CN113993737A

CN113993737A - Circuit arrangement for a trolley bus with a battery and method for stabilizing the direct voltage of a high-voltage direct-current intermediate circuit in such a motor vehicle

Info

Publication number: CN113993737A
Application number: CN202080041983.7A
Authority: CN
Inventors: H.瑙曼
Original assignee: Volkswagen AG
Current assignee: Volkswagen AG
Priority date: 2019-06-17
Filing date: 2020-06-16
Publication date: 2022-01-28
Also published as: WO2020254329A1; DE102019214870A1

Abstract

The invention relates to a circuit arrangement (1) for a motor vehicle, wherein the motor vehicle can be supplied with direct current at least temporarily via an overhead line (20), comprising: a high voltage battery (4) for providing electrical energy; a high-voltage direct-current intermediate circuit (5) which can be coupled to an overhead line (20) conducting direct current; and a direct voltage converter (7) between the high-voltage direct current intermediate circuit (5) and the high-voltage battery (4), wherein the direct voltage converter (7) is designed to support the direct voltage (UE) of the high-voltage direct current intermediate circuit (5) by energy transmission from the high-voltage battery (4) in the event of a voltage drop caused by a loss of contact between the high-voltage direct current intermediate circuit (5) and the overhead line (20) and/or to reduce the direct voltage (UE) by increasing the energy transmission into the high-voltage battery (4) in the event of a voltage rise caused by a loss of contact between the high-voltage direct current intermediate circuit (5) and the overhead line (20). The invention further relates to a method for stabilizing the direct voltage (UE) of a high-voltage direct current intermediate circuit (5) in a motor vehicle.

Description

Circuit arrangement for a trolley bus with a battery and method for stabilizing the direct voltage of a high-voltage direct-current intermediate circuit in such a motor vehicle

Technical Field

The invention relates to a circuit arrangement for a motor vehicle and to a method for stabilizing the direct voltage of a high-voltage direct-current intermediate circuit in a motor vehicle. The invention further relates to a motor vehicle.

Background

In the field of electric vehicles, designs for the electrification of the power train of commercial vehicles are also increasingly being developed. However, the insufficient energy density of the energy store used is a problem here. One solution to this problem is to provide electrical energy from the outside via overhead lines. The commercial vehicle can then be operated via the overhead line and/or the energy store can be charged during driving. If an electrical connection is made between the current collector and the overhead line of a motor vehicle, contact between the current collector and the overhead line may be briefly lost due to uneven road surfaces and vibrations. On one side of the motor vehicle, this brief loss of contact can lead to brief voltage fluctuations.

It is known that by smoothing the voltage over the time course, the voltage drop caused by the loss of contact is mitigated by the input filter. These input filters are usually constructed as choke inductors or LC filters.

Disclosure of Invention

The object of the present invention is to provide a circuit arrangement for a motor vehicle and a method for stabilizing the dc voltage of a high-voltage dc intermediate circuit in a motor vehicle, with which circuit arrangement and method an improved response to voltage fluctuations is possible.

According to the invention, this object is achieved by a circuit arrangement having the features of claim 1 and by a method having the features of claim 7. Advantageous embodiments of the invention result from the dependent claims.

In particular, a circuit arrangement for a motor vehicle is achieved, wherein the motor vehicle can be supplied with direct current at least temporarily via an overhead line, the circuit arrangement comprising: a high voltage battery for providing electrical energy; a high voltage direct current intermediate circuit that can be coupled to an overhead line conducting direct current; and a direct voltage converter between the high-voltage direct current intermediate circuit and the high-voltage battery, wherein the direct voltage converter is designed to support the direct voltage of the high-voltage direct current intermediate circuit by energy transmission from the high-voltage battery in the event of a voltage drop caused by a loss of contact between the high-voltage direct current intermediate circuit and the overhead line and/or to reduce the direct voltage of the high-voltage direct current intermediate circuit by increasing the energy transmission into the high-voltage battery in the event of a voltage rise caused by a loss of contact between the high-voltage direct current intermediate circuit and the overhead line.

