JP2011176394A - Power amplifier - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a power amplifier for setting a load of harmonic components independently so that the load of the harmonic components becomes an optimum load within a range from short-circuiting to open-circuiting without being affected by adjustment of a fundamental wave, and for obtaining high efficiency of power conversion. <P>SOLUTION: The power amplifier provides to output of a transistor 3: a harmonic-reflection circuit 4 for setting a load to harmonics for reflection; a load separation circuit 5 for separating an effect of the set load of a poststage to harmonics; and a fundamental wave matching adjustment circuit 6 for matching the transistor 3 to an output load for the fundamental waves. The power amplifier adjusts the load of the harmonics by adjusting length of a tip open stub 23 provided in the harmonic reflection circuit 4. Thus, the power amplifier independently achieves an optimum load adjustment for the harmonic components and the fundamental waves, and improves the efficiency of power conversion. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a power amplifier that amplifies a high-frequency signal, and more particularly to a power amplifier that can improve power conversion efficiency.

[Description of Prior Art]
The transmission power amplifier amplifies a high-frequency signal to a required transmission output, and is the part that consumes the most power in most radio devices.
The power consumed by the power amplifier is not only converted into a high-frequency output but also released as heat that causes internal loss.
Therefore, in order to reduce the amount of heat generation and reduce power consumption and improve reliability, it is required to increase the power conversion efficiency of the power amplifier to suppress useless internal loss.
In order to meet this demand, there are amplifiers incorporating various high-efficiency operation methods, for example, class F amplifiers using harmonic processing.

[Conventional class F amplifier]
A conventional class F amplifier will be briefly described.
A class F amplifier has a harmonic reflection circuit connected to the drain terminal of an FET (Field Effect Transistor), which is an active element, and the output load impedance viewed from the device at an even harmonic frequency. By opening the circuit at the short-circuit and odd harmonic frequencies, the FET drain voltage and drain current waveforms are prevented from overlapping.

As a result, the operation of the FET is that the drain voltage becomes zero when the drain current is flowing, and conversely the drain current becomes zero when the drain voltage is applied. The power can always be zero.
That is, ideally, the power consumption in the FET can be reduced to zero and the internal loss can be suppressed, assuming that the time waveforms of the FET drain voltage and drain current do not overlap.

[Configuration of Conventional Class F Amplifier: FIG. 6]
The configuration of a conventional class F amplifier will be described with reference to FIG. FIG. 6 is a block diagram showing a schematic configuration of a conventional class F amplifier. Here, a circuit in the case where harmonic components are taken into consideration up to the second order is shown.
As shown in FIG. 6, a conventional class F amplifier includes an input terminal 1, an input side fundamental wave matching circuit 2, a transistor 3, an output side fundamental wave / second harmonic matching circuit 12, and a second harmonic. A reflection circuit 13 and an output terminal 7 are provided.
The input side fundamental wave matching circuit 2 takes load matching between the input load and the transistor 3 for the fundamental wave.
The transistor 3 amplifies input power.
The output side fundamental wave / second harmonic matching circuit 12 performs load matching between the output of the transistor 3 and the second harmonic reflection circuit 13 for the fundamental wave and the second harmonic.
The second harmonic reflection circuit 13 reflects the second harmonic.

The operation of the class F amplifier will be described.
In the class F amplifier configured as described above, the fundamental wave input from the input terminal 1 is input to the transistor 3 through the input-side fundamental wave input circuit 2. The fundamental wave and the second harmonic output from the transistor 3 pass through the output side fundamental / second harmonic matching circuit 12 and are input to the second harmonic reflection circuit 13.

The second harmonic reflection circuit 13 functions as a reflection circuit for the second harmonic, and functions as a transmission line for the fundamental wave.
Therefore, by applying an appropriate load by the second harmonic reflection circuit 13, the second harmonic load viewed from the output of the transistor 3 becomes a short circuit. The fundamental wave output from the second harmonic reflection circuit 13 is output from the output terminal 7.
In this way, the operation of the conventional class F amplifier is performed.

In the class F amplifier configured as described above, the output side fundamental wave / second harmonic matching circuit 12 is load matched between the transistor 3 and the second harmonic reflection circuit 13 for both the fundamental wave and the second harmonic. This is difficult to design.
In addition, when the fundamental wave matching is adjusted, the matching of the second harmonic is broken at the same time, so that the second harmonic load viewed from the output of the transistor 3 is also changed.
The same is true when higher harmonics are taken into account.

