Reduction of heat sink common-mode currents in switching mode power supply circuits

In this paper, a new filter design for a heat sink is presented. The parasitic couplings between electric power devices and the heat sink are responsible for common-mode currents. The main focus is on the reduction of these currents to reduce the heat sink radiation. For this purpose a new filter design is proposed. In addition, experimental results are shown to validate the proposed filter.


Introduction
In general, power-switching semiconductors (MOS-FET's/IGBT's) are mounted on heat sinks to keep the power semiconductors within a given temperature range.A parasitic capacitance can be formed between the case of the semiconductors and the heat sink.The insulating thermal compound (Damiano et al., 2004) is the dielectric of this capacitance.It is shown as isolator 1 in Fig. 1.
Common-mode EMI is usually the result of parasitic effects (Tihanyi, 1995).Due to these capacitances commonmode currents are generated in Switching Mode Power Supply (SMPS) circuits.In consequence, these currents could violate the EMC standards by their radiation.Therefore, the heat sink should be well designed.
The drain-source voltage variation increases by decreasing the commutation time of the transistor and by increasing the insulation voltage level.Consequently, a high number of harmonic components are generated which makes the heat sink an EMI generator (Sinclair et al., 1993).
The shape and the dimension of the heat sinks play a major role in the power electronic system design.In general, as the size of the heat sink increases, the radiation efficiency also increases.However, the maximum radiation will take place Correspondence to: J. Kulanayagam (kulanayagam@hsu-hamburg.de) at different frequencies depending on the heat sink geometry (Brench, 1994), (Das and Roy, 1998).
In particular, the heat sink can become an efficient antenna when resonant phenomena occur (Damiano et al., 2004).This paper investigates the origin of common-mode currents generated by SMPS and shows a filter design to reduce common-mode currents of ungrounded heat sinks and an experimental setup for validating the input impedance and the heat sink radiation.

EMI generator and heat sink radiation
A parasitic capacitance C dh (see Fig. 2) exists between the metal case of the semiconductors and the heat sink.The insulating thermal compound acts as a dielectric for this capacitance.Due to this capacitance and the time varying drainsource voltage a noise current i noise can be calculated according to the following equation, as a first approach for low frequencies and where du ds /dt is the time derivative of the drain-source voltage.C dh can reach approximately 100 pF (Tihanyi, 1995).This noise current i noise is split into the conducted EMI current i c and the radiated EMI current i h The noise current paths through the heat sink in AC/DC converter are shown in Fig. 2 as an example.
In order to reduce the radiated emissions of the heat sink, it may be grounded.Consequently, the conducted EMI current i c raises in the power supply (Tihanyi, 1995).The results of the previous works (Li et al., 1993;Radhakrishnan et al., 2000;Archambeault et al., 2001), have proved that grounding a heat sink can reduce radiated emissions.
Published by Copernicus Publications on behalf of the URSI Landesausschuss in der Bundesrepublik Deutschland e.V. at different frequencies depending on the heat sink geometry (Brench, 1994), (Das and Roy, 1998).
In particular, the heat sink can become an efficient antenna when resonant phenomena occur (Damiano et al., 2004).This paper investigates the origin of common-mode currents generated by SMPS and shows a filter design to reduce common-mode currents of ungrounded heat sinks and an experimental setup for validating the input impedance and the heat sink radiation.

