7th International Symposium on Power-Line Communications and Its Applications Kyoto, Japan, March 26-28, 2003 Session A5: System Architecture
Practical Aspects of Component Selection and Circuit Layout for Modem and Coupling Circuitry Petrus A. JANSE VAN RENSBURG† and Hendrik C. FERREIRA‡ †
‡
Department of Electrical Engineering Border Technikon P.Bag 1421, East London, 5200, South Africa Phone: +27-82-200-6207, Fax +27-43-702-9226 E-mail:
[email protected]
Abstract This paper summarises the various aspects that have to be considered when choosing passive components for powerline communications. In section 1, it is stressed that in order to design effective communication electronics as well as interfacing electronics for power line coupling, various side effects of current, voltage and frequency extremes have to be understood. Section 2 discusses various detrimental effects that occur in conductors (often a result of circuit layout), while sections 3 to 6 discuss deviations from the ideal in resistors, capacitors, inductors and transformers respectively. A final conclusion is made in section 7. 1. Introduction The superimposing of a communication signal on a power waveform implies that communication circuitry and power circuitry would have to be carefully designed and/or interfaced for optimal compatibility between the two systems. Power systems and communication systems operate at two different extremes – power systems at very low frequencies and very high power, current and/or voltage levels and communication systems at very high frequencies and very low power, current and voltage levels. To be able to design said communication systems as well as a proper interface between power and communication systems, components as well as circuitry must be fundamentally understood at said extremes. This dilemma of designing for both the power waveform as well as the communication waveform is illustrated below: •
Department of Electrical and Electronic Engineering Rand Afrikaans University P.O.Box 524, Auckland Park, 2006, South Africa Phone +27-11-489-2463, Fax +27-11-489-2357 E-mail:
[email protected]
•
Coupling capacitors: these carry the communication current and thus have to be high-frequency capacitors (self-resonant point has to be higher than the modulation frequency). Conversely, they have to filter the power voltage (dropped across the component) as well as voltage surges and therefore need to be highvoltage capacitors.
•
Coupling transformers: the main function is galvanic isolation and impedance adaptation, but the coupling transformer has to freely pass the high-frequency communication signal and has to be designed as such. Unfortunately the power waveform has a much lower frequency and much higher voltage, and the power waveform would have a saturating influence of at least 105 compared to the communication waveform. Therefore the power waveform is typically first filtered before entering the coupling transformer.
In most designs, circuit diagrams are drawn using the lumped-parameter model. This model assumes that a component is purely resistive, capacitive or inductive. Actually all components have a mixture of these three attributes. The attributes not taken into account in the ideal lumped-parameter model, are called stray or parasitic components. In the following sections, the influences of these parasitic parameters as well as other obstacles will be discussed. Apart from the existence of parasitic impedances, their magnitudes and influence on the circuit are aggravated by voltage and current extremes. The effects of parasitic capacitances are worse at high voltages whilst the effects of parasitic inductances are aggravated by high currents. This implies that component behaviour in a power-line communications application could be totally different to laboratory behaviour. Magnetic components (inductors and transformers) are especially prone to unwanted side effects and have to be designed carefully. A real-world component’s behaviour depends mostly on frequency, current, voltage and temperature of which frequency is the
Blocking inductors: these have to be designed for the power frequency (to prevent saturation) and for the power current (to prevent volt-drops). But blocking inductors have to function properly especially at the modulation frequency, and therefore the self-resonant point needs to be above said frequency. Air-core inductors are well suited to this application.
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increase as frequency increases. Thus even component leads and interconnecting wires can cause unwanted parasitic effects at high frequencies. To minimise this parasitic inductance in practice, one would make connecting wires as short and thick as is practically convenient. Using two (or more) spaced wires to carry the same current, has almost the same effect on straight-line inductance as using one conductor with a diameter of the said spacing [4].
most common. Although temperature can have a substantial influence on the characteristics of components and circuits, its influence will generally only be mentioned in this paper. 2. Conductors and circuit layout Conductors are often overlooked during an electrical / electronic design, as these are always assumed to be ideal in circuit diagrams. But the negligible resistance of a certain conductor combined with the contact resistance at both ends, can cause a significant voltage drop if a large current passes through it. Furthermore, at high frequencies, the skin effect and proximity effect cause all conductors to have a higher ac resistance than its associated dc resistance. Other influences that need to be considered, are the parasitic inductance of straight conductors and loopforming conductors, and parasitic capacitance between closely spaced conductors.