[Configuration of Another Conventional Class F Amplifier: FIG. 7]
The configuration of another conventional class F amplifier will be described with reference to FIG. FIG. 7 is a block diagram showing a schematic configuration of another conventional class F amplifier.
As shown in FIG. 7, another conventional class F amplifier includes an input terminal 1, an input side fundamental wave matching circuit 2, a transistor 3, an output side fundamental wave matching / second harmonic reflection circuit 24, and an output. And a terminal 7.
The output side fundamental wave matching / second harmonic reflection circuit 24 is the same circuit as the output side fundamental wave / second harmonic matching circuit 12 and the second harmonic reflection circuit 13 of the class F amplifier shown in FIG. It is configured integrally and has a function of combining the output side fundamental wave / second harmonic matching circuit 12 and the second harmonic reflection circuit 13.
However, even in another conventional class F amplifier, it is not possible to independently adjust the fundamental matching and the second harmonic load by the output side fundamental matching / second harmonic reflection circuit 24. Have difficulty.

[Optimum load conditions]
As described above, the class F amplifier obtains high efficiency by making the output load viewed from the device short-circuited in the even-order harmonics and open in the odd-order harmonics. Due to the various characteristics possessed, the highest efficiency is not always obtained under the load conditions.
For example, when a state called an inverse class F amplifier in which the output load is open in the even-order harmonics and short-circuited in the odd-order harmonics is optimal, or an intermediate load condition between the class F amplifier and the inverse class F amplifier is It may be optimal.
As described above, when designing a matching circuit of an amplifier using harmonics, it is necessary to set the fundamental load, the even-order harmonic load, and the odd-order harmonic load to optimum conditions.

[Prior art documents]
As a prior art related to the class F amplifier, there is JP-A-6-204764 (Patent Document 1).
In Patent Document 1, in the power matching circuit, a 1/8 wavelength open-end transmission line of the fundamental wave is connected to the output terminal A of the transistor, and in parallel with this, transmission of 1/8 wavelength is performed at the A point. Connect the line, connect one or more open-ended transmission lines with 1/4 wavelength of odd-order harmonics to the point B of the transmission line, and connect a fundamental wave matching circuit to the point B. It is described that accurate short-circuiting or opening processing can be performed on waves.
However, in Patent Document 1, even harmonics can be short-circuited, but cannot be opened, and the load cannot be freely set from short-circuit to open.

Japanese Patent Laid-Open No. 6-204764

  However, in a power amplifier using harmonic processing such as a conventional class F amplifier or inverse class F amplifier, the matching circuit is optimal for all of the fundamental component, even harmonics, and odd harmonics at the same time. In other words, it is difficult to set a specific load, and the load for each frequency component cannot be adjusted independently.

  The present invention has been made in view of the above circumstances, and for each frequency component, an optimum load can be independently set in a range from short circuit to open circuit, and high power conversion efficiency can be obtained. An object of the present invention is to provide a power amplifier that can be used.

  The present invention for solving the problems of the above conventional example is a power amplifier having an amplifying element that amplifies an input high-frequency signal, and applies a load to a harmonic output from the amplifying element to reflect the harmonic. Connected to the output of the reflection circuit and the harmonic reflection circuit, the load separation circuit that isolates the influence of the subsequent load on the harmonic reflection circuit, and the output side connected to the output of the load separation circuit to perform load matching on the fundamental wave A first transmission line having a length of ¼ wavelength of a harmonic wave provided between the input terminal, the output terminal, and the input terminal and the output terminal. And a first open-ended stub having a length of a quarter wavelength of the harmonic connected between the first transmission line and the output terminal, the harmonic reflection circuit including the input terminal, the output terminal And the harmonics provided between the input and output terminals. A matching circuit, a second transmission line having a quarter wavelength of the fundamental wave connected between the matching circuit and the output terminal, and a second tip connected in series to the second transmission line A second tip open stub, comprising: an open stub; and a third tip open stub having a length of ¼ wavelength of the fundamental wave connected between the second transmission line and the second tip open stub. By adjusting the length, the harmonic load can be adjusted in the range from short circuit to open circuit.

