Step-by-Step Design of a Coupling Circuit with Bi-Directional Transmission Capabilities

Step-by-Step Design of a Coupling Circuit with Bi-Directional Transmission Capabilities 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: +27-82-2-627, Fax +27-43-72-9226 Phone +27-11-489-2463, Fax +27-11-489-2357 E-mail: pvanren@ingulube.bortech.ac.za E-mail: hcf@ing.rau.ac.za Abstract In this paper, the design of an impedance-adapting bidirectional transformer coupling circuit for low-voltage power-line communications is described. It is shown that transmission through the transformer is governed by series resonance of the leakage inductance and coupling capacitance. The coupling transformer, if properly designed, can equalize terminating impedances on either side for maximum power transfer. Furthermore, these equalized terminating impedances facilitate symmetrical bi-directional band-pass transmission 1. Keywords: modem design, coupling circuits, filters, impedance matching, transformers. 1. Introduction Transformer-capacitor coupling circuits are used extensively in low-voltage power-line communications, mainly because i) the transformer provides galvanic isolation from the powerline network and ii) the transformer acts as a limiter when saturated by high-voltage transients. As power-line access impedances are generally very low, poor power transfer is achieved because of the mismatch between modem impedance and power-line impedance. However, in this paper it is shown that a properly designed coupling circuit can i) adapt the impedance level of a certain modem to a chosen typical impedance level of the power line and ii) subsequently be used as a bi-directional coupler for two-way communication. The step-by-step design of a 1:7 coupling transformer is described, and amplitude response measurements clearly indicate the bi-directional symmetry. Also, it is shown that fluctuating power-line impedance values cause the 1 This work was supported in part by the S.A. National Research Foundation under Grant No. 25348. bandwidth of the coupling filter to fluctuate when a signal is transmitted. In the receiving direction though, the bandwidth of the coupling filter stays constant as the modem impedance stays constant. Lastly, some tradeoffs are discussed in order to choose a typical minimum power-line impedance value for design purposes. 2. Circuit In [1] a typical coupling circuit (shown in Fig. 1) was analyzed and shown to behave as a simple series-resonant band-pass filter at frequencies close to the series resonant point. The equivalent circuit is shown in Fig. 1. The center frequency of this band-pass filter is at the seriesresonant point f R Fuse C Transformer + + L LEAK V P Z P Z M V M Zener R P C L R M Fig. 1. Suggested coupling circuit and equivalent circuit for frequencies of interest. Z P and Z M refer to the power-line and modem terminating impedances respectively whereas R M represents the referred modem impedance to the power-line side. 1 = (1) 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 an external series inductor. The bandwidth of the filter is determined by the respective low-frequency and highfrequency 3dB cut-off points 1 f LF = and R f HF = (2,3) 2πRC 2π L where R refers to the terminating resistance (R P when transmitting and R M when receiving). Take note that R P, the equivalent impedance of the power line network (see Fig. 1) was not taken into account during measurements in [1]. Typical impedance values of.1ω to 2Ω for frequencies in the CENELEC (Comité Européen de Normalisation Electrotechnique) B, C, and D bands have been reported [2], [3]. This low impedance value implies that a large portion of the available signal power is dissipated unnecessarily. Even if it is possible to improve (raise) the power line impedance using network conditioning, the best practice is to design the input impedance of the modem to equal the power line impedance. This would mean a splitting of current (and power) at the series-resonant point and thus only 3dB of power is lost. If the modem input impedance cannot be designed to equal the power line impedance, it is absolutely necessary to equalize the impedance levels by using a step-up transformer. A transformer is a powerful impedancetransforming device, as any impedance is reflected by the square of the winding ratio. If a transformer is used to equalize the terminating impedances on either side of Fig. 1, another advantage results: the coupling network can now be used as a bi-directional coupler with the same filter characteristics from both sides. The step-by-step design of such a transformer coupling circuit for the CENELEC bands is discussed in the following section. See Fig. 2 below. 3. Design 3.1 Frequency specifications The bi-directional coupler will be designed for the CENELEC B, C, and D bands [3], [4], roughly from 9kHz to 15kHz. Thus 9kHz would be the worst-case frequency for core considerations (see (6)) and 15kHz would be the frequency where copper losses would be a maximum. 