EMI generator and heat sink radiation
A parasitic capacitance C dh (see Fig. 2) exists between the metal case of the semiconductors and the heat sink.The insulating thermal compound acts as a dielectric for this capacitance.Due to this capacitance and the time varying drainsource voltage a noise current i noise can be calculated ac- The time derivative of the drain-source voltage is du ds /dt.C dh can reach approximately 100 pF (Tihanyi, 1995).This noise current i noise is split into the conducted EMI current i c and the radiated EMI current i h The noise current paths through the heat sink in AC/DC converter are shown in Fig. 2 as an example.In order to reduce Fig. 2. Noise current paths through the heat sink in an AC/DC converter the radiated emissions of the heat sink, it may be grounded.Consequently, the conducted EMI current i c raises in the power supply (Tihanyi, 1995).The results of the previous works (Li et al., 1993), (Radhakrishnan et al., 2000), (Archambeault et al., 2001), have proved that grounding a heat sink can reduce radiated emissions.
The noise current loops are shown again in Fig. 3.The current path i c via C hg and ground represents the commonmode current and the current path i h via C hp and the PCB is the heat sink current.The common-mode current i c produces conducted EMI, while i h generates radiated EMI via the heat sink as an antenna.If the heat sink is not grounded, the conducted EMI current i c can be reduced but the radiated EMI current i h to the SMPS raises (Felic and Evans, 2001).

Heat sink
Heat sink An efficient method to reduce radiated emissions of a heat sink was introduced in a previous study (Nagel, 1999).By in-device the capacitance can be minimized.This screen is applied as a shield for the heat sink.Furthermore, the sides of the screen are insulated with a well thermally conducting dielectric material.This screening design is illustrated in  3) between the heat sink and PCB is considered.

Filter design
Due to the extensive use of digital information and communication equipment, EMC problems have increased.To mitigate this problem, ferrite cores are usually attached on the cable/ wire (see Fig. 5) to suppress electromagnetic noise emissions from digital information equipment (Samir and Fujiwara, 1999).This idea was integrated in the heat sink filter design to attenuate the heat sink radiated emissions.The heat sink is extended with a metallic ring bar which has the same material characteristics like the heat sink.Furthermore, on the extended part of the heat sink a ferrite core is attached.The ferrite core is fixed between the heat sink and the power device.This is illustrated in Fig. 6.The high frequency current is attenuated due to the ferrite core.This current can be calculated by the following equation : The noise current loops are shown in Fig. 2. The current path i c via C hg and ground represents the common-mode current and the current path i h via C hp and the PCB is the heat sink current.If the heat sink is not grounded, the conducted EMI current i c can be reduced but the radiated EMI current i h to the SMPS raises (Felic and Evans, 2001).
An efficient method to reduce radiated emissions of a heat sink was introduced in a previous study (Nagel, 1999).By inserting a copper screen between the heat sink and the power device the capacitance can be minimized.This screen is applied as a shield for the heat sink.Furthermore, the sides of the screen are insulated with a well thermally conducting dielectric material.This screening design is illustrated in Fig. 4.
In this work the radiated EMI current via the heat sink (see Fig. 3) is considered.
heat sink current.If the heat sink is not grounded, the conducted EMI current i c can be reduced but the radiated EMI current i h to the SMPS raises (Felic and Evans, 2001).

PCB u ds C hp
Heat sink C dh Fig. 3. Radiated EMI current via the heat sink An efficient method to reduce radiated emissions of a heat sink was introduced in a previous study (Nagel, 1999).By inserting a copper screen between the heat sink and the power The time derivative of the drain-source voltage is du ds /dt.C dh can reach approximately 100 pF (Tihanyi, 1995).This noise current i noise is split into the conducted EMI current i c and the radiated EMI current i h The noise current paths through the heat sink in AC/DC converter are shown in Fig. 2 as an example.In order to reduce Fig. 2. Noise current paths through the heat sink in an AC/DC converter the radiated emissions of the heat sink, it may be grounded.Consequently, the conducted EMI current i c raises in the power supply (Tihanyi, 1995).The results of the previous works (Li et al., 1993), (Radhakrishnan et al., 2000), (Archambeault et al., 2001), have proved that grounding a heat sink can reduce radiated emissions.
The noise current loops are shown again in Fig. 3.The current path i c via C hg and ground represents the commonmode current and the current path i h via C hp and the PCB is the heat sink current.The common-mode current i c produces conducted EMI, while i h generates radiated EMI via the heat sink as an antenna.If the heat sink is not grounded, the conducted EMI current i c can be reduced but the radiated EMI current i h to the SMPS raises (Felic and Evans, 2001).

