A non-reflective lumped parameter filter

Abstract

The application discloses a non-reflection lumped parameter filter, which comprises a first port, a second port, a low-pass part and a high-pass part, the low-pass part and / or the high-pass part is fused with a resonator; the first port is a signal input port, the second port is a signal output port, one port of the low-pass part and one port of the high-pass part are connected with the first port, the other port of the low-pass part is connected with the second port, the other port of the high-pass part is connected with a resistor, and the other end of the resistor is grounded; when working in a passband, the low-pass part signal is conducted, the high-pass part signal is not conducted, the signal is input from the first port, and all the signal is transmitted to the second port by the low-pass part; when working in a stopband, the low-pass part signal is not conducted, the high-pass part signal is conducted, the signal is input from the first port, when the signal is transmitted to the low-pass part, all the signal is reflected back, the reflected wave is transmitted to the resistor through the high-pass part, and all the reflected wave is absorbed by the resistor. The application can realize good non-reflection function.

Description

Technical Field

[0001] This invention relates to the field of radio frequency microwave circuit technology, and in particular to a non-reflective lumped parameter filter. Background Technology

[0002] With the development of radio frequency (RF) circuit technology, RF circuit systems have become increasingly complex due to the cascading of various passive and active devices. The mutual influence between these cascaded devices can cause the overall system performance to deviate from the designed performance. Filters are a widely used RF device in RF circuit systems. A typical ideal reflective filter transmits energy from the input to the output port within the passband, with no energy reflected back from the input. Within the stopband, energy is not transmitted within the passband; all energy is reflected back to the input port as a reflected wave. In RF systems, the energy reflected by the filter inevitably affects the preceding devices and sources, leading to a deviation in the overall circuit system performance. A non-reflective filter (also called an absorptive filter) is a filter that eliminates the energy of reflected waves from the input across the entire frequency band. By utilizing a specific circuit structure, the energy of the reflected wave is absorbed within the filter, preventing it from being transmitted to the input port and thus affecting the preceding stages. Furthermore, compared to traditional reflective filters, non-reflective filters offer advantages such as enhanced out-of-band rejection, harmonic elimination, and improved overall system linearity and efficiency. However, the performance of existing non-reflective filters still needs further improvement, and their size also needs further optimization to achieve a smaller structure. Summary of the Invention

[0003] The purpose of this invention is to address the technical deficiencies in the existing technology by providing a novel non-reflective lumped parameter filter that can effectively absorb reflected wave energy, provide a transmission zero in the stopband, extend the stopband, and improve the out-of-band rejection performance of the filter. By using a lumped parameter circuit, the size of the circuit can be made very small in the low-frequency band.

[0004] The technical solution adopted to achieve the purpose of this invention is:

[0005] A reflection-free lumped parameter filter includes a first port, a second port, a low-pass section, and a high-pass section, wherein the low-pass section and / or the high-pass section are integrated with a resonator; the first port is a signal input port, the second port is a signal output port, one port of the low-pass section and one port of the high-pass section are connected to the first port, the other port of the low-pass section is connected to the second port, and the other port of the high-pass section is connected to a resistor, the other end of which is grounded;

[0006] When operating in the passband, the low-pass signal is on, and the high-pass signal is off. The signal is input from the first port and transmitted entirely to the second port via the low-pass section. When operating in the stopband, the low-pass signal is off, and the high-pass signal is on. The signal is input from the first port, and when it is transmitted to the low-pass section, it is completely reflected back. The reflected wave is transmitted through the high-pass section to the resistor and is completely absorbed by the resistor.

[0007] The filter in the low-pass section is a low-pass filter, and the filter in the high-pass section is a high-pass filter.

[0008] The low-pass and high-pass components may use the same or different types of filters.

[0009] The low-pass and high-pass components may use filters of different or the same order.

[0010] Preferably, the resistor is a resistor that matches the high-pass circuitry.

[0011] As a preferred solution, the even-order 2n-order non-reflective filter consists of 3n inductors and 3n capacitors. The low-pass section integrates n low-pass resonators, which can provide n zeros, and the high-pass section integrates n low-pass resonators.