3.2 Impedance levels / winding ratio Although the power-line access impedance fluctuates between.2ω to 2Ω and more [2], [5], it has been decided that a 1Ω power-line impedance value satisfies various tradeoffs (discussed in section 5). It is also assumed that a 5Ω modem impedance needs to be adapted to the 1Ω impedance of the power-line. This can be done using a 1:7 transformer. The 5Ω modem impedance appears as (1/7) 2 5 1Ω on the power line side, whereas the 1Ω power line impedance appears as (7/1) 2 1 49Ω on the modem side. 3.3 Maximum voltage levels According to the CENELEC specifications, a maximum signal level of 116dBµV (.63V PEAK ) is allowed for the B, C, and D bands. Although this figure represents a measured value, the measurement set-up consists of a balanced voltage-divider network, which implies that only 5% of the true signal is measured [3], [4]. Thus a maximum voltage of 122dBµV (which represents 1.26V PEAK or.89v RMS ) can be injected into the power-line network and this represents a voltage of 8.81V PEAK or 6.23V RMS on the modem side of the transformer. 3.4 Maximum power and current In order to calculate the maximum power level, a minimum power-line impedance of.25ω is assumed. This gives a maximum power throughput of 3.17W and maximum currents of 3.56A RMS and.51a RMS for the power-line side and modem side respectively. 3.5 Core Fig. 2. Photographs of the coupling transformer designed in section 3 and a coupling transformer designed for a 25kHz to 5kHz carrier frequency. An E2 core was chosen, manufactured from MnZn ferrite material [6]. This core set has the following properties: core cross-sectional area A e = 31.2mm 2, flux path-length l e = 42.8mm, intrinsic permeability µ i = 38, and saturation flux density B SAT = 4mT.

3.6 Current density Billings [7] shows that the current density for a certain rise in conductor temperature is given by the empirical equation J α A P -.125 A/cm 2 (4) where α is a constant for a certain core shape and temperature rise, and A P refers to the area product of the core (product of core and window areas). The core under consideration has an α of 4.5 (for T = 3 C) and an area product A P =.8923cm 4. Equation (4) yields a current density of 6.1A/mm for a 3 C rise in conductor temperature. Reference [8] lists values of α for various other core shapes and temperatures. 3.7 Skin effect The optimum strand diameter is typically chosen between δ and 2δ, depending on the proximity effect and other design factors. For copper at a temperature of 5 C, the penetration depth δ at a certain frequency f is 1.699 δ = = (5) πσµ µ f f R S if the relative permeability µ R of copper is assumed as 1. Symbol σ represents the conductivity whereas µ is the permeability of free space. Equation (5) yields a δ of.18mm for 15kHz. The optimum strand diameter can also be obtained from graphs [7] and was.36mm for this design. The closest (lower) gauge available at the time of construction was a.25mm diameter copper wire with a cross-sectional area of.49mm 2. 3.8 Number of strands The number of insulated strands necessary to obtain a Litzwire bundle with sufficient cross-sectional area (for the current density of 6.1A/mm 2 ) can now be calculated as approximately twelve strands for the power-line side and two strands for the modem side. 3.9 Number of turns A typical window fill-factor is.5, and it is thus expected that only 8 power-line side turns and therefore 56 modemside turns would fit onto the transformer s bobbin. 3.1 Flux density Although the power waveform can have an overwhelming influence on the flux density (see [9]), the superimposing flux density contribution B M of the communication waveform on the total flux density is B M VM = 9mT (6) 2πfAN which is valid for a sine wave, subscript M referring to peak values on the modem side. Symbols f, A, and N refer to frequency, core cross-sectional area, and number of modemside turns respectively. As B SAT 4mT (depending on temperature), less than 3% of the available flux density is required by the communication waveform. 3.11 Leakage inductance The value of the transformer s leakage inductance (which is dependent on the number of turns and winding geometry) can now be calculated (see [9] for details): 2 L L = µ ( a + b + 3c) N 294nH (7) 3 T w This equation is valid for one primary and one secondary layer, i.e. no interleaving / sandwiching. T and w represent the mean turn length and window width respectively and a, b and c refer to the primary winding, secondary winding and insulation thickness respectively. N refers to the number of turns of the side to which the total leakage inductance needs to be referred to. 3.12 Enlarging of leakage inductance According to (3), L = 294nH would yield a high-frequency cut-off point of approximately 54kHz, which should preferably be lower for the CENELEC B, C, and D frequency bands. A cut-off frequency of 3kHz, one octave above the upper limit, would be more appropriate. This cutoff frequency requires a leakage inductance of 53nH, which can be accomplished by letting the single-layer primary winding on the power-line side protrude out of the transformer window. This enlarged leakage inductance was later measured and fine-tuned to approximately 53nH using a HP 4284 precision LCR meter. The primary winding layer had to protrude approximately 3mm from both sides of the transformer in order to obtain a 53nH leakage inductance. (Alternatively, an external 23nH inductor can be inserted in series with the transformer primary terminal.) Also see [9] for equations and alternative methods to enlarge/reduce leakage inductance.

