Ku, K and Ka frequency band active phased antenna dual-beam synthesizer
By combining microstrip lines and striplines in an interlayer transition structure and using isolation resistor design, the shortcomings of existing active phased array antenna synthesizers in terms of cost, process, and performance are solved, achieving highly integrated and highly isolated Ku, K, and Ka band active phased array antenna dual-beam synthesizers with efficient signal distribution and synthesis.
Patent Information
- Application Number
- CN202511015841.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-23
- Publication Date
- 2025-10-28
AI Technical Summary
Existing active phased array antenna synthesizers suffer from high cost, complex manufacturing processes, low performance, and limited application scope when implementing dual-beam combining, making it difficult to meet the requirements of high integration and high isolation.
A structure combining microstrip lines and striplines is adopted. Signal distribution and synthesis are achieved through interlayer transition structures and isolation resistors, forming a dual-beam synthesizer for active phased antennas in the Ku, K, and Ka bands. Low-temperature co-fired ceramic K05 is used as the dielectric layer. Combined with ohmic characteristic impedance calculation, efficient signal distribution and synthesis are achieved.
It achieves dual-beam synthesis of active phased array antennas with robust structure, high processing precision, and low batch cost, and has high consistency and good signal distribution capability.
Smart Images
Figure CN120854878A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of phased antenna technology, and specifically to a dual-beam synthesizer for an active phased antenna in the Ku, K, and Ka bands. Background Technology
[0002] In the field of phased antennas, active phased antennas are the most common type of antenna. Microwave signals only need to be amplified, phased, and amplitude controlled by transceiver components, while radio frequency signals need to be synthesized through a feed network.
[0003] There are three main ways to implement existing active phased array antenna synthesizers:
[0004] Method 1 involves connecting the PCB microstrip line to the gallium arsenide bare chip of the combiner, and then completing the interconnection through micro-assembly gold wire bonding process;
[0005] Method 2 involves connecting PCB microstrip lines with surface mount resistors using PCB surface mount technology (SMT).
[0006] Method 3: Interconnection is achieved through a combination of PCB striplines and embedded resistors using a multilayer PCB lamination process.
[0007] All of the above methods have drawbacks. The main drawbacks of method one are high cost and complex process. The process of bonding gallium arsenide bare chips with gold wire for micro-assembly is costly. The bonding of gallium arsenide bare chips with gold wire requires hermetically sealed packaging, which is not suitable for cost-sensitive products. The main drawback of method two is low performance. The surface mount resistor (SMT) introduces large errors and has high circuit losses. The main drawbacks of method three are high cost and narrow application scope. Due to material limitations, the range of applicable PCB substrates for embedded resistor materials is narrow. Most of the relevant materials are imported, and the range of PCB boards that can be adapted to the corresponding embedded resistor material manufacturers is limited. This method is not suitable for products that require domestic production or are cost-sensitive. The above three methods are difficult to achieve the high integration and high isolation requirements of dual-beam active phased array antennas. Therefore, a dual-beam synthesizer for Ku, K, and Ka band active phased array antennas is proposed. Summary of the Invention
[0008] To address the technical problems existing in the prior art, the present invention provides a dual-beam synthesizer for Ku, K, and Ka band active phased antennas.
[0009] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a dual-beam synthesizer for an active phased array antenna in the Ku, K, and Ka bands, comprising a synthesizer body, a first beam combining module, and a second beam combining module, wherein the first beam combining module and the second beam combining module are respectively disposed on both sides of the synthesizer body;
[0010] Both the first and second beamforming modules are used for signal synthesis.
[0011] Preferably, the first beamforming module includes a microstrip line 1, an interlayer transition structure 1, a matching stripline 1, an isolation resistor 1, a matching stripline 2, an isolation resistor 2, a stripline 1, an interlayer transition structure 2, and a microstrip line 2.
[0012] The first microstrip line is used as the input of the active phased antenna feed network signal. A set of interlayer transition structures is connected to the second microstrip line, a set of matching striplines is connected to the first interlayer transition structure, and a set of isolation resistors is connected to the first matching stripline. The active phased antenna feed network signal entering through the first microstrip line enters the first isolation resistor through the first interlayer transition structure and the first matching stripline.
[0013] The two sets of matching striplines are respectively connected to the two input and output terminals of the isolation resistor. Each input and output terminal of the matching stripline is connected to a set of isolation resistors. The two sets of striplines are respectively connected to the two input and output terminals of the isolation resistor. Each input and output terminal of the stripline is connected to a set of interlayer transition structures. Each input and output terminal of the interlayer transition structure is connected to a set of microstrip lines.
[0014] Preferably, the second beamforming module includes a microstrip line three, an interlayer transition structure three, a matching stripline three, an isolation resistor three, a matching stripline four, an isolation resistor four, a stripline two, an interlayer transition structure four, and a microstrip line four;
[0015] The microstrip line three is used for the input of the active phased antenna feed network signal. A set of interlayer transition structures three is connected to the microstrip line three, a set of matching striplines three is connected to the interlayer transition structure three, and a set of isolation resistors three is connected to the matching striplines three. The active phased antenna feed network signal entering through the microstrip line three enters the isolation resistor three through the interlayer transition structure three and the matching striplines three.