Another source of stray inductance is created when alternating current flows through any loop formed by conductors and other components. This loop is effectively a one-turn air core inductor. Apart from the parasitic inductance, the loop also acts as a transmitting and receiving antenna, aggravating EMI in the circuit [2]. To minimise these negative effects, circuit layout is extremely important – the cross-sectional area of every single loop in the circuit needs to be made as small as practically possible. Also, pairs of interconnecting wires are normally twisted for the same reason.
The dc resistance of any uniform conductor can be calculated using the classical R = ρl/A formula. It is not uncommon for long cables to have dc resistance figures of a few ohms. When large currents flow through these, large voltages develop across them. A cable carrying 100A of current that has a resistance of only 1Ω causes a loss of 100V across its terminals. This negative effect can be reduced by increasing the cross-sectional area of the conductor.
The term skin effect refers to the fact that high-frequency currents tend to flow on the surface of a conductor. As discussed in the straight-line inductance section, any change in current is opposed by the magnetic field surrounding the current, effectively manifesting as inductance. These magnetic fields are stronger in the centre of a conductor, resisting the flow of current more than on the surface. One could say that the impedance experienced by alternating current in the centre of the conductor is higher than for ac currents flowing on the surface.
Contact resistance falls beyond the scope of this discussion, but a few general guidelines can be followed to minimise its influence. Contact surface areas should be large, especially solder joints, as the resistivity of solder is much higher than that of copper. Any oxidation or dirt should be thoroughly removed, as these obstruct the flow of current and effectively reduce the contact area. In highcurrent applications, pressure is typically applied to the contact surface in order to reduce contact resistance.
Because a large portion of the cross-sectional area is not utilised, the conductor’s ac resistance for that specific frequency is higher than at 0Hz (dc) or any lower frequency. The distance from the surface at which the current density drops to 1/e or 0.368 of the maximum current density on the surface, is called the skin depth, depth of penetration or critical depth. Theoretically, skineffect calculations for various waveforms can get very involved [3], but the skin depth δ for a sinewave with frequency f is given by [4]:
The self-inductance of a straight length of conductor, carrying alternating current, is [1]: 4l (1) L = 2l 2.3 log10 − 0.75 [nH] d where l and d represent the length and diameter of the conductor. The fundamental reason for this phenomenon is that any change in current is opposed by the magnetic field surrounding the current, creating a back-EMF type voltage across the terminals of the cable. The longer the conductor, the larger its parasitic self-inductance becomes. The length / diameter ratio also influences a conductor’s stray inductance – the thicker the conductor, the lower its parasitic self-inductance. Although this inductance is independent of frequency, its reactance is directly proportional to frequency, causing its impact on a circuit to
δ =
1 πσµ 0 µ R f
(2)
where µR and σ are the relative permeability and conductivity of the conductor material respectively and µ0 is the permeability of free space. When designing a highfrequency practical circuit, one would first calculate the skin depth of the specific metal at the operating frequency. One could either use metal plate conductors or a twisted bundle of insulated strands, called Litz wire [5]. A metal plate conductor would have a thickness between δ and 2δ,
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Although resistors theoretically have a constant impedance magnitude and zero phase angle, they also show deviations from ideal when exposed to high frequencies. Some of the resistor-types that will be discussed are wire-wound, carbon composite, metal film and thin film chip resistors.
and the required width to produce cross-sectional area for a certain current density. Billings [6] gives guidelines for optimum (minimum ac resistance) plate thickness and strand diameter, which is influenced by various factors. For Litz wire, a circular enamel-insulated strand of wire with a diameter in the order of δ to 2δ would be chosen. The required cross-sectional area for a certain current density would then be obtained in order to calculate the required number of insulated strands.