  According to the present invention, a power amplifier having an amplifying element that amplifies an input high-frequency signal, a harmonic reflection circuit that applies a load to a harmonic output from the amplifying element and reflects it, and a harmonic reflection circuit A load separation circuit that is connected to the output and separates the influence of the subsequent load on the harmonic reflection circuit, and an output side fundamental wave matching adjustment circuit that is connected to the output of the load separation circuit and performs load matching on the fundamental wave; A load separation circuit includes an input terminal, an output terminal, a first transmission line having a length of ¼ wavelength of a harmonic wave provided between the input terminal and the output terminal, a first transmission line, and an output A first open-ended stub having a length of ¼ wavelength of the harmonic connected between the terminals and a harmonic reflection circuit comprising: an input terminal; an output terminal; and an input terminal and an output terminal. Harmonic matching circuit, matching circuit and output A second transmission line having a length of ¼ wavelength of the fundamental wave connected to the terminal, a second open-ended stub connected in series to the second transmission line, and a second transmission line And a third tip open stub having a quarter wavelength of the fundamental wave connected between the second tip open stub and the length of the second tip open stub is adjusted. Since the power amplifier is capable of adjusting the harmonic load in the range from short circuit to open circuit, it is possible to adjust the load independently for the harmonics and the fundamental wave to achieve the optimum load condition. There is an effect that efficiency can be improved.

1 is a configuration block diagram of a power amplifier according to an embodiment of the present invention. 3 is a circuit diagram of an output side load separation circuit 5. FIG. FIG. 4 is a circuit diagram of the output-side second harmonic reflection circuit 4. 5 is a circuit diagram showing another configuration of the output side load separation circuit 5. FIG. It is a circuit diagram which shows the fundamental structure of this power amplifier. It is a block diagram showing a schematic configuration of a conventional class F amplifier. It is a block diagram showing a schematic configuration of another conventional class F amplifier.

[Summary of Invention]
Embodiments of the present invention will be described with reference to the drawings.
A power amplifier according to an embodiment of the present invention includes a second-harmonic reflection circuit that reflects a second-order harmonic and sets a load on the second-order harmonic, and a set second-order harmonic load. A load separation circuit that separates the influence of the subsequent load on the signal and a fundamental wave matching adjustment circuit that matches the transistor and the output load with respect to the fundamental wave. The load is adjusted so as to obtain an optimum load for the second harmonic without being affected by the circuit, and the fundamental wave matching adjustment circuit can adjust the matching only for the fundamental wave. It is possible to improve the power conversion efficiency by performing optimum load adjustment without affecting the other of each of the fundamental waves.

  In addition, the power amplifier according to the embodiment of the present invention includes an n-order harmonic reflection circuit configured to reflect the output of the transistor by setting a load with respect to the n-order harmonic, and a subsequent load with respect to the set n-order harmonic. The n-th order harmonic processing circuit comprising the n-th order load separation circuit for separating the influence of the second order harmonic, the n-1st order harmonic,... A fundamental wave matching adjustment circuit for matching with an output load is provided, and optimum load adjustment can be performed independently for each of the n-th order, n-1st order,... The power conversion efficiency can be improved.

[Power Amplifier According to Embodiment: FIG. 1]
A power amplifier according to an embodiment of the present invention will be described with reference to FIG. FIG. 1 is a configuration block diagram of a power amplifier according to an embodiment of the present invention. Here, in order to simplify the description, first, a configuration in which only the second harmonic is considered as the harmonic will be described.
As shown in FIG. 1, this power amplifier includes an input terminal 1, an input side fundamental wave matching circuit 2, a transistor 3, an output side second harmonic reflection circuit 4, an output side load separation circuit 5, and an output. A side fundamental wave matching adjustment circuit 6 and an output terminal 7 are provided.

Each component will be described.
The input terminal 1, the input side fundamental wave matching circuit 2, the transistor 3, and the output terminal 7 are the same as those of the conventional class F amplifier shown in FIG.
The output-side second harmonic reflection circuit 4 is a characteristic part of the present power amplifier, reflects the second harmonic under the optimum load condition, and gives an optimum load to the second harmonic.