[0012] Multiple series-connected inductors L forming the low-pass section are each connected to a capacitor C at the output terminal. dd One end is connected to capacitor C dd The other end is connected to the inductor L, which acts as a low-pass resonator. dd One end is connected to the inductor L dd The other end is grounded; or multiple series-connected inductors L forming a low-pass section are each connected to a capacitor C at the output terminal. dd One end is connected to capacitor C dd One end is directly connected to ground;

[0013] The multiple capacitors C connected in series to form the high-pass filter are each connected to an inductor L at the output terminal. gg One end is connected to the inductor L gg The other end is connected to capacitor C, which forms a high-pass resonator. gg One end is connected to capacitor C gg The other end is grounded, or multiple capacitors C connected in series to form a high-pass section are each connected to an inductor L at the output. gg One end is connected to the inductor L gg One end is directly connected to the other.

[0014] As a preferred solution, the odd-order 2n+1 order non-reflective filter consists of 3n+1 inductors and 3n+1 capacitors. The low-pass section integrates n low-pass resonators, which can provide n zeros, and the high-pass section integrates n low-pass resonators.

[0015] Multiple series-connected inductors L forming the low-pass section are each connected to a capacitor C at the output terminal. dd One end is connected to capacitor C dd The other end is connected to the inductor L, which acts as a low-pass resonator. dd One end is connected to the inductor L dd The other end is grounded; or multiple series-connected inductors L forming a low-pass section are each connected to a capacitor C at the output terminal. dd One end is connected to capacitor C dd One end is directly connected to ground;

[0016] The multiple capacitors C connected in series to form the high-pass filter are each connected to an inductor L at the output terminal. gg One end is connected to the inductor L gg The other end is connected to capacitor C, which forms a high-pass resonator. gg One end is connected to capacitor C gg The other end is grounded, or multiple capacitors C connected in series to form a high-pass section are each connected to an inductor L at the output. gg One end is connected to the inductor L gg One end is directly connected to the other.

[0017] As a preferred embodiment, the low-pass section includes a third-order Gaussian low-pass filter with a resonant structure and a third-order Chebyshev low-pass filter with a resonant structure, the Gaussian low-pass filter and the Chebyshev low-pass filter being connected by a 50Ω transmission line, and the high-pass section includes a seventh-order high-pass filter without a resonator structure.

[0018] The non-reflective lumped parameter filter proposed in this invention can achieve good non-reflective function, fully absorb reflected waves to avoid affecting the preceding circuit, effectively suppress stopband harmonics, improve stopband suppression effect, and widen the stopband.

[0019] Because of the use of lumped parameter circuits, the size of the implemented circuit can be effectively reduced; the filtering performance, anti-reflection performance and cutoff frequency of the circuit can be adjusted by adjusting the size of the lumped parameter capacitors and inductors of the topology, which has the advantage of design flexibility. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of a reflectionless lumped parameter filter according to an embodiment of the present invention.

[0021] Figures 2-4 The circuit schematics of the third type of reflectionless lumped parameter filter according to the embodiments of the present invention are shown below. Figure 2 For an even-numbered 2n-order circuit, Figure 3 For an odd number of 2n+1 order circuits, Figure 4 It includes circuits from first to seventh order.

[0022] Figures 5-7 They are simulations Figures 2-4 The parameters of the reflectionless lumped-parameter low-pass filter, where, Figure 5 Scattering parameters in the range of 0-2 GHz; Figure 6 Scattering parameters in the range of 0-20 GHz; Figure 6 The passband group delay is 0-0.6GHz. Figures 8-10 The circuit schematic diagram of the second type of reflectionless lumped parameter filter according to an embodiment of the present invention, wherein, Figure 8 For an even-numbered 2n-order circuit, Figure 9 For an odd number of 2n+1 order circuits, Figure 10 It includes circuits from first to seventh order.

[0023] Figures 11-13 The circuit schematic diagram of the third type of reflectionless lumped parameter filter according to an embodiment of the present invention, wherein, Figure 11 For an even-numbered 2n-order circuit, Figure 12 For an odd number of 2n+1 order circuits, Figure 13 It includes circuits from first to seventh order.

