Coupling Circuitry: Understanding the Functions of Different Components 1

Transcription

1 Coupling Circuitry: Understanding the Functions of Different Components 1 Petrus A. JANSE VAN RENSBURG and Hendrik C. FERREIRA Department of Electrical Engineering Department of Electrical and Electronic Engineering Border Technikon Rand Afrikaans University P.Bag 1421, East London, 52, South Africa P.O.Box 524, Auckland Park, 26, South Africa Phone: , Fax Phone , Fax pvanren@ingulube.bortech.ac.za hcf@ing.rau.ac.za Abstract The design of coupling and de-coupling circuitry is often neglected at the expense of reduced signal levels and increased noise levels. This paper summarises the fact that coupling capacitors or de-coupling inductors don t merely pass or block signals, but that their filtering characteristics are quite dependent on the loads into which the waveforms terminate. The functioning of a coupling transformer is also investigated, and it is shown that the leakage inductance, together with a series capacitor, forms a seriesresonant band-pass filter that can be modelled as a simple LC-R circuit. Design equations are given and verified by measuring the transfer function of the coupling circuit for different values of L, C and R. 1. Filtering concepts Filtering (ability to discriminate between different frequencies) forms the basis of most coupling and decoupling circuits. De-coupling filters are typically used for network conditioning whereas coupling filters feed the communication signal to and from the power line. Other applications of filtering include the filtering of noise, filtering to improve phase distortion and filtering to prevent incoming and outgoing EMI. It is obvious from the above examples that proper filter design is i) essential for minimum signal attenuation when coupling to the power line and ii) can drastically improve signal to noise ratios. As any repetitive waveform can be expressed as a mathematical sum of sinusoids (called its Fourier expansion), a periodic waveform can be thought of as a unique mixture of sinusoids, each with a certain frequency and amplitude, that form one superimposed signal. Every possible sub-sinusoid of a signal is changed by the filtering process, depending on its frequency [1,2]. This change is two-fold: amplitude is attenuated by a certain factor, and phase angle is shifted to a certain degree. After the filtering process, the resultant waveform is once again the sum of the individual sub-sinusoids. Thus the filtered waveform is now composed to a lesser degree of some frequency (sinusoidal) components because they have been attenuated or filtered to a certain degree. As each subsinusoid is typically phase-shifted by a different angle, the filtered waveform does not only show phase delay but also phase distortion, a side-effect that has to be kept in mind [1,2]. Single and paired capacitors are used extensively in power-line communications to couple the communication signal to the power line while blocking the lowfrequency power signal [3,4]. This application is well known in transistor circuit theory, as a series capacitor is typically used to disconnect or block dc biasing voltages but pass small-signal ac voltages. This is possible due to the frequency-dependent impedance of a capacitor (valid for a specific frequency sinewave): 1 1 Z C = = 9 [Ω] (1) jωc 2πfC From (1) it is obvious that any capacitor s impedance will tend to infinity at dc (f = Hz), blocking any dc component of a signal. At low frequencies, such as power-line frequencies, its impedance is high enough to revert almost 1% of the signal to lower impedance paths of the power line (current divider rule). At the communication signal frequency though, the coupling capacitor would be designed to have a low enough impedance to admit a large portion of the communication signal, making it available to the receiver. If a power-line communication system uses a sinusoidal carrier signal of 5kHz superimposed on a 5Hz sinusoidal power waveform, the following conclusions can be made for a 1µF series capacitor: the capacitor can be modelled as two parallel impedances, one parallel path for low frequencies and another for high frequencies. See Fig. 1. The low-frequency (LF) path has a reactance of 3.18kΩ whereas the high-frequency (HF) path has a reactance of.318ω (inversely proportional to frequency). Both the HF and LF path impedances have the same phase angle though (-9 ). 1 Supported under NRF grant 25348

