Inductive and Capacitive Couplings in DC Motors with ... - IEEE Xplore

7 downloads 0 Views 234KB Size Report
Abstract —A quantitative analysis of parasitic coupling between elements of a 12V DC motor and its damping chokes is presented. This analysis deals both with ...
Inductive and Capacitive Couplings in DC Motors with Built-In Damping Chokes Jens Benecke ([email protected]), Stefan Dickmann ([email protected]) Helmut-Schmidt-Universit¨at (Universit¨at der Bundeswehr Hamburg), Germany Orthogonal orientation

11111 00000 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111 00000 11111

L

brushes

II. M OTOR C ONSTRUCTION The motor used as an example here is a 12 V DC motor used for air conditioning. It will consume approximately 25 A under load and can then emit HF noise with an amplitude of up to 100 dBµV, which might exceed some required EMC limits such as [5]. To attenuate the emitted HF noise, two chokes are inserted into the supply wires. An important technique for efficient filter design is the distinction between common and differential-mode currents, and optimizing the filter in question for the dominant mode [6]. For the motors in question and the given frequency range, the differential mode dominates

axis

Parallel

axis

Orthogonal

Radial

Fig. 1.

Possible orientations between motor axis and damping chokes.

C p (winding capacitance)

I. I NTRODUCTION The automotive industry uses 12 V DC motors for various applications, for example to drive air conditioning fans. These motors are integrated with damping chokes to suppress high frequency electromagnetic (EM) noise, which originates mostly from contact fluctuations and arcing due to forced commutation ([1], [2]). In [2], a model is presented for the impedance behaviour of the motor, as well as a description of its EM emissions and suggested filtering measures. Also, parasitic properties of conventional LC filters are discussed. However, when integrating these filters into the motor, new parasitic couplings between filter and motor elements appear which depend on their location and orientation. This changes the high frequency impedance of the motor and thus potentially also both conducted and radiated EM emissions, as both are closely connected [1]. It is therefore necessary to include the geometry of the motor parts in its electrical model ([3], [4]). In this paper, a quantitative analysis of both inductive and capacitive parasitic coupling between the elements of a motor and its damping chokes is presented, and a modified differential-mode model for the motor including damping chokes as well as couplings is introduced. A frequency range from 300 kHz to 300 MHz was chosen because it includes the FM radio range, where EM emissions are most critical, as well as lower frequencies to better characterize the armature inductance.

Possible orientations

+

Abstract — A quantitative analysis of parasitic coupling between elements of a 12V DC motor and its damping chokes is presented. This analysis deals both with inductive couplings between several chokes as well as armature windings, and with capacitive couplings between chokes and the motor casing. It produces a motor model to take these effects into account. It is shown that while both types of coupling depend on the orientation of the chokes within the motor, inductive couplings do not have much effect on its high frequency impedance. The capacitance between choke and casing, however, can significantly influence the impedance of the motor in cricital frequency ranges, such as the FM radio band.

L R s (ohmic losses in coil material) Rp Fig. 2.

(ohmic losses in core)

High frequency model of the choke used in the motor.

entirely. Thus, this paper only deals with differential mode. There are three basic ways of orientation for the chokes within the motor casing, as shown in Fig. 1. In the scope of this report they will be named as they are oriented to the main axis: “parallel”, “orthogonal” or “radial”, respectively. The motors currently in production contain chokes that are oriented “orthogonally”. Obviously, a change of their location and/or orientation can change the parasitic couplings between chokes and some motor elements. The main potential coupling paths between filter and motor elements are • inductive coupling between two chokes, • inductive coupling between choke and armature windings (the “load loop” inductance [7]), • capacitive coupling between choke and motor casing, • capacitive coupling between choke and commutator. These will be discussed in detail in the following chapters. The source loop inductance is kept very small by appropriate cabling and can therefore be ignored. III. P ROPERTIES OF THE CHOKE Two identical chokes are built into the example motor. Both have thirteen windings and a cylinder shaped ferrite core of 5 mm diameter and 18 mm length. The copper wire around the core has a diameter of 1.4 mm. A model was created to approximate the high frequency impedance of this choke, shown in Fig. 2. The values of the parasitic components in the model were determined by measuring the reflection factor r = S 11 of the choke and converting