Heat sink
Heat sink device the capacitance can be minimized.This screen is applied as a shield for the heat sink.Furthermore, the sides of the screen are insulated with a well thermally conducting dielectric material.This screening design is illustrated in

Filter design
Due to the extensive use of digital information and communication equipment, EMC problems have increased.To mitigate this problem, ferrite cores are usually attached on the cable/ wire (see Fig. 5) to suppress electromagnetic noise emissions from digital information equipment (Samir and Fujiwara, 1999).This idea was integrated in the heat sink filter design to attenuate the heat sink radiated emissions.The heat

Filter design
Due to the extensive use of digital information and communication equipment, EMC problems have increased.To mitigate this problem, ferrite cores are usually attached on the cable/ wire (see Fig. 5) to suppress electromagnetic noise emissions from digital information equipment (Samir and Fujiwara, 1999).This idea was integrated in the heat sink filter design to attenuate the heat sink radiated emissions.
The heat sink is extended with a metallic ring bar which has the same material characteristics like the heat sink.Furthermore, on the extended part of the heat sink a ferrite core is attached.The ferrite core is fixed between the heat sink and the power device.This is illustrated in Fig. 6.
C hg sink urrent heat y inower ble/ wire (see Fig. 5) to suppress electromagnetic noise emissions from digital information equipment (Samir and Fujiwara, 1999).This idea was integrated in the heat sink filter design to attenuate the heat sink radiated emissions.The heat sink is extended with a metallic ring bar which has the same material characteristics like the heat sink.Furthermore, on the extended part of the heat sink a ferrite core is attached.
The ferrite core is fixed between the heat sink and the power device.This is illustrated in Fig. 6.The high frequency current is attenuated due to the ferrite core.This current can be calculated by the following equation : The initial heat sink setup of Fig. 1 changes to the filter design of Fig. 6.An additional impedance Z f has to be added in series to the resonant circuit.Z f is the impedance of the ferrite core.
This new design has a higher heat transfer resistance than the original setup, but it has a lesser heat transfer resistance than the screening design.The first setup is an original heat sink design for measuring the input impedance as a reference.It was placed to the vector network analyzer to measure the scattering parameters where Z input is the input impedance to the network, the used normalization impedance Z 0 is 50 Ohms, and the measured scattering parameter data is S 11 .In this work, the frequency range from 300 kHz up to 1 GHz was considered.
4.2 Radiation of the heat sink I h is the heat sink current and U ds is the drain-source voltage of the transistor and Z is the impedance of the network.The initial heat sink setup of Fig. 1 changes to the filter design 6.An additional impedance Z f has to be added in series to the resonant circuit.Z f is the impedance of the ferrite core.
This new design has a higher heat transfer resistance than the original setup, but it has a lesser heat transfer resistance than the screening design.The initial heat sink setup of Fig. 1 changes to the filter design of Fig. 6.An additional impedance Z f has to be added in series to the resonant circuit.Z f is the impedance of the ferrite core.
This new design has a higher heat transfer resistance than the original setup, but it has a lesser heat transfer resistance than the screening design.The first setup is an original heat sink design for measuring the input impedance as a reference.It was placed to the vector network analyzer to measure the scattering parameters S 11 (see Fig. 7).A second and third measurement setup were made for the extended heat sink design without ferrite core and with ferrite core, respectively.The scattering parameters S 11 of these setups were measured by a vector network analyzer (see Fig. 8).From these scattering parameters of all three configurations, the input impedances were calculated where Z input is the input impedance to the network, the used normalization impedance Z 0 is 50 Ohms, and the measured scattering parameter data is S 11 .In this work, the frequency range from 300 kHz up to 1 GHz was considered.