[0024] Figure 14 This is a schematic diagram of a fourth type of reflectionless lumped parameter filter circuit according to an embodiment of the present invention. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0026] See Figure 1 As shown, the reflection-free lumped parameter filter of this embodiment has two ports, Port1 and Port2, where Port1 is the signal input port and Port2 is the signal output port. The overall circuit is divided into two parts: the upper part is a low-pass section and the lower part is a high-pass section. One port of the low-pass section and one port of the high-pass section are simultaneously connected to Port1, the other port of the low-pass section is connected to Port2, and the other port of the high-pass section is connected to a 50-ohm resistor. Both the low-pass and high-pass sections incorporate resonators within their own structures to improve filtering and reflection-free performance.

[0027] When the filter operates in the passband, the signal is input from Port1. At this time, the low-pass section is conducting, while the high-pass section is not. Therefore, when the signal is transmitted from Port1 to Port2, all the energy is transmitted from the low-pass section to Port2. When the filter operates in the stopband, the signal is input from Port1. At this time, the low-pass section is not conducting, while the high-pass section is conducting. Therefore, when the signal is transmitted from Port1 to the low-pass section, all the energy is reflected back. The reflected wave is transmitted through the high-pass section and is completely absorbed by the resistor. From the input port, the entire circuit exhibits the characteristic of no reflection.

[0028] In addition, the reflectionless lumped parameter filter of this invention improves the low-pass and high-pass sections by adding a resonator structure to the low-pass and high-pass filters and adding zeros in the stopband range, which greatly enhances the filter's stopband suppression capability, filtering effect, and reflectionless performance.

[0029] For the low-pass and high-pass sections of a non-reflective filter, the filters used can be of the Gaussian, Butterworth, or Chebyshev type, and their corresponding high-pass filters. The low-pass and high-pass sections can use the same type of filter or different types of filters, depending on the requirements. The order of the filters used in the high-pass and low-pass sections can be the same or different, and can be adjusted according to the non-reflective and filtering performance of the filter to be designed.

[0030] The reflectionless filter proposed in this invention can achieve low-pass, high-pass, band-pass, or band-stop functions through circuit modification. To achieve a low-pass function, it can be configured as follows: Figure 1 The schematic diagram shown is for implementation; to implement the high-pass function, you can... Figure 1 The low-pass filter corresponding to the low-pass portion is transformed into the corresponding high-pass filter, and the high-pass filter corresponding to the high-pass portion is transformed into the corresponding low-pass filter; if bandpass functionality is to be implemented, it can be... Figure 1 The low-pass portion is transformed into a band-pass filter, and the high-pass portion is transformed into a band-stop filter; to achieve band-stop functionality, the following can be used: Figure 1 The low-pass portion is transformed into a band-stop filter, and the high-pass portion is transformed into a band-pass filter.

[0031] The reflection-free filter proposed in this invention can be implemented as a lumped parameter circuit on platforms such as microstrip, coplanar waveguide, suspension line, stripline, and dielectric integrated suspension line. Alternatively, the lumped parameter circuit can be equivalent to a corresponding distributed circuit.

[0032] The non-reflective filter proposed in this invention has a circuit structure that can be extended step by step according to the order. Generally speaking, the higher the order, the stronger the non-reflective performance of the filter and the better the filtering effect. Figure 2 and Figure 3 The circuit topologies of even-order (2n) and odd-order (2n+1)-order non-reflective filters are presented. Figure 4 The circuit topologies of filters from first to seventh order are given.

[0033] The 2n-order filter consists of 3n inductors and 3n capacitors. The low-pass section contains n resonators, providing n zeros, and the high-pass section contains n resonators. The 2n+1-order filter consists of 3n+1 inductors and 3n+1 capacitors. The low-pass section contains n resonators, providing n zeros, and the high-pass section also contains n resonators.

[0034] As a special case of commonly used circuits, the number of capacitors, inductors, and resonators in first- to seventh-order filters can be derived from the above general formula.