2 1µF HF path.318ω 3.18kΩ LF path 1µH HF path 3.14kΩ.314Ω LF path Fig. 1. HF-LF model for a 1µF capacitor and 1µH inductor in a 5Hz sinusoidal power and 5kHz sinusoidal carrier scheme. Inductors function complementary to capacitors: high frequency signals (or harmonics) are blocked and low frequency signals (or harmonics) passed, reason being an ideal inductor has a unique impedance for each subsinusoid of a waveform, proportional to the sub-sinusoid s frequency f: Z L = jωl = 2 πfl + 9 Ω (2) In a power line network, any series inductor would impede the high frequency communication signal from flowing through that specific path to a certain degree. Unnecessary loss of transmitted power can be prevented by blocking off branches of the network that will not be utilised for power-line communications. If a 1µH inductor is inserted in series with the same power-line communication scheme as discussed above (5Hz with 5kHz carrier), it can be modelled as a.314ω reactance for low frequencies in parallel with a 3.14kΩ reactance for high frequencies. See Fig. 1. Both the HF and LF path impedances have the same phase angle of +9 as for an ideal inductor. It must be understood that a series capacitor or inductor usually functions as a first-order filter, as these typically terminate into a resistive measuring load or resistive power load. In Fig. 2, the HF-LF model is used further to illustrate a 1µF capacitor terminating into a 5Ω load resistor. The voltage-divider rule can be used to obtain the voltage transfer function as VOUT 5 = (3) VIN for the HF path, and V 5 OUT = (4) IN E3 9 V for the LF path. For this specific example of Fig. 2, the high-frequency sinusoid is hardly attenuated, and phase-shifted by only.364 whereas the low-frequency voltage signal is attenuated by 98.43% or 36dB (and phase-shifted by 89.1 ). Also refer to Fig. 3 which affirms latter calculations. HF path 1µF.318Ω 5Ω 3.18kΩ LF path 5Ω Fig. 2. The HF-LF model for a 1µF capacitor terminating into a 5Ω load resistor (5Hz sinusoidal power and 5kHz sinusoidal carrier scheme). Although the discussed HF-LF model facilitates the understanding of a simple filter circuit, the Bode plot presents a summary of attenuation and phase shift for a logarithmic range of frequencies. When designing a FSK modulation scheme for instance, the attenuation and phase shift of different modulation frequencies can be graphically considered. See Fig. 3. Inductor-capacitor combinations can also be utilised as second-order low-pass or high-pass filters, the main difference being a roll-off figure of 12dB/octave compared to 6dB/octave for first-order RC and RL filters. Band-pass and band-stop filters can also be realised with LC combinations, but only have a 6dB/octave roll-off figure [4]. Series resistance can also be introduced to dampen resonance and so reduce the Q-factor of the second order filter. As this technique involves an impedance mismatch, it is a non-selective attenuation technique and is therefore not recommended. If the mismatch is not severe, unattenuated frequencies closer to series resonant points are affected more than other attenuated frequencies. The more severe the mismatch, the more prone it is to attenuate all frequencies. Typically, filter circuits also terminate into resistive loads, thereby influencing the bandwidth of the second order system to be more selective (higher Q) or less selective (lower Q), depending on the configuration. If a filter circuit terminates into a reactive load, its characteristics could change to that of a higher order circuit, complicating the response of the system.

3 db -1dB for a transformer, assuming an ideal linear B-H curve. Practical B-H curves are non-linear though and depend on excitation levels. R P L LP L LS R S -2dB -3dB R P L M Ideal -4dB -5dB 1 1k 1k 1k 1M 1M 1M Fig. 4. Simplified model of an (ideally) linear transformer k 1k 1k 1M 1M 1M Fig. 3. Measured Bode plots for a 1µF capacitor terminating into a 5Ω load resistor: voltage transfer function and phase transfer function. Note the influence of stray effects above 1MHz. Instrument: HP3577B Network Analyser. 2. Transformers Transformers are often used as coupling devices as they provide galvanic isolation between their primary and secondary windings (between the power circuitry and communication circuitry) and act as limiters [5]. Other uses of transformers include voltage / current transformation, adaptation of impedance levels and filtering. Because transformer design involves so many parameters it is often a non-precise, experimental procedure. Therefore transformers are typically not suitable for accurate complex impedance matching but rather for crude equalling of resistive impedances or else reactance magnitudes. Fig. 4 shows a simplified equivalent circuit When designing a transformer, it is important to limit the maximum flux density in the core for various reasons: The higher the flux density, the more non-linear the B-H curve, and the more distortion is introduced in the signal across the secondary winding. If the core is saturated, induction ceases (no signal reaches the secondary), and the primary winding appears as a short circuit as it has a very low magnetising impedance (that of an air core, as µ(t) = db/dh). The enclosed area of the B-H curve is proportional to the power losses in the core. The core losses can influence the transformer s frequency response and also cause it to overheat. Practically, B can be controlled by implementing one or more of the following: Choose a core with a large enough cross-sectional area. Limit the maximum applied voltage and minimum applied frequency (see (5)). Interleave layers of primary and secondary turns. Increase the number of turns, keeping the same winding ratio. The latter increases a transformer s magnetising inductance L M by factor N 2, and so limits the magnetising current necessary to excite the transformer. Smaller magnetising current implies less dissipation in the core. In general, the more effective a transformer s window surface is filled with primary and secondary turns, the more efficient the transformer will be. Wire diameter is typically optimised to produce equal losses in the windings and the core. Interleaving layers of primary and secondary conductors will further reduce the MMF and so reduce leakage inductance, core losses and copper losses.