The wire-wound resistor exhibits the worst performance when high-frequency currents are applied. The manufacturing method involves the winding of a highresistivity wire around a cylindrical heat-resistant substrate, which typically has a relative permeability (µR) close to 1. This means that the wire-wound resistor is essentially also a cylindrical air core inductor. See [2] for the necessary formulas to calculate this parasitic inductance. The distributed capacitances between adjacent windings are lumped as a parasitic shunt capacitor. See Fig. 1.
The proximity effect is caused by the magnetic fields of other high-frequency alternating currents in close proximity to the conductor in which the effect is observed. The stronger the magnetic field, the stronger the opposition to changes in current. As the skin effect, the proximity effect can also increase the effective ac resistance experienced by alternating currents. Fortunately this effect only plays a substantial role in inductors and transformers, where conductors are in close proximity, and especially where windings are tightly wound to fit into a certain core window.
L
L ZT
Although not as commonly observed as magnetic effects, parasitic capacitance can play an important role where conductors are closely spaced, as predicted by the parallel plate capacitance formula
εε A C= 0 R . d
R
a)
C
b)
small R big R fRES
f
Fig. 1 a) General equivalent parallel-resonant circuit for resistors [1], and b) typical ZTOTAL vs logarithmic frequency plot.
(3)
Symbols A and d represent shared cross-sectional area and distance between two parallel conducting surfaces, ε0 the permittivity of free space and εR the relative permittivity of the material between the conducting surfaces. A typical example of a parasitic capacitance would be the interwinding capacitance of a transformer, which manifests between the primary and secondary windings, as the area between the two layers of conductors is big while the separating distance between them is small [7]. Often insulating materials have a higher εR than air, which increases this parasitic effect. Co-axial cables are also well known for this effect, as the two co-axial conductors have a large common area between them, directly proportional to the cable length.
Furthermore, the straight-wire inductance of each terminal lead also adds to the total value of the parasitic series inductance. Special high-frequency wire-wound resistors that are useful for frequencies up to 200kHz, are crosswound or bifilarly wound in a special way to cancel fluxlinkages and so minimise the parasitic inductive effect [2,10]. Also, the cross-sectional area of the ceramic substrate (effectively an air-core), and thus the parasitic inductance, is minimised by using a thin, flat substrate instead of a cylindrical one (see (7)). Take note that the general equivalent circuit for resistors is a parallel-resonant one. Instead of having a constant resistance (reactance) and zero phase shift, any resistor will first show inductive, resonant and ultimately capacitive characteristics if the frequency is raised high enough. See Fig. 1 b). Furthermore, the magnitude of the resistive part influences the quality factor (relative width of resonant peak). The bigger the magnitude of a wirewound resistor compared to its parasitic reactances, the lower the resonant peak, and the less significant the influence of the parasitic reactances. Thus low-value wirewound resistors are more susceptible to parasitic effects, and should be treated with greater care. For carbon composite and metal film resistors, the contrary is true.
3. Resistors For power-line communications in general, one would try to avoid using resistors, as resistance, in essence, implies a loss of power, either of the communication signal or the power waveform. However, a resistor can be used for various purposes such as a linear current-measuring device (low-resistance, series connected resistor strangely called a shunt [8]), as a voltage sensing device (voltage divider circuit [9]), to bias transistor circuits or to shape the quality factor / selectivity of a filter or resonant circuit [1].
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communication signal to the power line [12], but also as part of more sophisticated, higher-order filters [13] and general communication / modem circuitry [14]. Just as any other passive electronic component, a real-world capacitor has all three L, R and C parameters, but is called a capacitor because the C component dominates. Fig. 3 shows the equivalent circuit that is generally valid for capacitors [1,15]. Often the series inductance is omitted [15,16] to simplify the model, but sometimes more complicated models are used [17]. Take note that Fig. 3a) is a series-resonant one, incorporating losses associated with contacts and terminals (RS) as well as the dielectric (RP). RS is typically small, in the order of 1/10 ohm to 1 ohm, but RP is usually in the mega-ohm to giga-ohm range [1].