Radiation of the heat sink
In order to validate the attenuation of the heat sink radiated emissions of the proposed heat sink design an experimental test was done inside an anechoic chamber to avoid the presence of environmental EMI noises in EMI measurements.A simplified schematic of the experimental setup is shown in Fig. 9.The RF signal generator was connected via a coax- The initial heat sink setup of Fig. 1 changes to the filter design of Fig. 6.An additional impedance Z f has to be added in series to the resonant circuit.Z f is the impedance of the ferrite core.
This new design has a higher heat transfer resistance than the original setup, but it has a lesser heat transfer resistance than the screening design.The first setup is an original heat sink design for measuring the input impedance as a reference.It was placed to the vector network analyzer to measure the scattering parameters S 11 (see Fig. 7).A second and third measurement setup were made for the extended heat sink design without ferrite core and with ferrite core, respectively.The scattering parameters S 11 of these setups were measured by a vector network analyzer (see Fig. 8).From these scattering parameters of all three configurations, the input impedances were calculated where Z input is the input impedance to the network, the used normalization impedance Z 0 is 50 Ohms, and the measured scattering parameter data is S 11 .In this work, the frequency range from 300 kHz up to 1 GHz was considered.

Radiation of the heat sink
In order to validate the attenuation of the heat sink radiated emissions of the proposed heat sink design an experimental test was done inside an anechoic chamber to avoid the presence of environmental EMI noises in EMI measurements.A simplified schematic of the experimental setup is shown in Fig. 9.The RF signal generator was connected via a coax- 4 Input impedance of the heat sink

Experimental setup
Three different configurations were necessary to analyze the input impedance of the heat sink designs.The first setup is an original heat sink design for measuring the input impedance as a reference.It was placed to the vector network analyzer to measure the scattering parameters S 11 (see Fig. 7).A second and third measurement setup were made for the extended heat sink design without ferrite core and with ferrite core, respectively.The scattering parameters S 11 of these setups were measured by a vector network analyzer (see Fig. 8).
From these scattering parameters of all three configurations, the input impedances were calculated by using (Diepenbrock et al., 2001) www.adv-radio-sci.net/9/317/2011/Adv.Radio Sci., 9, 317-321, 2011  10.Equivalent circuit for original heat sink design impedance of the reference heat sink design can be expressed as: The impedance of the heat sink is given by The resonant frequency of the original heat sink design can be expressed as: Up to the resonant frequency f res1 , the input impedance behaves like a capacitance and above the resonant frequency f res1 the impedance behaves like an inductance.The resonant frequency f res2 of the second configuration was shifted into the lower MHz frequency range because the extended heat sink design has a larger current loop than the reference design.In other words, the second configuration has a larger inductance than the original heat sink setup.In consequence, the resonant frequency f res2 is smaller than the resonant frequency f res1 .The resonant frequencies of the first and second configuration are 300 MHz and 180 MHz, respectively.
The capacitances of the third configuration (extended heat sink with ferrite core) are the same as first and second configuration.But the inductances of the heat sink are increased by the ferrite cores.This is because all two ferrite core consist of different materials and therefore different magnetic characteristics.The quality factor of the system is reduced by the ferrite core.Furthermore, it depends on the ferrite materials which is used.
The input impedance of the heat sink is increased because a ferrite core has a very large impedance due to its permeability.This means that the heat sink currents will be minimized by adding the ferrite core between the heat sink and power device and the heat sink radiation is attenuated by this filter.In order to validate the attenuation of the heat sink radiated emissions of the proposed heat sink design an experimental test was done inside an anechoic chamber to avoid the presence of environmental EMI noises in EMI measurements.A simplified schematic of the experimental setup is shown in Fig. 12.The RF signal generator was connected via a coaxial cable to the heat sink ferrite design.On the other side a biconical/ logarithmic periodic antenna receives the emitted electromagnetic fields from the heat sink.This received RF signal V is detected by a spectrum analyzer.
From these RF signals of with and without ferrite core on the ungrounded heat sink, the attenuation of the heat sink radiated emissions is calculated using where A hs is the attenuation of the heat sink radiated emissions, V w/o Ferrite is the received RF signal of the heat sink   10.Equivalent circuit for original heat sink design impedance of the reference heat sink design can be expressed as: The impedance of the heat sink is given by The resonant frequency of the original heat sink design can be expressed as: Up to the resonant frequency f res1 , the input impedance behaves like a capacitance and above the resonant frequency f res1 the impedance behaves like an inductance.The resonant frequency f res2 of the second configuration was shifted into the lower MHz frequency range because the extended heat sink design has a larger current loop than the reference design.In other words, the second configuration has a larger inductance than the original heat sink setup.In consequence, the resonant frequency f res2 is smaller than the resonant frequency f res1 .The resonant frequencies of the first and second configuration are 300 MHz and 180 MHz, respectively.
The capacitances of the third configuration (extended heat sink with ferrite core) are the same as first and second configuration.But the inductances of the heat sink are increased by the ferrite cores.This is because all two ferrite core consist of different materials and therefore different magnetic characteristics.The quality factor of the system is reduced by the ferrite core.Furthermore, it depends on the ferrite materials which is used.
The input impedance of the heat sink is increased because a ferrite core has a very large impedance due to its permeability.This means that the heat sink currents will be minimized by adding the ferrite core between the heat sink and power device and the heat sink radiation is attenuated by this filter.In order to validate the attenuation of the heat sink radiated emissions of the proposed heat sink design an experimental test was done inside an anechoic chamber to avoid the presence of environmental EMI noises in EMI measurements.A simplified schematic of the experimental setup is shown in Fig. 12.The RF signal generator was connected via a coaxial cable to the heat sink ferrite design.On the other side a biconical/ logarithmic periodic antenna receives the emitted electromagnetic fields from the heat sink.This received RF signal V is detected by a spectrum analyzer.
From these RF signals of with and without ferrite core on the ungrounded heat sink, the attenuation of the heat sink radiated emissions is calculated using where A hs is the attenuation of the heat sink radiated emissions, V w/o Ferrite is the received RF signal of the heat sink where Z input is the input impedance to the network, the used normalization impedance Z 0 is 50 Ohms, and the measured scattering parameter data is S 11 .In this work, the frequency range from 300 kHz up to 1 GHz was considered.