17th International Zurich Symposium on Electromagnetic Compatibility, 2006

69

17th International Zurich Symposium on Electromagnetic Compatibility, 2006

I1

Rs1

I’1

U1

L1−M

U’1

Cp1 Rp1

L2−M I’ 2

Rs2

U’2

Rp2 Cp2

M

M . (5) L1 L2 Due to the fact that all elements in the circuit are symmetric, the indexes 1 and 2 in (4) are interchangeable. A MATLAB program was written to simulate the mutual inductance using the model in Fig. 3. For a distance of 44 mm, which equals the distance of the chokes in the motor, a value of M = 50 nH was found to agree well with the measurements (Fig. 4). This corresponds to a coupling factor of k ≈ 0.003. However, above 100 MHz, additional parasitic effects increase the difference between simulation and measurements slightly. The self-resonance peaks of both chokes in the simulation also correspond closely to the measurements. This shows that the mutual inductance is not influenced significantly by the resonance behaviour of the choke. Thus, M can be regarded as frequency independent here. k= √

I2 U2

Fig. 3. Two chokes modeled as a transformer, including their parasitic properties, to determine their mutual inductance.

this value into a frequency dependant impedance Z using Z = Z0 ·

1 + S 11 , 1 − S 11

(Z0 = 50 Ω).

(1)

Two chokes were measured in this way, and the results were matched with a MATLAB plot of the simulated impedance of the circuit in Fig. 2, which corresponds to 1 1 = jωCp + . jωL · Rp Z + Rs jωL + Rp

(2)

|Z /jω| (measured) 12

|Z /jω| (simulated) 12

choke 1 choke 2

Cp 0.95 pF 1.8 pF

Rs 3 mΩ 3 mΩ

Rp 10 kΩ 10 kΩ

−8

10

(3)

6

10

The capacitances differ due to different supply wire lengths and connectors. This made it possible to distinguish between resonance effects caused by the chokes and the wiring. With these values, the above model will accurately reflect the complex impedance of the chokes up to a frequency of 300 MHz. Saturation effects as well as thermic effects of the ferrite core were not taken into account since the HF noise stays far below saturation amplitudes. [8] gives a more detailed analysis of the effects of core materials on the electrical properties of chokes.

Fig. 4. parallel.

7

10 f (Hz)

8

10

|Z12 /jω| = |U1 /(jωI2 )| between two chokes oriented in

B. Mutual Inductance between chokes and armature A similar approach was taken to measure the mutual inductance between each choke and the motor armature. However, measuring the impedance of the armature reveals a lower first resonance frequency due to its high capacitance and inductance. Moreover, a mathematical high frequency model of the armature is much more complex than the same for a choke (see Fig. 7). Thus, the same measurements were made with the armature, but the values for the mutual inductance were only regarded for frequencies below the first resonance at approximately 1 MHz. This value was also assumed to be frequency independant. There are several ways of orientating the chokes in respect to the armature (see Fig. 1), and the armature’s magnetic field is too complex to calculate at which orientation the coupling would be strongest. Three batches of measurements were made to determine the mutual induction levels of each choke and the armature. The chokes were placed in various positions around the armature and the maximum mutual inductance that was found for each orientation is displayed in Fig. 5. Here, as expected, the parasitic components begin to appreciably influence the results above 1 MHz, which correspondends approximately to the self-resonance frequency of the armature windings. Below 1 MHz, the maximum mutual inductance is approx. 0.3 µH, which corresponds to a coupling factor of (see 5)

IV. I NDUCTIVE C OUPLINGS A. Mutual Inductance between Chokes Inductive couplings exist where parts of a magnetic field created by a current in one conductor induce a voltage in a different conductor [9]. In this case, it is possible that the magnetic fields of the two coils interact [7]. This is described by their mutual inductance. However, because of the complex geometry in the motor and the ferrite core, it is not feasible to model the mutual inductance analytically. Instead, several measurements were made and the resulting full S matrix was converted to a Z matrix, and thus to self-inductance and mutual inductance values. The two chokes were modeled as a transformer and their parasitic properties were included in the model as shown in Fig. 3. Due to the capacitances of the windings, modeled in parallel to the main inductance, a parallel resonance appears at approx. 100 MHz and 140 MHz for choke 1 and 2, respectively. The mutual inductance M and the coupling factor k are defined as follows (see Fig. 3):   U 1  U 1  ≈ = Z12 ; (4) M = jω · I 2 I =0 jω · I 2 I  =0 1

−7

10

12

L 1.4 µH 1.4 µH

|Z /jω| (H)

This gave the following values for the chokes’ parasitic compontents:

kd,max ≤ √

1

70

M 0.3 µH = √ ≈ 0, 07. (6) L1 · L2 12 · 1.4 µH

17th International Zurich Symposium on Electromagnetic Compatibility, 2006

−6

V. C APACITIVE C OUPLINGS

10

−7

12

|Z /jω| (H)

10

−8

10

−9

parallel orientation orthogonal radial

10

6

7

10

10 f (Hz)

8

10

Capacitive couplings appear between conducting surfaces. In this case, there are three potentially relevant parasitic couplings between chokes and motor (Fig. 8). Cdk is the capacitance between one choke and the commutator surfaces, Cdg is the capacitance between one choke and the motor casing, and Cdd is the capacitance between one choke and the armature windings (not displayed).