Carbon composite resistors are manufactured from densely packed carbon or dielectric granules, and a very small capacitance exists between each granule. The aggregate of these form the resistor’s parasitic shunt capacitance [11]. Because the lead inductance of this type of resistor is negligible compared to its resistance and parasitic capacitance, the impedance of this component is reasonably constant at low frequencies where the resistance dominates, but rolls off at high frequencies where the capacitance dominates. This effect is known as the Boella effect, named after its discoverer from Italy [11]. See Fig. 2. R %ZT
low R
ZT
high R L C
1
a)
b)
10 100 f [MHz]
RS
RP
a) Fig. 2 a) General equivalent RC circuit for carboncomposite and metal film resistors, and b) typical normalised ZTOTAL vs logarithmic frequency plot [1]. Carbon composite is indicated by dotted line, and metal film by solid line.
b)
fRES
f
Generally, capacitors are quite linear up to a certain point in frequency, called the self-resonant frequency. This frequency, fRES is determined by the product of the capacitance C with its parasitic inductance L:
f RES =
1 2π LC
(4)
Above resonance though, the parasitic inductance dominates, making the capacitor behave inductively. For an ideal capacitor, L would be zero, and the resonant response and associated inductive response above resonance, would be shifted to an infinite frequency. Thus for very high frequency applications, capacitance values together with their parasitic inductances, must be minimised in order to shift the self-resonant frequency higher than the operating frequency.
Thin-film chip resistors have recently been developed to minimise stray effects. These are manufactured on alumina or beryllia substrates, and show negligible parasitic reactance from dc to frequencies in the order of 2GHz [1]. Because surface mount technology is used, lead inductance is virtually done away with. Also, in contrast to a granular material, the uniform metal resistive layer has a negligible stray capacitance [2]. Unfortunately, these surface-mount chip resistors can only carry small currents due to thermal constraints. For high-power applications, band resistors can be used, made from a strip of boron-carbon encapsulated by a heat-radiating material [2].
The quality factor Q of a capacitor is determined by its total internal parasitic resistance at a certain frequency, called equivalent series resistance (abbreviated ESR), made up of the combination of RS and RP. Q is the inverse of the capacitor’s power factor, and its relationship with the ESR (symbol r) at a certain frequency f is as follows:
Q=
1 1 = cos φ 2πfrC
(5)
Apart from frequency, temperature is the second-most important factor that influences the characteristics of capacitors negatively. Generally, the higher a capacitor’s εR, the smaller its physical dimensions for a certain capacitance, and the more prone it is to have non-linear
4. Capacitors used most
C
Fig. 3 a) General equivalent circuit for capacitors [1], and b) typical ZTOTAL vs logarithmic frequency plot.
Metal-film resistors show excellent linear characteristics for frequencies as high as 10MHz, above which the shunt parasitic capacitance dominates, producing a roll-off effect similar to carbon-composite resistors. For low-value resistors (< 10kΩ) at very high frequencies, resistance caused by the skin effect reduces the roll-of slope by neutralising the parasitic capacitive reactance to a certain degree. In resistors smaller than 100Ω, resonance can also be observed between the parasitic lead inductance and shunt capacitance [1].
Capacitors are communications,
ideal C
extensively in power-line commonly to couple the
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solenoid often used for high frequencies [11]. Unfortunately, this spacing degrades the inductive coupling behaviour of the component, resulting in a smaller effective inductance.
temperature characteristics. Also, a high Q value (low power factor) means that very little power is dissipated in the capacitor, making it operate at a lower, more stable temperature than a low-Q counterpart.
L
Many different materials and manufacturing processes are used to produce capacitors. Three different groups of dielectrics exist, and can be used to classify capacitors as air-dielectric, solid-dielectric or liquid-dielectric [5]. Airdielectric capacitors are typically used as variable capacitors for tuning applications. Low permittivity (εR) capacitors are also used where good temperature stability is required. An insulator with εR ≈ 1 can be used to raise the breakdown voltage for high-voltage applications. Solid-dielectric capacitors include ceramic, mica, paper and metallised plastic film capacitors of which ceramic capacitors are generally suitable for high frequencies [2]. Some ceramic capacitors are specially manufactured for high-frequency applications, using ribbon connector leads, or as surface mount chip capacitors [1]. Metallised plastic film capacitors exhibit very high tolerances (typically 2%) for temperatures below 900C and are generally used where space is not a constraint. Liquid-dielectric capacitors include electrolytic capacitors and super capacitors [2]. These are used where large capacitances are required such as for filtering or UPS applications.