Furthermore, a method for stabilizing a direct voltage of a high-voltage direct-current intermediate circuit in a motor vehicle is provided, comprising the following steps: providing electrical energy by means of a high voltage battery; providing a high voltage direct current intermediate circuit that can be coupled to an overhead line conducting direct current; and supporting the direct voltage of the high-voltage direct current intermediate circuit by energy transmission from the high-voltage battery with a direct voltage converter in the event of a voltage drop caused by a loss of contact between the high-voltage direct current intermediate circuit and the overhead line, and/or reducing the direct voltage of the high-voltage direct current intermediate circuit by increasing the energy transmission into the high-voltage battery with a direct voltage converter in the event of a voltage rise caused by a loss of contact between the high-voltage direct current intermediate circuit and the overhead line.

The circuit arrangement and the method make it possible to actively compensate for voltage drops and/or voltage rises and thus to maintain or stabilize the direct voltage of the high-voltage direct-current intermediate circuit at a predefined voltage value. This is done in the event of a power drop in the overhead line by compensating for the voltage drop caused by a loss of contact between the high-voltage direct-current intermediate circuit or a current collector connected thereto and the overhead line by means of a direct-current voltage converter (also referred to as a DC/DC converter). For this purpose, the dc voltage converter generates, in particular on the side facing the high-voltage dc intermediate circuit, a supporting voltage which keeps the dc voltage in the high-voltage dc intermediate circuit constant and for which the direction of the power flow from the high-voltage battery to the high-voltage dc intermediate circuit is reversed. Conversely, if electrical power is fed into the overhead line system, for example by means of an electrical machine which operates as a generator, the voltage increase in the direct voltage intermediate circuit caused by the loss of contact is also compensated by means of the direct voltage converter. For this purpose, the dc voltage converter reduces the dc voltage in the dc voltage intermediate circuit on the side facing the high-voltage dc intermediate circuit by increasing the energy transfer into the high-voltage battery.

An advantage of the invention is that voltage drops and/or voltage rises can be actively compensated, so that voltage drops and/or voltage rises can be completely compensated. On the contrary, with the prior art switching devices according to the input filter and choke inductance based circuit arrangement, i.e. purely passive components, complete compensation is not possible. With the circuit arrangement and the method, in particular a supporting or constant and stable voltage can be provided, for example for operating an electric machine and further high-voltage consumers, and thus normal operation can be maintained even in the event of a loss of contact.

A further advantage of the invention is that the input filter can be completely eliminated, or at least the components of the input filter or choke inductance can be smaller in size, due to the active compensation or stabilization. This can be cost-effective.

The circuit arrangement, in particular the dc voltage converter, is controlled or regulated by means of a control device. The control means may be constructed as a combination of hardware and software, for example as program code executed on a microcontroller or microprocessor.

The electric machine of the motor vehicle or the drive converter of the electric machine is in particular connected to the high-voltage direct current intermediate circuit and can be supplied with electrical energy both from the overhead line and from the high-voltage battery. Furthermore, the electric machine can also be operated in particular as a generator.

In one embodiment, it is provided that the dc voltage converter is designed as a bidirectional dc voltage converter, wherein the dc voltage converter is also designed to convert, if necessary, a dc voltage supplied by the overhead line into a charging voltage for the high-voltage battery. In the first operating state, the dc voltage converter can convert the voltage of the overhead line into a charging voltage of the high-voltage battery, so that the high-voltage battery can be charged via the overhead line. In a second operating state, the power flow can be reversed and the dc voltage converter is used to support a dc voltage in the high-voltage dc intermediate circuit in the event of a voltage drop. The first operating state is also used for reducing the dc voltage in the dc voltage intermediate circuit. By the bidirectional design, components can be saved overall, since the dc voltage converter can be operated in both directions.

In one embodiment, it is provided that the circuit arrangement has at least one voltage sensor arranged on the high-voltage direct-current intermediate circuit, wherein the at least one voltage sensor has a sampling frequency of at least 100kHz, and wherein the direct-current voltage converter is designed to adjust the support and/or reduction of the direct-current voltage on the basis of sensor data recorded by the at least one voltage sensor. With a sampling frequency of at least 100kHz, the voltage dip or the voltage rise and the course thereof can be detected with a corresponding resolution and therefore without a large delay after the occurrence.

In one embodiment, it is provided that the dc voltage converter has a control frequency of at least 10kHz for controlling the voltage on the side facing the high-voltage dc intermediate circuit. This enables a fast reaction to voltage drops or voltage rises and to rapidly changing voltages in the high voltage direct current intermediate circuit.