The output side load separation circuit 5 is a characteristic part of the present power amplifier. In order to prevent the subsequent circuit from affecting the secondary harmonic load set by the output side secondary harmonic reflection circuit 4, The second harmonic is adjusted so that the load adjustment of the second harmonic does not affect the fundamental wave matching in the subsequent stage.
The output side fundamental wave matching adjustment circuit 6 performs load matching between the output load connected to the output terminal and the transistor 3 for the fundamental wave.

[Output-side load separation circuit 5: FIG. 2]
Next, the circuit configuration of the output side load separation circuit 5 will be described with reference to FIG. FIG. 2 is a circuit diagram of the output side load separation circuit 5.
As shown in FIG. 2, the output side load separation circuit 5 includes an input terminal 14, a transmission line 16, a tip open stub 17, and an output terminal 15.
The transmission line 16 and the open-ended stub 17 have a length of λ / 8 where λ is the wavelength of the fundamental wave.

  Since the transmission line 16 and the open-ended stub 17 have a length of λ / 8 with respect to the fundamental wave, no matter what load is connected to the output terminal 15, The load at 0 is 0, and the load at point A is infinite. For this reason, the second harmonic is always infinite when viewed from the input terminal 14 of the output side load separation circuit 5 regardless of the load connected to the subsequent stage of the output side load separation circuit 5.

The output side load separation circuit 5 operates as a prematch circuit of the output side fundamental wave matching adjustment circuit 6 for the fundamental wave.
When impedance matching is performed in a wide band, the characteristic impedance of each transmission line of the output side load separation circuit 5 is selected so as to keep the Q value low.

[Output-side second harmonic reflection circuit 4: FIG. 3]
Next, the output-side second harmonic reflection circuit 4 will be described with reference to FIG. FIG. 3 is a circuit diagram of the output-side second harmonic reflection circuit 4.
As shown in FIG. 3, the output side second harmonic reflection circuit 4 includes an input terminal 18, a matching circuit 20, a transmission line 21, a tip open stub 22, a tip open stub 23, and an output terminal 19. I have.

The transmission line 21 and the open end stub 22 have a length of λ / 4 where λ is the wavelength of the fundamental wave.
The tip open stub 23 has an arbitrary length L.

The matching circuit 20 is a circuit that matches the second harmonic load impedance of the output of the transistor 3 with the circuits after the matching circuit 20 in the second harmonic.
The matching circuit 20 operates as a prematch circuit for the fundamental wave.

  The characteristic impedances of the transmission line 21 and the open-ended stubs 22 and 23 depend on the relationship between the second harmonic load and the fundamental wave load so that the Q value of the fundamental wave does not become too high due to impedance conversion by the matching circuit 20. , Is set arbitrarily.

The operation of the output side second harmonic reflection circuit 4 will be described.
Since the transmission line 21 has a length of λ / 4 with respect to the fundamental wave, the load at the point D and the load Z _C21 viewed from the point C toward the transmission line 21 are the same for the secondary harmonics ( Z _C = Z _C21 ).
Since the tip open stub 22 has a length of λ / 4 with respect to the fundamental wave, the load on the tip open stub 22 side at the point D becomes infinite for the second harmonic, and the tip open stub 22 Load does not affect point D.
Therefore, the second harmonic load at point D is determined by the length L of the open end stub 23.

The load at the point C is a combination of the load on the transmission line 21 side and the load Z _A connected to the output of the output-side second harmonic reflection circuit 4.
By connecting the output side load separation circuit 5 described above to the output terminal 19, the load Z _A becomes infinite in the second harmonic, so the load of the second harmonic at the point _C is Z _C = Z _D It is not affected by the subsequent load.
Thus, by changing the length L of the open end stub 23, the secondary harmonic load can be adjusted from a short circuit to an open circuit regardless of the circuit load at the subsequent stage.
Here, assuming that the length of the open end stub 23 when the secondary harmonic load is short-circuited is L1, and the length when the open end stub 23 is open is L2, the variable range of L is L1 ≦ L when L1 <L2. When L ≦ L2 and L2 <L1, L2 ≦ L ≦ L1.