[0016] The two sets of matching striplines four are respectively connected to the two input and output terminals of the isolation resistor three. Each input and output terminal of the matching stripline four is connected to a set of isolation resistor four. The two sets of striplines two are respectively connected to the two input and output terminals of the isolation resistor four. Each input and output terminal of the stripline two is connected to a set of interlayer transition structure four. Each input and output terminal of the interlayer transition structure four is connected to a set of microstrip lines four.
[0017] Preferably, the synthesizer body is composed of stacked dielectric layers and circuit layers. From top to bottom, the circuit layers are located in the first, fifth, ninth, thirteenth, seventeenth and twentieth layers of the synthesizer body, respectively. The first, ninth and seventeenth layers are shielding ground layer circuits, the fifth and thirteenth layers are stripline circuit layers, and the twentieth layer is a shared layer for microstrip line circuit layers and shielding ground layer circuits.
[0018] Preferably, the dielectric layer is made of low-temperature co-fired ceramic K05, the dielectric constant of the dielectric layer is 5.2, and the thickness of a single dielectric layer after sintering is 0.096 mm.
[0019] Preferably, the microstrip line 1 of the twentieth layer in the first beamforming module is connected to the stripline 1 of the fifth layer by the interlayer transition structure 1, and the microstrip line 2 of the twentieth layer in the first beamforming module is connected to the stripline 1 of the fifth layer by the interlayer transition structure 2.
[0020] Preferably, the microstrip line 3 of the twentieth layer in the second beamforming module is connected to the stripline 2 of the thirteenth layer by the interlayer transition structure 3, and the microstrip line 4 of the twentieth layer in the second beamforming module is connected to the stripline 2 of the thirteenth layer by the interlayer transition structure 4.
[0021] Preferably, microstrip line one, microstrip line two, microstrip line three, and microstrip line four all adopt ohmic characteristic impedance, and the characteristic impedance Z0 of microstrip line one, microstrip line two, microstrip line three, and microstrip line four is calculated using the following formula:
[0022] Z0=87 / r+1.41ln5.98H / (0.8W+T)
[0023] Where r is the dielectric constant, H is the dielectric thickness, W is the conductor width, and T is the conductor thickness.
[0024] Preferably, interlayer transition structure one, interlayer transition structure two, interlayer transition structure four all adopt ohmic characteristic resistance, and the characteristic impedance Z of interlayer transition structure one, interlayer transition structure two, interlayer transition structure four is calculated by the following formula:
[0025] Z0 = [60 / √εr] × Ln(b / a)
[0026] Where b is the inner diameter of the outer conductor of the coaxial grounding via, a is the outer diameter of the coaxial signal via, and εr is the relative permittivity of the insulating medium between the conductors.
[0027] Preferably, the impedance of stripline one and stripline two is ohms, and the impedances of matching stripline one, matching stripline two, matching stripline four are transformed from ohmic characteristic impedances. The characteristic impedance Z0 of a stripline structure is calculated using the following formula:
[0028] Z0=[60 / sqrt(Er)]ln{4H / [0.67π(T+0.8W)]}
[0029] Where H is the distance between the two reference planes, W is the line width, T is the copper thickness of the trace, H is the distance from the trace to the reference plane, and Er is the dielectric constant of the dielectric material.
[0030] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0031] 1. When the microwave signal is transmitted, the active phased antenna feed network enters the synthesizer through the microstrip line, enters the stripline through the interlayer transition structure, and the signal is distributed into 4 equal-amplitude and in-phase transmission signals by the signal distribution and synthesis network and output to the stripline. Then, it is output to the microstrip line through the interlayer transition and then interconnected with the feed network of the active phased antenna through the microstrip line.
[0032] When receiving microwave signals, the active phased antenna feed network enters the combiner through the microstrip line, enters the stripline through the interlayer transition structure, and the four equal-amplitude and in-phase received signals are combined into one output to the stripline through the signal distribution and combining network. Then, it is output to the microstrip line through the interlayer transition structure, and then interconnected with the feed network of the active phased antenna through the microstrip line. It has the advantages of robust structure, high processing precision, good consistency and low batch cost. Attached Figure Description
[0033] Figure 1 This is a schematic diagram of the structure of the present invention;
[0034] Figure 2 This is a connection block diagram of the first beamforming module of the present invention;
[0035] Figure 3 This is a connection block diagram of the second beamforming module of the present invention;
[0036] Figure 4 This is a schematic diagram of the hierarchical structure of the present invention;
[0037] Figure 5 This is a schematic diagram of the circuit configuration of the first beamforming module of the present invention;
[0038] Figure 6 This is a schematic diagram of the circuit configuration of the second beamforming module of the present invention;
[0039] Figure 7 The following is a simulation result diagram of the Ku-band synthesizer of the present invention;
[0040] Figure 8 The figure shows the simulation results of the K-band synthesizer of this invention;
[0041] Figure 9 The figure shows the simulation results of the Ka-band synthesizer of the present invention.