R
ideal L ZT
a)
C
b)
fRES
f
Fig. 4 a) General parallel-resonant equivalent circuit for inductors [1], and b) typical ZTOTAL vs logarithmic frequency plot. A fundamental equation defining inductance L carrying a current i, is given by Faraday’s law and can be written in different forms:
d dL di e = − n dΦ = − ( Li ) = − L + i dt dt dt dt
(6)
Symbol e represents the induced voltage across the inductor (often called back-EMF) that always opposes the cause, hence the negative sign. Symbols n and φ represent the number of turns and flux linked by the turns. Take note that the last term of (6) is often neglected, assuming L constant. Practically, this can often be very inaccurate. Various factors can cause L to change abruptly [2], the most critical being 1) non-linearity of core µE at higher excitation levels as the B-H curve flattens, 2) frequency dependency of µE indirectly caused by skin and proximity effects, influencing effective dimensions of coil and 3) temperature dependency of µE as core heats to reach operating temperature. (It is important to understand that the effective permeability, µE, is not a predetermined value, but rather an observed ratio between B and H for a certain core under certain operating conditions.)
5. Inductors In power-line communications, inductors are commonly used to de-couple portions of the power line from the power-line communications network, as inductors impede high-frequency signals. This technique prevents the unnecessary dissipation of transmitted power in certain sections of the power line and associated loads [12]. Inductors also often form part of coupling circuits, filter circuits and tuning circuits [13]. The most common equivalent circuit for inductors is shown in Fig. 4, and is very similar to a resistor’s equivalent circuit [1,18,19]. In this parallel-resonant circuit though, the inductance dominates the other parameters at low frequencies, and thus functions as an inductor.
Air-core inductors have definite advantages over magnetic core inductors: they are almost 100% linear with respect to excitation, and saturation effects do not apply. If the conductors are well designed for high frequencies (e.g. Litz wire), the air core inductor is also very linear with respect to frequency and to a lesser degree, temperature changes [2]. The disadvantages of air-core inductors coincide with the advantages of magnetic core inductors: air-core inductors are generally large and require many turns compared to cored inductors. Because of the higher number of turns, the parasitic resistance and capacitance is higher than for a cored inductor. Also, the large crosssectional area makes the inductor act as a radiating and receiving antenna, aggravating EMI in the circuit and surroundings where it is used.
The resistance in Fig. 4 a) models losses in the winding as well as magnetic core (and strictly speaking dielectric losses associated with the stray capacitance as well as any radiated losses) [2]. The capacitance C is the lumped value of the total stray capacitance, formed between neighbouring conductors that have a volt-drop between them. Thus for high-voltage applications, the influence of C is much more significant, as higher volt-drops exist between conductors. To minimise the parasitic capacitance one would space conductors as far apart as possible, increasing the distance between any two miniature capacitive layers. This is achieved in the single-layer
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At high frequencies though, and for very sensitive applications, the parasitic influences of a transformer has to be modelled more accurately. Fig. 5 shows a more comprehensive model [7] that can be used for any transformer. LM and RC represent the magnetising impedance and core losses (hysteresis and eddy current) respectively. Both the primary and secondary windings have conduction losses represented by R as well as leakage inductance represented by LL. The parasitic capacitances are the lumped values of capacitance between different turns and layers of the same winding (CP and CS) and capacitance between the primary and secondary windings (CPS). In order to design a transformer where parasitic influences are minimal, some practical guidelines can be followed:
Magnetic cores having an effective permeability µE of 1000 is not uncommon, and therefore would boost the inductance of an air-core counterpart by factor 1000. See (7), the general design equation for an ideal homogeneous thyroidal inductor (having N turns wound on a core with effective cross-sectional area A and flux path-length l) [2]:
L = µ0 µ E N 2 ⋅
A l
(7)
Symbols µ0 and µE are permeability of free space and the effective relative permeability of the core material respectively. If one compares a cored inductor with an aircore inductor at a certain fixed inductance, the physical dimensions (factor A/l) of the cored inductor is smaller by factor µE if N is kept constant. Alternatively, the number of turns is reduced by a factor equal to the square root of µE (keeping geometry fixed). Practically, a combination of both is implemented, yielding a smaller inductor with a fewer number of turns. Fewer turns implies a smaller parasitic capacitance as well as a smaller parasitic resistance (that can lead to an increase in Q, depending on the introduced core losses). Another advantage is the adjustability of a cored inductor, which can be realised by moving the core in and out of the winding.