Results and discussions
The results of all three configurations are illustrated in Fig. 9.The curves of the first (reference heat sink design) and second (extended heat sink without ferrite core) configuration show, that the heat sink structures behave like series resonant circuits.
The result of the first configuration can be explained by the following equivalent circuit (see Fig. 10.) The input impedance of the reference heat sink design can be expressed as: without ferrite core and V w/ Ferrite is the received RF signal of the heat sink with ferrite core.The measurement setups were configured for frontal and lateral radiation.In this work, the frequency range from 20 up to 300 MHz was considered.

Results and discussions
The attenuation of the heat sink radiation is calculated for frontal and lateral measurement of the heat sink is illustrated in Fig. 11.The maximum attenuation value and the average attenuation value of the frontal measurement of the heat sink are 25 dB and 15 dB, respectively.Furthermore, the maximum attenuation value and the average attenuation value of the lateral measurement of the heat sink are 10 dB and 5 dB, respectively.

Conclusions
In this paper a new filter design was introduced.It can be used to reduce the heat sink common-mode currents in Switching Mode Power Supply circuits.The validation of the input impedances of the heat sinks have verified that the input impedances can be increased at some frequencies up to 45 dB due to the ferrite core between the heat sink and the power device.Therefore, the heat sink current can be minimized.In addition, the radiated emissions from the heat sink are attenuated by the filter.Again, our proposed filter design reduces the heat sink noise currents and attenuates the heat sink radiated emissions.