3.13 Series capacitor The required series capacitor can be calculated by either choosing a centre point for the band-pass filter (see (1)) or by choosing a low-frequency cut-off point (see (2)). A lowfrequency cut-off point of 5kHz was chosen, also roughly an octave below the lower limit of the CENELEC bands. Equation (2) yields a series capacitor of 3.2µF, and together with the series leakage inductance has a series resonant point of 122kHz. As this capacitor carries the power waveform s voltage, it needs to be rated as such, including a safety factor. 4. Bi-directional measurements In order to verify that the constructed coupling circuit (see Fig. 2) does function as designed, the amplitude response ( H(jω) vs. frequency) was measured with an HP 3577B 5Hz to 2MHz network analyzer with 5Ω output and input impedances. +2 +1 3.14 Magnetizing inductance The value of the magnetizing inductance L M does not influence the pass-band of the coupling circuit, but is required to determine the filtering of the low-frequency power waveform. See[9]. The total inductance (magnetizing plus leakage inductance) of a transformer is given by 2log1[VM/VP] (db) -1-2 L T = µ µ e Ae 2 2 N AL N (8) le where subscript e refers to effective. A e and l e represent the core cross-sectional area and flux path-length respectively and N represents the number of turns (of the side to which the inductance needs to be referred to). A L is called the inductance factor of a certain core set, and is supplied by manufacturers in order to easily calculate inductance values for different air gaps and number of turns. To obtain a more accurate value of magnetizing inductance, a transformer s leakage inductance needs to be subtracted from the above value. For this design, L M 1µH. 3.15 Check combined flux density levels -3-15 -25 2log1[VP/VM] (db) -35-45 -55 1 1k 1k 1k 1M 1M Because of its low frequency, the power waveform can easily saturate the transformer, depending on how well it is filtered. See [9] for details and equations. For this design, it is expected that the power waveform would cause a flux density of 43mT. Combined with the communication waveform, a total flux density of 52mT is expected well below the saturation flux density of 4mT. 3.16 Reducing magnetizing inductance If the combined flux density level of the transformer is not sufficiently low, the magnetizing inductance of the transformer can be made smaller by introducing an air-gap to lower L M. A smaller magnetizing inductance would help to filter low frequencies more effectively. Refer to [9]. -65 1 1k 1k 1k 1M 1M Fig. 3. Measured amplitude response of the coupling circuit designed for CENELEC B, C, and D band when receiving a signal from the power line side and transmitting a signal into the 1Ω resistor (emulating a power line access impedance). Take note of the bi-directional symmetry: in both Fig. 3 and it can be seen that the measured values correspond to the calculated values of f R 122kHz, f LF 5kHz and f HF 3kHz. The difference in reference levels is caused by the 1:7 transformer winding ratio. Take note of the bi-directional symmetry the coupling circuit shows very similar filter characteristics in both receiving and transmitting directions. The measured center

frequency and cut-off points correspond to the calculated values of f R 122kHz, f LF 5kHz and f HF 3kHz. Another interesting observation is the +15dB and 19dB peaks when receiving and transmitting respectively. This is caused by the 1:7 transformer winding (voltage) ratio that implies approximately +17dB when receiving and 17dB when transmitting. It must be emphasized that the amplitude response represents voltage ratios expressed as decibels and not power levels. Thus the +17dB and 17dB levels should be taken as reference levels, as indicated on Fig. 3 and. 2log1[VM/VP] (db) 2log1[VP/VM] (db) +2 +1-1 -2-3 -1-2 -3-4 -5-6 1 1k 1k 1k 1M 1M 1 1k 1k 1k 1M 1M Fig. 4. Measured amplitude response of the coupling circuit designed for 25kHz to 5kHz when receiving a signal from the power line side and transmitting a signal to the power line side (1Ω resistor). Take note of the bi-directional symmetry and different reference levels caused by the 1:7 transformer winding ratio. Another coupling circuit for frequencies between 25kHz and 5kHz (typical in USA / Japan), was designed and constructed. See Fig. 2. Because of the higher cut-off frequencies, smaller reactive component values are required (refer to (2),(3)). Cut-off frequencies of 167kHz and 75kHz were chosen, yielding C.95µF and L L 21nF and a center point of 35kHz. This coupling circuit also showed good symmetry and correlated well with the model in Fig. 1. Measured amplitude responses for the receiving and transmitting directions can be seen in Fig. 4 and respectively. 5. Influence of fluctuating power-line impedance Equation (1) shows that the terminating impedance does not influence the resonant point (center point) of the band-pass filter. However, (2) and (3) show that a varying terminating impedance does influence the respective cut-off points and therefore the bandwidth of the filter. 2log1[VP/VM] (db) 2log1[VP/VM] (db) -1-2 -3-4 -5-1 -2-3 -4-5 1 1k 1k 1k 1M 1M 1 1k 1k 1k 1M 1M Fig. 5. Measured amplitude response for a 1:1, 8kHz coupling circuit with 5Ω terminating impedance and 25Ω terminating impedance. Take note how the bandwidth is reduced by a lower terminating impedance. For this circuit L 19µH and C.22µF.