[0035] The reflection-free filter proposed in this invention can have its filtering performance, reflection-free performance, and cutoff frequency adjusted by regulating the corresponding capacitors and inductors. Figure 2 For example, adjusting the inductor and capacitor of the low-pass section can adjust the overall filter's filtering performance, anti-reflection performance, and cutoff frequency. Adjusting the resonator connected to the low-pass section can adjust the position of the zero point of the overall circuit to adjust the filtering performance. Adjusting the inductor and capacitor of the high-pass section can adjust the filter's anti-reflection performance and cutoff frequency. Adjusting the resonator connected to the high-pass section can adjust the high-pass section's ability to absorb reflected waves, thereby adjusting the overall circuit's anti-reflection performance.

[0036] Taking a seventh-order non-reflective low-pass filter as an example, a Gaussian low-pass filter is used as the low-pass filter, and a Gaussian high-pass filter is used as the high-pass filter. The capacitance and inductance at the end of the Gaussian high-pass filter are adjusted due to their excessively large values. The proposed topology is as follows: Figure 4 The seventh-order circuit is shown in the figure.

[0037] In this embodiment, 10 inductors and 10 capacitors are included, where L1 = 12.22nH, C2 = 2.38pF, L3 = 4.69nH, C4 = 1.51pF, L5 = 2.83nH, C6 = 0.70pF, L7 = 0.60nH, C1 = 3.95pF, L2 = 20.24nH, C3 = 10.30pF, L4 = 31.87nH, C5 = 17.05pF, L6 = 25nH, C7 = 25pF, L... 02 =13.258nH,L 04=16.15nH,L 06 =26.052nH,C 02 =3.676pF,C 04 =11.065pF,C 06 =25pF.

[0038] The designed non-reflective filter is a low-pass filter with a cutoff frequency of 0.6 GHz and transmission zeros designed at 0.9 GHz, 1.02 GHz and 1.18 GHz.

[0039] The scattering parameters and group delay results of the simulated reflectionless filter are as follows: Figures 5-7 As shown.

[0040] The simulated filter has a cutoff frequency of 0.6 GHz. The full-band return loss is better than 30 dB, the passband insertion loss is less than 0.029 dB, the stopband attenuation is greater than 20 dB in frequencies above 0.88 GHz, and the passband group delay is less than 1.07 ns.

[0041] To illustrate the effect of this topology on other types of filters, no specific type of low-pass filter is specified; only adjustments are made. Figure 4 The values ​​of the capacitors and inductors in the seventh-order circuit were adjusted and optimized to obtain another set of values ​​that meet the requirements of non-reflective performance and low-pass filter performance. Specifically, L1 = 8.1988nH, C2 = 2.9835pF, L3 = 7.5124nH, C4 = 1.8587pF, L5 = 2.4630nH, C6 = 0.8382pF, L7 = 0.4051nH, C1 = 2.4948pF, L2 = 8.5176nH, C3 = 3.0459pF, L4 = 12.9307nH, C5 = 17.3825pF, L6 = 20.6730nH, C7 = 18.1206pF, L... 02 =3.4414nH,L 04 =3.0309nH,L 06 =3.8606nH,C 02 =3.2748pF,C 04 =7.6232pF,C 06 =6.2167pF.

[0042] The designed non-reflective filter is a low-pass filter with a cutoff frequency of 1 GHz and transmission zeros designed at 1.57 GHz, 2.12 GHz and 2.8 GHz.

[0043] The simulated filter has a cutoff frequency of 1 GHz. The full-band return loss is better than 80 dB, the passband insertion loss is less than 0.032 dB, the stopband attenuation is greater than 20 dB in frequencies above 1.4 GHz, and the passband group delay is less than 0.9356 ns.

[0044] To illustrate the feasibility of other types of reflectionless low-pass filters, Figures 8-10 A second type of reflectionless lumped-parameter filter circuit is proposed. This topology also includes a low-pass section and a high-pass section. The low-pass section consists of a low-pass filter with a resonant structure, while the high-pass section consists of a conventional high-pass filter. The proposed reflectionless filter circuit structure can be extended sequentially with increasing order. Generally, the higher the order, the stronger the reflectionless performance of the filter and the better the filtering effect.