Fig. 5. Frequency dependant meausrement of |Z12 /jω| between one choke and the motor armature. Below 1 MHz, this value consists mainly of the mutual inductance. Above 1 MHz, parasitic effects dominate.

C. Results and Conclusion 3

10

simulated |Z| magnified (3 MHz .. 30 MHz)

Fig. 8.

|Z| (Ω)

Except for Cdg , none of the above can easily become larger than 0.1 pF due to their small area. Therefore, they cannot become relevant below 400 MHz for possible resonances, because the largest inductances relevant above 1 MHz are the chokes with 1.4 µH. Also, adding a ground capacitance to Fig. 7 does not visibly change the motor’s impedance. However Cdg , the capacitance to ground (the motor casing), is of importance. An approximation of this capacitance (which considers the choke as a single short wire with a diameter of 7 mm, and the motor casing as a flat ground plate), can be calculated as

2

10

Possible capacitive coupling paths between chokes and motor.

k=0 k =0.07 d

ko=0.003 7

10 Frequency (Hz)

Fig. 6. Influence of the inductive coupling between chokes and armature. (ko : between chokes, kd : choke and armature)

This coupling factor, as well as the coupling factor between the two inductances themselves, was used as input values for SPICE simulation of an electrical circuit approximation of the motor (Fig. 7, [2]). A plot of the simulation results (Fig. 6) reveals that the change in motor impedance is very small, and therefore should not impose a large change on the attenuation of EM emissions that originate from within the motor. For k = 0.07 (6), a change of approximately 1 dB was visible only between 10 and 20 MHz. Only a coupling factor of more than approx. 0.2 would cause a change of over 3 dB.



C ≈ ln

a r

+

2πεl   a 2 r

, −1

(7)

where r is the wire radius, l is its length and a the distance between wire center and ground. This yields a capacitance of about 0.8 pF for the values given in Fig. 8. This can become cricital, because a slight change of the position of the choke can change the location of a resonance near 80 MHz noticeably. To confirm the relevance of Cdg , the chokes were taken out of the motor and soldered in at the same connection points, but outside of the motor casing. The original configuration shows a parallel resonance at about 80 MHz. As visible in Fig. 9, the resonance frequency increased about 10 MHz to 90 MHz due to the reduction of Cdg . In a second experiment, the chokes were covered with an insulated copper foil which lowered the frequceny of this resonance by about 20 MHz due to the larger capacitance to ground. Connecting the foil to to the motor case however radically lowers the motor impedance. These changes were confirmed to be caused by Cdg by performing simulations with variable values of Cdg with SPICE. One such result is included in Fig. 9. It agrees well with the measurement. An additional impedance minimum, which was found to be a series resonance between L6 (approx. 90 nH, see Fig. 7) and C6 as well as the choke’s parasitic capacitance

Fig. 7. Electrical circuit simulation of the motor, including the damping chokes (LD1 and LD2), and mutual inductances defined within each object’s properties. L6 and C6 represent the inductance and capacitance of the brushes and the commutator contact surface, the remaining parts represent the armature. The voltage source represents the impedance measuring point.

71

17th International Zurich Symposium on Electromagnetic Compatibility, 2006

from (3), was found at 1  ≈ 401 MHz. 2π 90 nH · (0.95 + 0.8) pF

capacitances have a much bigger impact, as the results of the third motor (grounded copper foil around chokes) demonstrate. 2) The radially oriented chokes seem to work best due to their small Cdg . 3) A small peak at about 80 MHz is caused by resonances due to inductive energy stored in the armature (modeled as an additional source in [2]). Since the armature has a large parasitic capacitance to ground, this leads to believe that using the foil short circuits this energy past the chokes. Summarizing, too large a Cdg can significantly enlarge the HF emissions of the motor, more than inductive coupling. Above 30 MHz, the emissions decline with rising frequency due to the choke’s rising impedance and due to the declining amplitude of the emissions [10].