The design of the method is characterized in that the description of the design of the circuit arrangement follows. The advantages of this method are in each case the same as in the design of the circuit arrangement.

Furthermore, a motor vehicle is realized, comprising at least one circuit arrangement according to any of the described embodiments. In particular, it can be provided that the motor vehicle is a commercial vehicle.

Drawings

The invention is explained in more detail below on the basis of preferred embodiments with reference to the drawings. In this drawing:

fig. 1 shows a schematic diagram of an embodiment of a circuit arrangement for a motor vehicle;

fig. 2a shows a schematic diagram of the time course of the current and voltage during a loss of contact without voltage support;

fig. 2b shows a schematic diagram of the temporal course of the current and voltage during a loss of contact with voltage support;

FIG. 2c shows a schematic diagram of the associated load characteristic curve and operating point;

fig. 3a shows a schematic diagram of the time course of the current and voltage during a loss of contact without voltage reduction (the electric machine is operated as a generator);

fig. 3b shows a schematic diagram of the time course of the current and voltage during a loss of contact with a voltage reduction (the electric machine is operated as a generator);

fig. 3c shows a diagram of the associated load characteristic curve and operating point.

Detailed Description

Fig. 1 shows a schematic diagram of an embodiment of a circuit arrangement 1 for a motor vehicle. The motor vehicle can be supplied with electrical energy via an overhead line 20. For this purpose, an electrical connection must be established between the overhead line 20 and the high-voltage network 3 of the motor vehicle. The circuit arrangement 1 is connected to a collector 2 of a motor vehicle.

The circuit arrangement 1 comprises a high-voltage battery 4 for providing electrical energy, a high-voltage direct-current intermediate circuit 5 and a direct-voltage converter 7 between the high-voltage direct-current intermediate circuit 5 and the high-voltage battery 4. The circuit arrangement 1, in particular the dc voltage converter 7, is controlled or regulated by means of a control device (not shown).

In particular, it is provided that the dc voltage converter 7 is designed as a bidirectional dc voltage converter 17, wherein the dc voltage converter 7 is also designed to convert the dc voltage UF supplied by the overhead line 20 to a charging voltage of the high-voltage battery 4, if required.

The high-voltage direct current intermediate circuit 5 can be electrically connected to the overhead line 20 via the coupling device 6.

The motor vehicle further comprises an electric machine 10 which can be connected both to the high-voltage battery 4 and to the high-voltage direct current intermediate circuit 5 via a drive converter 11 and a further coupling device 12. For this purpose, the further coupling device 12 comprises, for example,

circuit arrangements

13, 14, with which the electric machine 10 can be connected to the high-voltage battery 4 or to the high-voltage direct-current intermediate circuit 5 via the drive converter 11. Furthermore, a further electrical high-voltage consumer 15 can be connected to the high-voltage battery 4.

The collector 2 comprises a choke inductance 18, an electrical safety device 19 and a pre-charge resistor 22. The high-voltage battery 4 comprises an electrical safety device 8 and an internal circuit arrangement 9 for breaking an electrical connection to the high-voltage network 3 in the event of an overload.

If the contact between the overhead wire 20 and the sliding contact 21 of the collector 2 is lost, for example, due to unevenness of the road or vibration, a drop in the voltage UP is caused when the power of the overhead wire 20 drops.

This is schematically shown in fig. 2 a. Fig. 2a shows the course of current 30 and voltage 31 over time 32. It is assumed herein that the power consumption is constant throughout the period shown. At time t0, a normal operating state is present and the circuit arrangement 1 is at the first operating point 40. The current flow of the current IE to the electric machine 10 and the current flow of the current ID to the dc voltage converter 7 are such that a power flow to the electric machine 10 and a power flow to the high voltage battery 4 via the dc voltage converter 7 is achieved. The dc voltage converter 7 charges the high-voltage battery 4.

A loss of contact occurs at time point t 1. The loss of contact continues until time point t 2. This loss of contact typically lasts for several milliseconds. During this time between time points t1 and t2, a drop in voltage UP occurs. Due to the choke inductance 18 (fig. 1), the course of the voltage drop is smoothed and thus relaxed, so that the voltages UD and UE in the high-voltage direct-current intermediate circuit 5 drop and the circuit arrangement 1 is at the second operating point 41. However, the trend is smoothed over time 32. Due to the assumed constant power consumption, the currents IE and ID are larger in the time between t1 and t2 compared to the normal operating state at the first operating point 40.