[0045] Figure 8 and Figure 9 The circuit topologies of even-order (2n) and odd-order (2n+1) reflectionless filters are presented. Figure 10 The circuit topologies of filters from first to seventh order are given.

[0046] The 2n-order filter consists of 3n inductors and 2n capacitors, and its low-pass section contains n resonators, providing n zeros; the 2n+1-order filter consists of 3n+1 inductors and 2n+1 capacitors, and its low-pass section contains n resonators, providing n zeros.

[0047] As a special case of commonly used circuits, the number of capacitors, inductors, and resonators for first- to seventh-order filters can be derived from the above general formulas. This circuit eliminates the resonators in the high-pass section, uses fewer capacitors, and has a smaller group delay in the passband, but sacrifices some filtering and anti-reflection performance.

[0048] Figures 11-13 A third type of reflectionless lumped-parameter filter circuit is proposed. This topology also includes low-pass and high-pass sections. The low-pass section is composed of a conventional low-pass filter, and the high-pass section is composed of a high-pass filter with a resonant structure. The proposed reflectionless filter circuit structure can be extended sequentially with increasing order. Generally, the higher the order, the stronger the reflectionless performance of the filter and the better the filtering effect.

[0049] Figure 11 and Figure 12 The circuit topologies of even-order (2n) and odd-order (2n+1)-order non-reflective filters are presented. Figure 13 The circuit topologies of filters from first to seventh order are given.

[0050] The 2n-order filter consists of 2n inductors and 3n capacitors, with the high-pass section containing n resonators; the 2n+1-order filter consists of 2n+1 inductors and 3n+1 capacitors, with the high-pass section containing n resonators.

[0051] As a special case of commonly used circuits, the number of capacitors, inductors, and resonators for first- to seventh-order filters can be derived from the above general formulas. This circuit eliminates the resonator in the low-pass section, uses fewer inductors, and has a smaller group delay across the entire frequency band, but sacrifices some filtering and anti-reflection performance.

[0052] Figure 14 A fourth type of reflection-free lumped-parameter filter circuit is proposed. This topology also includes a low-pass section and a high-pass section. The low-pass section consists of two low-pass filters with resonant structures, connected by a 50Ω transmission line of a certain electrical length. The first low-pass filter smooths the amplitude and phase of the overall filter, making it easier for the reflected waves from the low-pass section to be absorbed by the high-pass section. The second filter can be a filter with better selectivity, as its amplitude and phase generally change drastically with frequency, requiring the first filter to smooth them. The 50Ω transmission line balances the phase of the two connected filters. The high-pass section consists of a regular high-pass filter, or a high-pass filter with added resonators, primarily used to absorb reflected waves.

[0053] Figure 14 The proposed fourth type of reflectionless filter circuit structure can be extended step by step according to the order. Generally speaking, the higher the order, the stronger the reflectionless performance of the filter and the better the filtering effect. Figure 14 The paper presents a circuit example of such a reflectionless filter. The low-pass section includes a third-order Gaussian low-pass filter with a resonant structure and a third-order Chebyshev low-pass filter with a resonant structure, connected by a 50Ω transmission line (TL1). The high-pass section includes a seventh-order high-pass filter without a resonator. This circuit combines the characteristics of both filters by connecting them together in the low-pass section, resulting in a smaller group delay in the passband and a certain degree of improved selectivity, but at the cost of some reflectionless performance.

[0054] Distributed circuits and lumped parameter circuits are two commonly used types of RF circuits in RF device design. Distributed circuits are mainly composed of transmission lines, while lumped parameter circuits are mainly composed of discrete capacitors, inductors, and other components. Compared to distributed circuits, the capacitors, inductors, and other components in lumped parameter circuits are smaller and can be flexibly arranged. Therefore, lumped parameter circuits have the advantage of miniaturization in low-frequency bands. The embodiments of this invention use lumped parameter circuits, which make it easy to make the circuit size very small in the low-frequency band.

[0055] The reflection-free lumped parameter filter of this invention achieves excellent reflection-free performance in both the passband and stopband, effectively suppressing reflected waves across the entire frequency band, while also exhibiting good harmonic suppression and a significantly widened stopband. As a lumped parameter circuit, its size can be easily minimized in the low-frequency band.