For the fundamental wave, the load at the point D is always zero regardless of the length of the tip open stub 23 because the tip open stub 22 has a length of λ / 4 with respect to the fundamental wave.
Further, since the transmission line 21 has a length of λ / 4 with respect to the fundamental wave, the load on the transmission line 21 side at the point C becomes infinite, and even if the length L of the open end stub 23 is changed, the fundamental wave The load of is not changed.
That is, the output side second harmonic reflection circuit 4 and the output side load separation circuit 5 serve as prematch circuits for the fundamental wave.

[Another configuration: FIG. 4]
Another configuration of the output side load separation circuit 5 will be described with reference to FIG. FIG. 4 is a circuit diagram showing another configuration of the output side load separation circuit 5.
As shown in FIG. 4, another output-side load separation circuit 5 performs load matching between the transmission line 21 and the open-ended stub 23 between the point D to which the open-ended stub 22 is connected and the open-ended stub 23. The matching circuit 25 is provided.
In the configuration of FIG. 3, when the matching circuit 20 cannot sufficiently match the load of the transmission line 21 and the open-ended stub 23 with respect to the second harmonic, the matching circuit 25 performs load adjustment. .

[Matching fundamental wave components]
The matching between the transistor 3 and the output load in the fundamental wave component will be described.
For the fundamental wave component, the output side second harmonic reflection circuit 4, the output side load separation circuit 5 and the output side fundamental wave matching adjustment circuit 6 are combined with the output terminal 7 in the output side fundamental wave matching adjustment circuit 6. The load matching between the output load and the transistor 3 is performed.

  At this time, the adjusted second harmonic load is not affected by the load on the circuit after the output side load separation circuit 5 by the output side load separation circuit 5, so that the output is adjusted to adjust the matching of the fundamental component. Even if the side fundamental wave matching adjustment circuit 6 is adjusted, the fundamental wave matching can be independently adjusted without affecting the second harmonic load set by the output side second harmonic reflection circuit 4. Is.

  The input side bias and the output side bias can be applied from arbitrary circuits. However, the bias circuit does not affect the fundamental wave and the second harmonic, or functions as a part of the matching circuit.

[Principle configuration of this power amplifier: FIG. 5]
Next, the basic configuration of the power amplifier will be described with reference to FIG. FIG. 5 is a circuit diagram showing the basic configuration of the power amplifier.
As shown in FIG. 5, the fundamental configuration of this power amplifier is that an input side fundamental wave matching circuit 2 that takes load matching between an input load and a transistor is connected to the input side of the transistor 3, and the output side of the transistor 3 is connected. Is a plurality of harmonic processing circuits that reflect and perform load adjustment independently of the load of the subsequent circuit for the nth order (n is an integer of 3 or more) to second order harmonics, and output side fundamental wave matching adjustment The circuit 6 is connected in series. In the example of FIG. 5, n−1 harmonic processing circuits are provided.

The nth-order harmonic processing circuit includes an output-side nth-order harmonic reflection circuit 8 that matches and reflects the nth-order harmonics, and an output-side nth-order load separation circuit 9 that separates the influence of the subsequent load.
The configuration of the output-side nth-order harmonic reflection circuit 8 is the same as that of the output-side second-order harmonic reflection circuit 4 shown in FIG. 3, and the length of the open-end stub 23 depends on the load condition of the nth-order harmonic. Is L which is optimal.

  The output side n-th order load separation circuit 9 has the same configuration as that of the output side load separation circuit 5 shown in FIG. 2, but the lengths of the transmission line 16 and the open-ended stub 17 are the wavelength of the n-th order harmonic. The length is 1/4.

The n-1st order harmonic processing circuit matches the n-1st order harmonic and reflects the output side n-1st order harmonic reflection circuit 10 and the output side n- And a primary load separation circuit 11.
Similarly, for each order of harmonics, a harmonic processing circuit including an output side harmonic reflection circuit and an output side load separation circuit is provided, and the output side load separation circuit of the secondary harmonic processing circuit is the output side basic. The wave matching adjustment circuit 6 is connected.

  As a result, the harmonics of the respective orders of n to 2nd order are not affected by the load of the subsequent stage, and without affecting the load of the lower frequency than each harmonic (adjusted at the subsequent stage). Independently, load conditions can be optimized in the range from short circuit to open circuit.

Then, the load of the output side fundamental wave matching adjustment circuit 6 is optimized so as to match the load between the transistor 3 and the output load connected to the output terminal 7 in the fundamental wave.
In this way, the power amplifier can optimize the loads of the fundamental wave and the harmonics up to the n-th order independently and obtain high efficiency.