In the event of a voltage drop caused by a loss of contact between the current collector 2 and the overhead line 20, the direct voltage converter 7 supports the direct voltage UE of the high-voltage direct current intermediate circuit 5 by energy transfer from the high-voltage battery 4.

The support for the voltage is schematically shown in fig. 2 b. The time profile of the contact loss is the same as that shown in fig. 2a, and the same reference numerals denote the same terms and features. In order to support the direct voltage UE in the high-voltage direct current intermediate circuit 5, the direct voltage converter 7 reverses the current direction of the current ID between the points in time t1 and t2 and thereby causes a power flow from the high-voltage battery 4 into the high-voltage direct current intermediate circuit 5. This is achieved by means of voltage regulation on the side facing the high-voltage direct-current intermediate circuit 5. By changing the current ID, the voltages UE and UD in the high voltage direct voltage intermediate circuit 5 are increased to the value of the voltages UE, UD before a loss of contact occurs. The dc voltage converter 7 therefore provides a current difference to support the original voltage UE present at the time t 0.

It can be provided that the circuit arrangement 1 has a voltage sensor 16 arranged on the high-voltage direct-current intermediate circuit 5, wherein the voltage sensor 16 has a sampling frequency of at least 100kHz, and wherein the direct-current voltage converter 7 adjusts the voltage support on the basis of sensor data detected by the voltage sensor 16.

Provision can also be made for the dc voltage converter 7 to have a control frequency of at least 10kHz for the voltage control on the side facing the high-voltage dc intermediate circuit 5.

Fig. 2c shows a schematic illustration of load

characteristic curves

43, 44 with different operating points 40, 41, 42. The x-axis 33 represents the current and the y-axis 34 represents the voltage UE (═ UD) in the high-voltage direct-current intermediate circuit 5. The operating points 40, 41, 42 are also shown in fig. 2a and 2 b.

The load

characteristic curves

43, 44 show the dependence of the voltage UE (═ UD) in the high-voltage direct-current intermediate circuit on the current with the assumed constant power consumption. The load characteristic curve 43 describes the dependence here during normal operating conditions in which there is electrical contact between the current collector 2 and the overhead line 20. In contrast, the load characteristic curve 44 describes the dependence during a loss of contact. It is assumed here that the contact is not completely broken, but only the resistance increases. For this reason, the load characteristic curve 44 has a greater slope in terms of quantity than the load characteristic curve 43.

In the normal operating state, the circuit arrangement 1 operates in the first operating point 40 on the characteristic curve 43. The currents IE and ID are added. If there is a loss of contact, the circuit arrangement 1 is located in the second operating point 41 on the characteristic curve 44 by the increased currents IE and ID without supporting the voltage UE (═ UD). In the case of a support for the voltage UE, in which the current ID acts opposite to the current IE, the circuit arrangement 1 is instead at the third operating point 42, i.e. at the same voltage UE as the first operating point 40 on the load characteristic curve 43 (i.e. in the normal operating mode).

Conversely, if the electric machine 10 is in generator operation and electrical power is fed into the overhead line 20, the voltage UP increases when a loss of contact between the overhead line 20 and the sliding contact 21 of the collector 2 occurs.

This is schematically shown in fig. 3 a. Fig. 3a shows the course of current 30 and voltage 31 over time 32. It is assumed here that the generative power is constant over the entire time period shown. At time t0, a normal operating state is present and the circuit arrangement 1 is at the first operating point 40. The current flow of the current IE from the motor 10 and the current flow of the current ID to the dc voltage converter 7 are such that a power flow from the motor 10 to the overhead line 20 and a power flow to the high-voltage battery 4 via the dc voltage converter 7 are achieved. The dc voltage converter 7 charges the high-voltage battery 4.

A loss of contact occurs at time point t 1. The loss of contact continues until time point t 2. This loss of contact typically lasts for several milliseconds. During this time between time points t1 and t2, a rise in voltage UP occurs. Due to the choke inductance 18 (fig. 1), the course of the voltage drop is smoothed and thus relaxed, so that the voltages UD and UE in the high-voltage direct-current intermediate circuit 5 rise and the circuit arrangement 1 is at the second operating point 41. However, the trend is smoothed over time 32. Due to the assumed constant generative power consumption, the amounts of currents IE and ID are reduced in the time between t1 and t2 compared to the normal operating state at the first operating point 40.