Fig. 5 shows the influence of terminating impedance on the amplitude response of a 1:1 coupling circuit designed around a 8kHz center point. In Fig. 5, the narrower pass-band caused by a lower terminating impedance is evident. When receiving a signal, this problem is not encountered: as the modem input impedance and transformer winding ratio is constant, the referred modem impedance stays constant. This implies a constant amplitude response when receiving a signal through the coupling circuit. Fig. 3 and 4 would therefore stay constant because the terminating impedance stays constant. However, when transmitting a communication signal into the power line, the terminating impedance varies with time. As stated before, typical impedance values are.2ω to 2Ω for frequencies in the CENELEC B, C, and D bands [2], [3]. Impedance values as low as.1ω and as high as 1Ω are also not uncommon [2], [5]. The lowest power-line impedance value would result in the narrowest pass-band whilst the maximum power-line impedance value would result in the widest pass-band. It is therefore best to design the filter for the lowest impedance values expected for a certain power-line network. If the power-line impedance (and transmitting bandwidth) then increases, no harm is done: a wider pass-band usually has no detrimental effect when transmitting a communication signal. (Rather, when a signal is received, it is of paramount importance that proper filtering takes place to improve signal-to-noise ratios.) The minimum power-line impedance that is designed for, must be chosen wisely, taking various interdependent factors into consideration. The lowest value of power-line impedance will determine the maximum power level (and thus transformer core size) for a certain voltage level. This power rating then influences the conductor cross-sectional area, and number of turns that can physically fit into the transformer window. Again, the number of turns influences magnetizing and leakage inductance as well as flux density. 6. Conclusion The first step when designing a coupling circuit would be to decide on a typical minimum power-line impedance value. The coupling transformer s turns ratio is then chosen to adapt the modem impedance to be roughly equal to this chosen power-line impedance. (This facilitates symmetrical filtering in both directions.) The maximum power output of the modem would be matched to the coupling transformer s maximum power in order not to overload the coupling circuit. If the power-line impedance drops below the chosen design value, the communication signal is still transmitted at the modem s maximum power level, but below the maximum voltage levels as determined by government regulations. Thus transformer size and cost (for optimum performance at a chosen minimum power-line impedance level) is traded against reduced performance at lower power-line impedance levels. References [1] P. A. Janse van Rensburg, H. C. Ferreira, Coupling circuitry: understanding the functions of different components, Proc. 7th Int. Symp. Power-Line Comm., 23, pp. 24-29. [2] H. C. Ferreira, H. M. Grové, O. Hooijen, and A. J. H. Vink, Power Line Communication (in Wiley Encyclopaedia of Electrical and Electronics Engineering), New York: John Wiley & Sons, 1999, pp. 76-716. [3] K. Dostert, Powerline Communications, Upper Saddle River: Prentice Hall PTR, 21, pp. 74, 92. [4] Signalling on Low-Voltage Electrical Installations in the Frequency Range 3kHz to 148.5kHz, CENELEC Standard EN 565-1, 1991. [5] O. Hooijen, Aspects of Residential Power Line Communications, Aachen: Shaker Verlag, 1998, pp. 52-65. [6] Soft Ferrites Data Handbook MA1, Philips Components, 1991, pp. 6, 83. [7] K. H. Billings, Handbook of Switchmode Power Supplies, New York: Mc Graw-Hill, 1989, pp. 3.78, 3.17. [8] W. T. McLyman, Transformer and Inductor Design Handbook, New York: Marcel Dekker, 1978. [9] P.A. Janse van Rensburg, H.C. Ferreira, The role of magnetizing and leakage inductance in transformer coupling circuitry, Submitted for Proc. 8th Int. Symp. Power-Line Comm., 24.