CPS RP LLP CP
a)
Magnetic core inductors also have disadvantages. All magnetic materials saturate at a certain level of excitation, and this causes harsh non-linearity in a circuit. Saturation of inductors and transformers has to be carefully considered for power-line communications applications, as signals get distorted when large currents saturate magnetic cores. Also, different magnetic materials have different losses, influencing the quality factor. The uniqueness of a certain magnetic material though, is summarised by its permeability characteristics, which varies with temperature, frequency and excitation. Consequently, the inductance changes from its original intended value, causing impedance mismatches, ineffective filtering and mistuning, to name a few negative effects.
RC
ZT
LLS RS CS LM b)
f
Fig. 5 a) Comprehensive lumped equivalent circuit for transformers [7], and b) typical ZP (no-load impedance seen from primary) vs logarithmic frequency plot. Leakage inductances are largely dependent on transformer geometry. Langsdorf [20] shows that the total leakage inductance is almost proportional to the height-to-width ratio of the windings. Using a transformer core that facilitates a winding of double the original width, would necessitate only half the winding height for the same number of turns, effectively reducing the leakage inductance by factor 4. Interleaving of layers of primary and secondary turns can have a significant impact on parasitic reactances, as interleaving reduces the magneto-motive force MMF, magnetic field strength H and associated flux density B inside the transformer core and windings. Leakage inductance is further reduced by a factor almost equal to the number of layers used, for instance by a factor 4 when using two primary and two secondary layers [20].
6. Transformers A transformer is a device with two or more inductors that are magnetically coupled. Typically a high permeability magnetic core is used in order to effectively couple the two (or more) windings. At low frequencies (most power applications), it is sufficiently accurate to model a transformer by a magnetising and leakage inductance. The magnetising inductance models the energy storage in the magnetic core, whilst the leakage inductance models the energy stored outside of the core (flux in the windings as well as air, oil or resin surrounding the transformer). A well-designed transformer would have a large magnetising inductance compared to its leakage inductance, implying effective coupling.
This technique can also reduce the effect of inter-winding capacitance (CPS), as the relative voltage between layers is smaller. A larger capacitive area is introduced though, which could aggravate CPS, depending on the specific geometry and design. Furthermore, CP and CS are drastically reduced because the distance between capacitive layers is increased by factor 10 or even more. Core losses is also less (RC smaller) because of lower
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excitation of the core. [3] C.-S. Yen et al, “Time-domain skin-effect model for transient analysis of lossy transmission lines,” Proceedings of the IEEE, vol. 7, pp. 750-757, July 1982. [4] J. Auvray, M.Fourrier, Problems in Electronics, including lumped constants, transmission lines and high frequencies, ISBN 0-08-016982-1, Oxford: Pergamon Press, 1973. [5] F.E. Terman, Electronic and Radio Engineering, 4th edition, New York: Mc Graw-Hill, 1955. [6] K. H. Billings, Handbook of Switchmode Power Supplies, New York: Mc Graw-Hill, 1989. [7] A. Baccigalupi et al, “On a circuit theory approach to evaluate the stray capacitances of two coupled inductors,” IEEE Transactions on Instrumentation and Measurement, vol. 43(5), pp. 774-776, October 1994. [8] D.W. Braudaway, “Behaviour of resistors and shunts: with today’s high-precision measurement capability and a century of materials experience, what can go wrong?” IEEE Transactions on Instrumentation and Measurement, vol. 48(5), pp. 889-893, October 1999. [9] S.R. Naidu, A.F.C. Neto, “The stray-capacitance equivalent circuit for resistive voltage dividers,” IEEE Transactions on Instrumentation and Measurement, vol. IM-34, pp. 393-398, September 1985. [10] D.W. Braudaway, “Precision resistors: a review of material characteristics, resistor design, and construction practices,” IEEE Transactions on Instrumentation and Measurement, vol. 48(5), pp. 878-883, October 1999. [11] K. Henney, Radio Engineering Handbook, 5th edition, New York: Mc Graw-Hill, 1959. [12] H.