(8)

4

10

L outside L inside (orig.) L inside (simulation, ko=.07) L inside, covered L inside, covered and grounded

3

|Z| (Ω)

10

2

10

1

10

6

10

7

10 Frequency (Hz)

8

10

VII. C ONCLUSION A quantitative analysis of parasitic coupling between different elements of a 12V DC motor and its damping chokes was presented. Both inductive and capacitive coupling was analyzed and it was shown that inductive coupling between the chokes and the armature, while small, did have some effect on its impedance. Capacitive coupling had a bigger effect, though, and its consequences are important because the motor impedance and its EM emissions can be changed significantly within a frequency range where EM emissions are cricital. Further research in this field could take into account the geometry and arrangements of more parts within the motor case, and the shape of the case itself. If damping chokes are installed within the motor, they should be placed well away from any ground potential, as capacitive coupling can radically change the behaviour of the filter.

Fig. 9. Measured and simulated variation of the motor impedance by changing the position of the chokes.

Clearly, the motor impedance is dominated by the armature windings up to 1 MHz, and by the chokes which have a impedance maximum around 100 MHz. Without the chokes, the motor would have an impedance minimum at about 80 MHz resulting in higher EM emissions. These results are significant, because they are very sensitive to small changes in the motor construction, and these small changes influence the impedance of the motor exactly in the FM radio frequency range. The efficiency of the chokes deteriorates significantly if they are too near to a ground plate, such as the motor casing. VI. EM

EMISSION MEASUREMENTS

To confirm the effect of the choke orientation on the motor HF behaviour, the EM emissions of several motors were measured using a measuring setup from [5] which is specified up to 108 MHz. A ventilator was used as the load on the axis with which the motor consumed approximately 26 A DC. Fig. 10 shows the results above 30 MHz – below this frequency, all graphs were virtually identical.

R EFERENCES [1] Suriano, C. R. and Suriano, J. R. and Thiele, G. and Holmes, T. W., “Prediction of Radiated Emissions From DC Motors,” IEEE Trans. Electromagn. Compat., p. 790, 1998. [2] J. Sack, “St¨orspannungssemission kleiner GleichstromKommutatoren im Bereich der H¨orfunkfrequenzen,” Ph.D. dissertation, Universit¨at der Bundeswehr M¨unchen, 1985. [3] S. Chen and T.W. Nehl and J.-S. Lai and x. Huang and E. Pepa and R. de Doncker and I. Voss, “Towards EMI Prediction of a PM Motor Drive for Automotive Applications,” IEEE Trans. Magn., p. 14, 2003. [4] N. Boules, “Design optimization of permanent magnet DC motors,” 1990. [5] CISPR25, Radio disturbance characteristics for the protection of receivers used on board vehicles, boats and on devices – Limits and methods of measurement, International Electrotechnical Commission (CISPR), August 2002. [6] Paul, C. R. and Hardin, K. B., “Diagnosis and Reduction of Conducted Noise Emissions,” IEEE Trans. Electromagn. Compat., vol. 30, p. 553, 1988. [7] Wang, Shuo and Lee, F. C. and Chen, D. Y. and Odendaal, W. G., “Effects of Parasitic Parameters on EMI Filter Performance,” IEEE Trans. Electromagn. Compat., p. 73, 2003. [8] S. Weber and M. Schinkel and E. Hoene and S. Guttowski and W. John and H. Reichl, “Radio Frequency Characteristics of High Power Common-Mode Chokes,” EMC Z¨urich, p. 507, 2005. [9] Wang, Shuo and Lee, F. C. and Odendaal, W. G., “Characterizaion and Parasitic Extracion of EMI Filters Using Scattering Parameters,” IEEE Trans. Power Electron., vol. 20, p. 502, 2005. [10] Stubenbord, Linh Tao and Hackstein, D., “Methode zur Berechnung der elektromagnetischen Felder von elektrischen Kleinmotoren mittels der Geometrie-orientierten Simulation,” Ph.D. dissertation, Fernuniversitt Hagen, 2005, in progress.

Voltage (dBµV)

70

60 50

40

without chokes original position grounded copper foil chokes parallel chokes radial

30

8

10 Frequency (Hz)

Fig. 10.

Motor EM emissions under load (30..110 MHz).

The graph leads to the following conclusions: 1) As expected due to the small values of k, the orientation of the chokes makes only a small difference (max 5dBµV) in motor emissions. The parasitic 72