In the event of a voltage rise caused by a loss of contact between the current collector 2 and the overhead line 20, the dc voltage converter 7 reduces the dc voltage UE of the high-voltage dc intermediate circuit 5 by increasing the energy transfer into the high-voltage battery 4.

The reduction of the dc voltage is schematically shown in fig. 3 b. The time profile of the contact loss is the same as that shown in fig. 3a, and like reference numerals denote like terms and features. In order to reduce the direct voltage UE in the high-voltage direct current intermediate circuit 5, the direct voltage converter 7 increases the current ID between the points in time t1 and t2 and thus causes an (increased) power flow from the high-voltage direct current intermediate circuit 5 into the high-voltage battery 4. This is achieved by means of voltage regulation on the side facing the high-voltage direct-current intermediate circuit 5. By changing the current ID, the voltages UE and UD in the high-voltage direct-current voltage intermediate circuit 5 are reduced to the value of the voltages UE, UD before a loss of contact occurs. The dc voltage converter 7 therefore provides a current difference to set the original voltage UE present at the time t 0.

It can be provided that the circuit arrangement 1 has a voltage sensor 16 arranged on the high-voltage direct-current intermediate circuit 5, wherein the voltage sensor 16 has a sampling frequency of at least 100kHz, and wherein the direct-current voltage converter 7 adjusts the voltage reduction on the basis of sensor data acquired by the voltage sensor 16.

Fig. 3c shows a schematic illustration of load

characteristic curves

43, 44 with different operating points 40, 41, 42. The x-axis 33 represents the current and the y-axis 34 represents the voltage UE (═ UD) in the high-voltage direct-current intermediate circuit 5. The operating points 40, 41, 42 are also shown in fig. 3a and 3 b.

The load

characteristic curves

43, 44 show the dependence of the voltage UE (═ UD) in the high-voltage direct-current intermediate circuit 5 on the current with the assumed constant power of formation. The load characteristic curve 43 describes the dependence here during normal operating conditions in which there is electrical contact between the current collector 2 and the overhead line 20. In contrast, the load characteristic curve 44 describes the dependence during a loss of contact. It is assumed here that the contact is not completely broken, but only the resistance increases. For this reason, the load characteristic curve 44 has a greater slope in terms of quantity than the load characteristic curve 43.

In the normal operating state, the circuit arrangement 1 operates in the first operating point 40 on the characteristic curve 43. The current IE in the high voltage direct current intermediate circuit is reduced by the current ID. If there is a loss of contact, the circuit arrangement 1 is located in the second operating point 41 on the characteristic curve 44 by means of the quantitatively decreasing currents IE and ID without a decrease in the voltage UE (═ UD). To reduce the voltage UE, the current ID in the dc voltage converter 7 is increased, so that an (increased) power flow from the dc voltage intermediate circuit 5 into the high-voltage battery 4 is achieved. Assuming that the generated power is the same, the current IE is correspondingly increased by decreasing the voltage UE. The circuit arrangement 1 is then at the third operating point 42, i.e. at the same voltage UE as the first operating point 40 on the load characteristic curve 43 (i.e. in the normal operating mode).

The circuit arrangement 1 and the method have the advantage that even in the event of a loss of contact, a supporting or constant and stable direct voltage UE can be provided for operating the electric machine 10 and the further high-voltage consumers 15 in the high-voltage direct current intermediate circuit 5, and therefore normal operation is not interrupted or disturbed even during the loss of contact.