4 In a power-line communication application, the B-H curve of a transformer would show small high-frequency hysteresis curves superimposed on a large low-frequency (5 Hz) hysteresis curve. The sum of the low-frequency and high-frequency flux densities is limited to B SAT and therefore the two signals have to share the available maximum flux density. A transformer s maximum excitation limit is always determined by the highest voltage level and lowest operating frequency [7] as (5) (valid for sine wave) clearly illustrates: vmax BMAX = (5) 2πNAf MIN From (5), it can be shown that the 5Hz, 311V (PEAK) power signal would waste the majority of the available B SAT compared to a 5kHz, 1V (PEAK) communication signal. The frequency difference of factor 1 4 multiplied with the voltage difference of factor 31, shows that the power signal would saturate a core of B SAT = 6mT while the communication signal has not even utilised 2µT of the 6mT available flux density. For this very reason, the low frequency power sinusoid needs to be filtered to reduce its amplitude drastically before entering the coupling transformer. This is typically achieved by connecting a series capacitor to one or both of the transformer primary terminals [5,8]. Most transformers show natural band-pass filtering characteristics because of internal impedances [9,1]. Remember than any transformer will saturate at a frequency too low for its design (see (5)). As the core goes into saturation, the induced secondary voltage drops to zero. At high frequencies though, the small series leakage inductances dominate to form a low-pass LR filter in association with parallel load resistance and other resistances [9,1]. The series capacitor that is used to prevent saturation of the coupling transformer in conjunction with the transformer s leakage inductance creates a series resonant coupling circuit. If this series resonant circuit is terminated into a resistive load, a second order band-pass filter is realised. This band pass filter has a roll-off figure of 6dB/octave or 2dB/decade (see Fig. 6 ). If a higher rolloff figure is required, parallel capacitors have to be introduced to both the primary and secondary windings. See [11,12] for details. The centre frequency of this bandpass filter is at the series-resonant point 1 f R = (6) 2π LC where L refers to the series inductance and C refers to the series capacitance. L typically consists only of the leakage inductance referred to primary, but can be enlarged with a series inductor. The bandwidth of the filter is determined by the respective low-frequency and high-frequency 3dB cut-off points 1 R f LF = and f 2πRC = HF 2π L (7,8) where R refers to the terminating resistance. The model of the suggested coupling circuit is shown in Fig. 5 below: Z P Fuse C Transformer L EXT L LEAK Fig. 5. Suggested coupling circuit. db -1dB -2dB -3dB -4dB -5dB db -1dB -2dB -3dB -4dB -5dB Z M Zener 1 1k 1k 1k 1M 1M 1 1k 1k 1k 1M 1M Fig. 6 Measured amplitude response of 1:1 transformer only and 1:1 transformer with.22µf capacitor in series with primary terminal (both 5Ω secondary termination).

5 Fig. 6 shows the measured amplitude response ( H(jω) vs frequency) of a RS :1 coupling transformer only, terminating in the 5Ω instrument input impedance. All measurements were done with a HP 3577B 2MHz network analyser with a 5Ω output impedance. The measured cut-off point in Fig. 6 of 382kHz corresponds to the theoretical value (see (8)) of 419kHz, caused by leakage inductance (typical value 19µH) terminating in the 5Ω load resistor. The low-frequency cut-off point in Fig. 6 did not manifest during the measurement, as the lowest frequency measured was 2Hz, and the applied voltage was too low to cause saturation at this frequency (see (5)). It was determined experimentally that the low-frequency cut-off point is 9Hz for a 2V P-P sine wave and 65Hz for a 2V P-P sine wave. The maximum test signal that could be applied without overloading the instrument was -6dBm, approximately 112mV if a 5Ω load is assumed. db -1dB -2dB -3dB -4dB -5dB db -1dB -2dB 1 1k 1k 1k 1M 1M Fig. 6 shows the transfer function of the 1:1 transformer with a.22µf capacitor in series with primary terminal (also 5Ω secondary termination). The measured centre frequency and cut-off points correspond closely to the calculated values of f R 78kHz, f LF 14.5kHz and f HF 419kHz. The influence of both the terminating and series resistances on the filter characteristics was investigated. See Fig. 7 below. Fig. 7 is a follow-up of Fig. 6, but the terminating resistance was decreased to 25Ω. The centre frequency is still 78kHz, but the cut-off points have moved closer to form a narrower pass band. The theoretical values of f R 78kHz, f LF 29kHz and f HF 21kHz correspond closely to the measured values. In Fig. 7 the influence of series resistance (as discussed in a previous paragraph) is shown. Fig. 7 is a follow-up of Fig. 7, but a 5Ω resistor was inserted in series with the transformer primary. Although the impedance mismatch caused by the 5Ω resistor does cause a broader pass-band, the pass-band region is attenuated by approximately 1dB, whereas already filtered frequencies (compare with Fig. 6 ) are not attenuated further. This implies a worsening of signalto-noise ratio and is therefore not recommended. The use of a series resistor is only warranted when impedance matching is improved by its insertion into the circuit. -3dB -4dB -5dB 1 1k 1k 1k 1M 1M Fig. 7 and Measured amplitude response of a 1:1 transformer with.22µf capacitor in series with primary terminal but with 25Ω secondary termination. Fig. 7 illustrates that a decreased termination resistance decreases the bandwidth. Fig. 7 shows the effect of an impedance mismatch (5Ω series resistor) on the filter characteristics. For confirmation purposes, both the series inductance and capacitance were made larger. Fig. 8 follows on Fig. 7 but a series inductor of 12µH has been added to the leakage inductance of 19µH. Fig. 8 confirms that the centre frequency has moved down to 61kHz and the high-frequency cut-off point has dropped to 128kHz. Fig. 8 shows the measured amplitude response of a 1µF capacitor in series with 69µH of inductance terminating in a 5Ω load, one again confirming the theoretical expectations. As a final step in the measurement process, back-to-back zener diodes were inserted in parallel with the secondary and these caused no visible change in the amplitude

