resistor, 1 A will flow into (or out of) it. Now imagine that, without changing the supply’s connections, you arrange that the previously earthy end of the resistor is automatically ja...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Preface to second edition
• 1: Advanced circuit techniques, components and concepts
• 2: Audio
• 3: Measurements (audio and video)
• 4: Measurements (rf)
• 5: Opto
• 6: Power supplies and devices
• 7: RF circuits and techniques
• Index