List of reference numerals

1 Circuit arrangement

2 Current collector

3 high voltage network

4 high-voltage battery

5 high-voltage direct current intermediate circuit

6 coupling device

7 DC voltage converter

8 electric safety device

9 internal circuit device

10 electric machine

11 drive converter

12 further coupling device

13 Circuit arrangement

14 circuit arrangement

15 high-voltage consumer

16 voltage sensor

17 bidirectional DC voltage converter

18 choke inductance

19 electric safety device

20 overhead line

21 sliding contact

22 precharge resistor

30 current (l)

31 voltage

32 hours

33 x axis

34 y axis

40 first operating point

41 second operating point

42 third operating point

43 load characteristic curve (Normal operation)

44 load characteristic curve (support operation)

51 electric safety device

52 internal circuit device

time points t0-t2

UP Voltage (Current collector)

IP Current (Current collector)

UE Voltage (intermediate Circuit)

IE Current (intermediate Circuit)

UD Voltage (DC Voltage converter)

ID Current (DC Voltage converter)

UB voltage (high voltage battery)

IB Current (high Voltage Battery)

IE Current (intermediate Circuit)

Claims

1. A circuit arrangement (1) for a motor vehicle which can be supplied with direct current at least temporarily via an overhead line (20), comprising:

a high-voltage battery (4) for providing electrical energy;

a high-voltage direct-current intermediate circuit (5) which can be coupled to an overhead line (20) conducting direct current; and

a DC-voltage converter (7) between the high-voltage DC intermediate circuit (5) and the high-voltage battery (4),

wherein the direct voltage converter (7) is designed to support the direct voltage (UE) of the high-voltage direct current intermediate circuit (5) by energy transmission from the high-voltage battery (4) in the event of a voltage drop caused by a loss of contact between the high-voltage direct current intermediate circuit (5) and the overhead line (20) and/or to reduce the direct voltage (UE) of the high-voltage direct current intermediate circuit (5) by increasing the energy transmission into the high-voltage battery (4) in the event of a voltage rise caused by a loss of contact between the high-voltage direct current intermediate circuit (5) and the overhead line (20).

2. Circuit arrangement (1) according to claim 1, characterised in that the direct voltage converter (7) is constructed as a bidirectional direct voltage converter (17), wherein the direct voltage converter (7) is also constructed to convert the direct voltage (UF) provided by the overhead line (20) to a charging voltage of the high-voltage battery (4) when required.

3. Circuit arrangement (1) according to claim 1 or 2, characterized by at least one voltage sensor (16) arranged on the high-voltage direct current intermediate circuit (5), wherein at least one voltage sensor (16) has a sampling frequency of at least 100kHz, and wherein the direct voltage converter (7) is constructed to adjust the support and/or reduction of the direct voltage (UE) based on sensor data acquired by at least one voltage sensor (16).

4. A circuit arrangement (1) as claimed in any one of the preceding claims, characterized in that the adjustment of the voltage on the side facing the high-voltage direct current intermediate circuit (5) by the direct-voltage converter (7) has an adjustment frequency of at least 10 kHz.

5. A motor vehicle comprising at least one circuit arrangement (1) according to any one of claims 1 to 4.

6. A motor vehicle according to claim 5, characterised in that the motor vehicle is a commercial vehicle.

7. A method for stabilizing a direct voltage (UE) of a high voltage direct current intermediate circuit (5) in a motor vehicle, the method comprising the steps of:

providing electrical energy by means of a high-voltage battery (4);

providing a high-voltage direct-current intermediate circuit (5) which can be coupled to an overhead line (20) conducting direct current; and

supporting the direct voltage (UE) of the high-voltage direct-current intermediate circuit (5) by energy transmission from the high-voltage battery (4) by means of a direct-voltage converter (7) in the event of a voltage drop caused by a loss of contact between the high-voltage direct-current intermediate circuit (5) and the overhead line (20); and/or

By means of the DC voltage converter (7), the DC voltage (UE) of the high-voltage DC intermediate circuit (5) is reduced by increasing the energy transfer into the high-voltage battery (4) in the event of a voltage rise caused by a loss of contact between the high-voltage DC intermediate circuit (5) and the overhead line (20).

8. Method according to claim 7, characterized in that the direct voltage converter (7) is constructed as a bidirectional direct voltage converter (17), wherein the direct voltage (UF) provided by the overhead line (20) is converted, when required, into a charging voltage of the high-voltage battery (4).

9. Method according to claim 7 or 8, characterized in that the direct voltage (UE) is regulated on the basis of sensor data of at least one voltage sensor (16) arranged on the high voltage direct current intermediate circuit (5), wherein the direct voltage (UE) is acquired with a sampling frequency of at least 100 kHz.

10. Method according to any of claims 7 to 9, characterized in that the voltage regulation of the side facing the high voltage direct current intermediate circuit (5) is performed with a regulation frequency of at least 10 kHz.