-K Podszeck, Carrier Communication over Power Lines, 4th Edition, New York: Springer-Verlag, 1972. [13] IEEE Guide for Power-Line Carrier Applications, IEEE Standard 643-1980. [14] K.K. Clarke, D.T. Hess, Communication circuits: analysis and design, Reading: Addison-Wesley, 1971. [15] J.-Y. Kim et al, “High-frequency response of amorphous tantalum oxide thin films,” IEEE Transactions on Components and Packaging Technologies vol. 24(3), pp. 526-533, September 2001. [16] C.-H. Lai, T.-Y. Tseng, “Analysis of the ac electrical response for (Ba,Pb)TiO3 positive temperature coefficient ceramics,” IEEE Transactions on Components, Packaging, and Manufacturing Technology – Part A, vol. 17(2), pp. 309-315, June 1994. [17] Y. Sakabe et al, “High-frequency measurements of multilayer ceramic capacitors,” IEEE Transactions on Components, Packaging, and Manufacturing Technology – Part B, vol. 19(1), pp. 7-14, February 1996. [18] J. Muciek, A. Muciek, “A comparison of low-frequency models of inductance standards,” IEEE Transactions on Instrumentation and Measurement, vol. IM-36, pp. 830-833, September 1987. [19] R. Hanke, K. Dröge, “Calculated frequency characteristic of GR1482 inductance standards between 100Hz and 100kHz,” IEEE Transactions on Instrumentation and Measurement, vol. 40(6), pp. 893-896, December 1991. [20] A.S. Langsdorf, Theory of alternating-current machinery, New York: McGraw-Hill, 1955.
Winding losses represented by RP and RS can be minimised by using Litz wire or plate conductors to minimise the skin effect. See section 2. Also, the proximity effect can be minimised by using a certain number of layers when applying the interleaving technique [6]. In general, thyroidal transformers exhibit good characteristics (low parasitic reactances) compared to other cores. When few turns is required for a specific design, parasitic capacitances can be minimised by spacing windings apart to minimise CPS and by spacing turns equally to minimise CP and CS [1]. 7. Conclusion Power systems and communication systems operate at two different extremes – power systems at very low frequencies and very high power, current and/or voltage levels and communication systems at very high frequencies and very low power, current and voltage levels. These extremes can cause unwanted behaviour if components are not selected carefully and / or circuit layout is planned properly. Frequency behaviour of passive components was discussed, and practical design guidelines were given. Generally components are chosen to have a self-resonant point of at least an octave above the operating frequency. The self-resonant point of a certain component can be raised by either reducing the parasitic values (as discussed) or if not possible, designing the circuit using smaller component values (not true for wire-wound resistors though). Parasitics introduced by circuit layout should also be minimised and / or designed for. Finally, it is suggested that components be characterised at low-frequency power-line voltages and currents where applicable, but first and foremost over the range of modulation frequencies, applying low power. Acknowledgements This material is based upon work supported by the National Research Foundation (South Africa) under grant number 2053408. References [1] C. Bowick, RF Circuit Design, ISBN 0-672-21868-2, Carmel: Howard W. Sams & Co, 1991. [2] W.K. Chen (ed.), The Circuits and Filters Handbook, ISBN 0-8493-8341-2, Boca Raton: CRC Press and IEEE Press, 1995.
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