In the above configuration, the harmonic reflection circuit, the load separation circuit, and the fundamental wave matching adjustment circuit are connected only to the output side, but the input side harmonic reflection circuit and the input side load separation circuit are similarly configured on the input side. By connecting the input side fundamental wave matching adjustment circuit, the input side harmonic load and the input side fundamental wave matching can be optimized independently.
Further, the harmonic orders of the harmonic reflection circuit and the load separation circuit do not necessarily have to be in the order of higher order from the transistor side, and it is possible to provide a harmonic processing circuit only for the even order or only for the odd order. .

[Effect of the embodiment]
According to the power amplifier of the present embodiment, the output side second harmonic reflection circuit 4 that applies a load to the output of the transistor 3 and reflects the second harmonic, and the load of the subsequent circuit is a second harmonic load. Since the power amplifier is provided with an output side load separation circuit 5 that separates so as not to affect the output, and an output side fundamental wave matching adjustment circuit 6 that performs load matching between the transistor 3 and the output load for the fundamental wave, the fundamental wave The second harmonic load condition can be set optimally without being affected by the matching adjustment, and the fundamental wave matching can be adjusted without being affected by the second harmonic load. And the fundamental wave can be adjusted independently to the optimum load, and the power conversion efficiency can be improved.

  Further, according to the present power amplifier, the output of the transistor 3 is affected by the influence of the nth-order harmonic reflection circuit 8 that reflects the nth-order harmonic by setting the load to the nth-order harmonic and the subsequent load on the set nth-order harmonic. An n-order harmonic processing circuit comprising an n-order load separation circuit 9 for separation is provided for n-order harmonics, n-1st-order harmonics,... And a fundamental wave matching adjustment circuit 6 for matching with each other, and can perform optimum load adjustment independently for each of the n-th order, n-1st order,... Conversion efficiency can be improved.

  The present invention is suitable for a power amplifier that can improve power conversion efficiency using harmonic processing.

  DESCRIPTION OF SYMBOLS 1 ... Input terminal, 2 ... Input side fundamental wave matching circuit, 3 ... FET, 4 ... Output side 2nd harmonic reflection circuit, 5 ... Output side load separation circuit, 6 ... Output side fundamental wave matching adjustment circuit, 7 ... Output 8: Output side nth order harmonic reflection circuit, 9 ... Output side nth order load separation circuit, 10 ... Output side n-1st order harmonic reflection circuit, 11 ... Output side n-1st order load separation circuit, 12 ... Output side fundamental / second harmonic matching circuit, 13 ... second harmonic reflection circuit, 14 ... input terminal, 15 ... output terminal, 16 ... transmission line, 17 ... open stub, 18 ... input terminal, 19 ... output Terminals, 20 ... matching circuit, 21 ... transmission line, 22 ... open end stub, 23 ... open end stub, 24 ... output side fundamental wave matching / second harmonic reflection circuit, 25 ... matching circuit

Claims (1)

A power amplifier having an amplifying element for amplifying an input high-frequency signal,
A harmonic reflection circuit that applies a load to the harmonics output from the amplification element and reflects the harmonics;
A load separation circuit that is connected to an output of the harmonic reflection circuit and separates an influence of a subsequent load on the harmonic reflection circuit;
An output side fundamental wave matching adjustment circuit that is connected to the output of the load separation circuit and takes load matching for the fundamental wave;
The load separation circuit includes an input terminal, an output terminal, a first transmission line having a length of ¼ wavelength of the harmonics provided between the input terminal and the output terminal, and the first A first open-ended stub having a length of ¼ wavelength of the harmonic connected between the transmission line and the output terminal,
The harmonic reflection circuit is connected between an input terminal, an output terminal, the harmonic matching circuit provided between the input terminal and the output terminal, and between the matching circuit and the output terminal. A second transmission line having a length of ¼ wavelength of the fundamental wave, a second open-ended stub connected in series to the second transmission line, the second transmission line, and the second transmission line. A third tip open stub having a length of ¼ wavelength of the fundamental wave connected between the tip open stub and the length of the second tip open stub is adjusted, A power amplifier characterized in that the harmonic load can be adjusted in a range from a short circuit to an open circuit.

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