6 response. Furthermore a 1µF electrolytic capacitor was placed in series with the final output stage (often required at the input port of instruments) and this also had no visible effect on the amplitude response. db -1dB coupling equipment be designed as symmetrical, bidirectional passive filters with additional protective circuitry [13]. A simple series-resonant LC-R band-pass filter (which behaves the same as the circuit in Fig. 5) can be designed with (6) to (8). This coupling circuit could include varistors on the power line side and zener diodes on the communication side for protection. 3. Conclusion -2dB -3dB -4dB -5dB db -1dB 1 1k 1k 1k 1M 1M The design of coupling and de-coupling circuitry is often neglected at the expense of reduced signal levels and increased noise levels. This paper summarised the fact that coupling capacitors or de-coupling inductors don t merely pass or block signals, but that their filtering characteristics are quite dependent on the loads into which the waveforms terminate. The functioning of a coupling transformer was also investigated, and it was shown that the leakage inductance together with a series capacitor, form a seriesresonant band-pass filter that can be modelled as a simple LC-R circuit. Design equations were given and these were verified by measuring the voltage transfer function of the coupling circuit for different values of L, C and R. References -2dB -3dB -4dB -5dB 1 1k 1k 1k 1M 1M Fig. 8 Measured amplitude response of a 1:1 transformer with.22µf capacitor in series with primary terminal, total series inductance of 31µH and terminating in 25Ω load. Measured amplitude response of a 1:1 transformer with 1µF capacitor in series with primary terminal, total series inductance of 69µH and terminating in 5Ω load. Measured values correspond well with (6) to (8). If the only function that a transformer provides over and above filtering, is that of protection, its necessity in the coupling circuit must be seriously considered, as transformers are bulky, heavy and expensive compared to other passive components. If it is possible to design a system such that impedance levels (at the carrier frequency) are nearly equal, a coupling transformer becomes redundant. In such a case it is suggested that [1] D.S. Humpherys, Analysis, Design and Synthesis of Electrical Filters, Englewood Cliffs: Prentice-Hall, 197. [2] W.K. Chen, Passive and Active Filters: Theory and Implementations, New York: John Wiley & Sons, [3] H.-K Podszeck, Carrier Communication over Power Lines, 4th Edition, New York: Springer-Verlag, [4] IEEE Guide for Power-Line Carrier Applications, IEEE Standard [5] K. Dostert, Powerline Communications, ISBN , Upper Saddle River: Prentice Hall PTR, 21. [6] K.C. Abrahams, A novel high-speed PLC communication modem, IEEE Transactions on Power Delivery, vol. 7(4), October [7] J. Millman, H. Taub, Pulse, Digital and Switching Waveforms, New York: McGraw-Hill, [8] W. Downey, Central control and monitoring in commercial buildings using power line communications, Proceedings of the 1 st International Symposium on Power-Line Communications and its Applications (ISPLC 97), pp , [9] Philips Components, Soft Ferrites Data Handbook MA1, [1] K.K. Clarke, D.T. Hess, Communication circuits: analysis and design, Reading: Addison-Wesley, [11] F.E. Rogers, The Theory of Networks in Electrical Communications and Other Fields, London: Macdonald & Co, [12] F.E. Terman, Electronic and Radio Engineering, 4 th edition, New York: Mc Graw-Hill, [13] G. Telkamp, A low-cost power-line node for domestic applications, Proceedings of the 1 st International Symposium on Power-Line Communications and its Applications (ISPLC 97), pp , 1997.