[0056] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention.

[0057] Therefore, the embodiments should be regarded as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of the equivalents of the claims be included within the invention.

[0058] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A reflectionless lumped parameter filter, characterized in that, It includes a first port, a second port, a low-pass section, and a high-pass section, wherein the low-pass section and / or the high-pass section are integrated with a resonator; the first port is a signal input port, the second port is a signal output port, one port of the low-pass section and one port of the high-pass section are connected to the first port, the other port of the low-pass section is connected to the second port, and the other port of the high-pass section is connected to a resistor, the other end of which is grounded; When operating in passband, the low-pass signal is on and the high-pass signal is off. The signal is input from the first port and transmitted entirely to the second port by the low-pass section. When operating in the stopband, the low-pass section signal is not connected, and the high-pass section signal is connected. The signal is input from the first port. When the signal is transmitted to the low-pass section, it is completely reflected back. The reflected wave is transmitted through the high-pass section to the resistor and is completely absorbed by the resistor. The low-pass section includes a third-order Gaussian low-pass filter with a resonant structure and a third-order Chebyshev low-pass filter with a resonant structure, the Gaussian low-pass filter and the Chebyshev low-pass filter being connected by a 50Ω transmission line, and the high-pass section includes a seventh-order high-pass filter without a resonator structure.

2. The reflectionless lumped parameter filter according to claim 1, characterized in that, The low-pass and high-pass sections employ low-pass prototype filters, including Gaussian, Butterworth, and Chebyshev.

3. The reflectionless lumped parameter filter according to claim 2, characterized in that, The low-pass section and the high-pass section may use the same or different types of low-pass prototype filters.

4. The reflectionless lumped parameter filter according to claim 2, characterized in that, The low-pass section and the high-pass section use low-pass prototype filters of different or the same order.

5. The reflectionless lumped parameter filter according to claim 1, characterized in that, The resistor is a 50-ohm resistor.

6. The reflectionless lumped parameter filter according to claim 1, characterized in that, An even-order 2n-order non-reflective filter consists of 3n inductors and 3n capacitors. The low-pass section integrates n low-pass resonators, providing n zeros, while the high-pass section integrates n low-pass resonators. Multiple inductors connected in series to form the low-pass section L Each has a capacitor at the output terminal. C dd One end is connected to capacitor C dd The other end is connected to the inductor, which acts as a low-pass resonator. L dd One end is connected to the inductor. dd The other end is grounded; or multiple inductors connected in series to form a low-pass section. L Each has a capacitor at the output terminal. C dd One end is connected to the capacitor. C dd One end is directly connected to ground; Multiple capacitors connected in series to form the high-pass section C Each has an inductor at its output. L gg One end is connected to the inductor. L gg The other end is connected to the capacitor that forms a high-pass resonator. C gg One end is connected to the capacitor. C gg The other end is grounded, or it is one of multiple capacitors connected in series to form the high-pass section. C Each has an inductor at its output. L gg One end is connected to the inductor. L gg One end is directly connected to the other.

7. The reflectionless lumped parameter filter according to claim 1, characterized in that, An odd-order 2n+1 order non-reflective filter consists of 3n+1 inductors and 3n+1 capacitors. The low-pass section integrates n low-pass resonators, which can provide n zeros. The high-pass section integrates n low-pass resonators. Multiple inductors connected in series to form the low-pass section L Each has a capacitor at the output terminal. C dd One end is connected to capacitor C dd The other end is connected to the inductor, which acts as a low-pass resonator. L dd One end is connected to the inductor. L dd The other end is grounded; or multiple inductors connected in series to form a low-pass section. L Each has a capacitor at the output terminal. C dd One end is connected to the capacitor. C dd One end is directly connected to ground; Multiple capacitors connected in series to form the high-pass section C Each has an inductor at its output. L gg One end is connected to the inductor. L gg The other end is connected to the capacitor that forms a high-pass resonator. C gg One end is connected to the capacitor. C gg The other end is grounded, or it is one of multiple capacitors connected in series to form the high-pass section. C Each has an inductor at its output. L gg One end is connected to the inductor. L gg One end is directly connected to the other.

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