References
Fig. 10.Equivalent circuit for original heat sink design impedance of the reference heat sink design can be expressed as: The impedance of the heat sink is given by The resonant frequency of the original heat sink design can be expressed as: Up to the resonant frequency f res1 , the input impedance behaves like a capacitance and above the resonant frequency f res1 the impedance behaves like an inductance.The resonant frequency f res2 of the second configuration was shifted into the lower MHz frequency range because the extended heat sink design has a larger current loop than the reference design.In other words, the second configuration has a larger inductance than the original heat sink setup.In consequence, the resonant frequency f res2 is smaller than the resonant frequency f res1 .The resonant frequencies of the first and second configuration are 300 MHz and 180 MHz, respectively.
The capacitances of the third configuration (extended heat sink with ferrite core) are the same as first and second configuration.But the inductances of the heat sink are increased by the ferrite cores.This is because all two ferrite core consist of different materials and therefore different magnetic characteristics.The quality factor of the system is reduced by the ferrite core.Furthermore, it depends on the ferrite materials which is used.The input impedance of the heat sink is increased because a ferrite core has a very large impedance due to its permeability.This means that the heat sink currents will be minimized by adding the ferrite core between the heat sink and power device and the heat sink radiation is attenuated by this filter.In order to validate the attenuation of the heat sink radiated emissions of the proposed heat sink design an experimental test was done inside an anechoic chamber to avoid the presence of environmental EMI noises in EMI measurements.A simplified schematic of the experimental setup is shown in Fig. 12.The RF signal generator was connected via a coaxial cable to the heat sink ferrite design.On the other side a biconical/ logarithmic periodic antenna receives the emitted electromagnetic fields from the heat sink.This received RF signal V is detected by a spectrum analyzer.
From these RF signals of with and without ferrite core on the ungrounded heat sink, the attenuation of the heat sink radiated emissions is calculated using where A hs is the attenuation of the heat sink radiated emissions, V w/o Ferrite is the received RF signal of the heat sink The impedance of the heat sink is given by The resonant frequency of the original heat sink design can be expressed as: Up to the resonant frequency f res1 , the input impedance behaves like a capacitance and above the resonant frequency f res1 the impedance behaves like an inductance.The resonant frequency f res2 of the second configuration was shifted into the lower MHz frequency range because the extended heat sink design has a larger current loop than the reference design.In other words, the second configuration has a larger inductance than the original heat sink setup.In consequence, the resonant frequency f res2 is smaller than the resonant frequency f res1 .The resonant frequencies of the first and second configuration are 300 MHz and 180 MHz, respectively.The capacitances of the third configuration (extended heat sink Adv.Radio Sci., 9, 317-321, 2011 www.adv-radio-sci.net/9/317/2011/with ferrite core) are the same as first and second configuration.But the inductances of the heat sink are increased by the ferrite cores.This is because all two ferrite core consist of different materials and therefore different magnetic characteristics.The quality factor of the system is reduced by the ferrite core.Furthermore, it depends on the ferrite materials which is used.
The input impedance of the heat sink is increased because a ferrite core has a very large impedance due to its permeability.This means that the heat sink currents will be minimized by adding the ferrite core between the heat sink and power device and the heat sink radiation is attenuated by this filter.

Experimental setup
In order to validate the attenuation of the heat sink radiated emissions of the proposed heat sink design an experimental test was done inside an anechoic chamber to avoid the presence of environmental EMI noises in EMI measurements.A simplified schematic of the experimental setup is shown in Fig. 11.
The RF signal generator was connected via a coaxial cable to the heat sink ferrite design.On the other side a biconical/ logarithmic periodic antenna receives the emitted electromagnetic fields from the heat sink.This received RF signal V is detected by a spectrum analyzer.
From these RF signals of with and without ferrite core on the ungrounded heat sink, the attenuation of the heat sink radiated emissions is calculated using A hs (dB) = V w/o Ferrite (dBµV ) − V w/ Ferrite (dBµV ), where A hs is the attenuation of the heat sink radiated emissions, V w/o Ferrite is the received RF signal of the heat sink without ferrite core and V w/ Ferrite is the received RF signal of the heat sink with ferrite core.The measurement setups were configured forfrontal and lateral radiation.In this work, the frequency range from 20 up to 300 MHz was considered.

Results and discussions
The attenuation of the heat sink radiation is calculated for frontal and lateral measurement of the heat sink is illustrated in Fig. 12.The maximum attenuation value and the average attenuation value of the frontal measurement of the heat sink are 25 dB and 15 dB, respectively.Furthermore, the maximum attenuation value and the average attenuation value of the lateral measurement of the heat sink are 10 dB and 5 dB, respectively.

Conclusions
In this paper a new filter design was introduced.It can be used to reduce the heat sink common-mode currents in Switching Mode Power Supply circuits.The validation of the input impedances of the heat sinks have verified that the input impedances can be increased at some frequencies up to 45 dB due to the ferrite core between the heat sink and the power device.Therefore, the heat sink current can be minimized.In addition, the radiated emissions from the heat sink are attenuated by the filter.Again, our proposed filter design reduces the heat sink noise currents and attenuates the heat sink radiated emissions.
et al.: Reduction of Heat Sink Common-Mode Currents in Switching Mode Power Supply Circuits cording to the following equation, as a first approach for low frequencies and

Fig. 5 .
Fig. 5. Block diagram of the filter design

Fig. 2 .
Fig. 2. Noise current paths through the heat sink in an AC/DC converter.
et al.: Reduction of Heat Sink Common-Mode Currents in Switching Mode Power Supply Circuits cording to the following equation, as a first approach for low frequencies and

Fig. 5 .
Fig. 5. Block diagram of the filter design

Fig. 5 .Fig. 6 .
Fig. 5. Block diagram of the filter design.J.Kulanayagam et al.: Reduction of Heat Sink Common-Mode Currents in Switching Mode Power Supply Circuits 3

4
Experimental setup 4.1 Input impedance of the heat sink Three different configurations were necessary to analyze the input impedance of the heat sink designs.

Fig. 7 .Fig. 8 .
Fig. 7. Measurement setup for the input impedance of the reference heat sink design

Fig. 6 .
Fig. 6.Schematic representation of filter design and equivalent circuit.

Fig. 6 .
Fig. 6.Schematic representation of filter design and equivalent circuit impedance of the heat sink Three different configurations were necessary to analyze the input impedance of the heat sink designs.

Fig. 7 .Fig. 8 .
Fig. 7. Measurement setup for the input impedance of the reference heat sink design

Fig. 7 .Fig. 6 .
Fig. 7. Measurement setup for the input impedance of the reference heat sink design.
impedance of the heat sink Three different configurations were necessary to analyze the input impedance of the heat sink designs.

Fig. 7 .Fig. 8 .
Fig. 7. Measurement setup for the input impedance of the reference heat sink design

Fig. 8 .
Fig. 8. Measurement setup for the input impedance of the ferrite heat sink design.

Fig. 9 .
Fig. 9. Input impedance of the reference, the enhanced heat sink with and without ferrite core

Fig. 11 .
Fig. 11.Attenuation of the heat sink ferrite design in the frequency range for frontal and lateral measurements

Fig. 9 .
Fig. 9. Impedance of the reference, the enhanced heat sink with and without ferrite core.

Fig. 9 .
Fig. 9. Input impedance of the reference, the enhanced heat sink with and without ferrite core

Fig. 11 .
Fig. 11.Attenuation of the heat sink ferrite design in the frequency range for frontal and lateral measurements

Fig. 9 .
Fig. 9. Input impedance of the reference, the enhanced heat sink with and without ferrite core

Fig. 11 .
Fig. 11.Attenuation of the heat sink ferrite design in the frequency range for frontal and lateral measurements

Fig. 12 .
Fig. 12. Attenuation of the heat sink ferrite design in the frequency range for frontal and lateral measurements.