[0042] The numbers in the image represent:
[0043] 1. Synthesizer body; 2. First beamforming module; 21. Microstrip line one; 22. Interlayer transition structure one; 23. Matching stripline one; 24. Isolation resistor one; 25. Matching stripline two; 26. Isolation resistor two; 27. Stripline one; 28. Interlayer transition structure two; 29. Microstrip line two; 3. Second beamforming module; 31. Microstrip line three; 32. Interlayer transition structure three; 33. Matching stripline three; 34. Isolation resistor three; 35. Matching stripline four; 36. Isolation resistor four; 37. Stripline two; 38. Interlayer transition structure four; 39. Microstrip line four. Detailed Implementation
[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments, which illustrate the above and other technical features and advantages of the present invention. However, the following embodiments are merely preferred embodiments of the present invention and are not exhaustive.
[0045] Example:
[0046] like Figures 1-9 As shown, the present invention provides a dual-beam synthesizer for an active phased array antenna in the Ku, K, and Ka bands, comprising a synthesizer body 1, a first beam combining module 2, and a second beam combining module 3, wherein the first beam combining module 2 and the second beam combining module 3 are respectively disposed on both sides of the synthesizer body 1.
[0047] The first beamforming module 2 includes a microstrip line 21, an interlayer transition structure 22, a matching stripline 23, an isolation resistor 24, a matching stripline 25, an isolation resistor 26, a stripline 27, an interlayer transition structure 28, and a microstrip line 29.
[0048] The microstrip line 21 is used for the input of the active phased antenna feed network signal. A set of interlayer transition structures 22 is connected to the microstrip line 29. A set of matching striplines 23 is connected to the interlayer transition structure 22. A set of isolation resistors 24 is connected to the matching stripline 23.
[0049] The two sets of matching striplines 25 are respectively connected to the two input and output terminals of the isolation resistor 24. Each input and output terminal of the matching stripline 25 is connected to a set of isolation resistors 26. The two sets of striplines 27 are respectively connected to the two input and output terminals of the isolation resistors 26. Each input and output terminal of the stripline 27 is connected to a set of interlayer transition structures 28. Each input and output terminal of the interlayer transition structures 28 is connected to a set of microstrip lines 29.
[0050] When a microwave signal is transmitted, the active phased antenna feed network signal entering through microstrip line 21 passes through interlayer transition structure 22 and matching stripline 23 and enters isolation resistor 24. Isolation resistor 24 distributes the active phased antenna feed network signal into two equal-amplitude and in-phase transmit signals and outputs them to matching stripline 25. Isolation resistor 26 distributes the signal into four equal-amplitude and in-phase transmit signals and outputs them to stripline 27. Then, through interlayer transition structure 28, the signal is output to microstrip line 29. Finally, through microstrip line 29, the signal is interconnected with the microstrip line of the active phased antenna feed network.
[0051] When receiving microwave signals, the signal enters the synthesizer's microstrip line 29 through the active phased antenna feed network microstrip line, enters the stripline 27 through the interlayer transition structure 28, and is combined into two equal-amplitude and in-phase received signals through the isolation resistor 26 and output to the matching stripline 25 through the isolation resistor 24. The two equal-amplitude and in-phase received signals are combined into one received signal and output to the matching stripline 23 through the interlayer transition structure 22. Then, it is output to the microstrip line 21 through the interlayer transition structure 22, and then interconnected with the microstrip line of the active phased antenna feed network through the output of the microstrip line 21.
[0052] The second beamforming module 3 includes a microstrip line 31, an interlayer transition structure 32, a matching stripline 33, an isolation resistor 34, a matching stripline 45, an isolation resistor 46, a stripline 2 37, an interlayer transition structure 4 38, and a microstrip line 4 39.
[0053] The microstrip line 31 is used for the input of the active phased antenna feed network signal. A set of interlayer transition structures 32 is connected to the microstrip line 31, a set of matching striplines 33 is connected to the interlayer transition structure 32, and a set of isolation resistors 34 is connected to the matching stripline 33. The active phased antenna feed network signal entering through the microstrip line 31 enters the isolation resistor 34 through the interlayer transition structure 32 and the matching stripline 33.
[0054] The two sets of matching striplines 35 are respectively connected to the two input and output terminals of the isolation resistor 34. Each input and output terminal of the matching stripline 35 is connected to a set of isolation resistor 36. The two sets of striplines 37 are respectively connected to the two input and output terminals of the isolation resistor 36. Each input and output terminal of the stripline 37 is connected to a set of interlayer transition structure 38. Each input and output terminal of the interlayer transition structure 38 is connected to a set of microstrip lines 39.
[0055] When a microwave signal is transmitted, the active phased antenna feed network signal entering through microstrip line 31 passes through interlayer transition structure 32 and matching stripline 33 and enters isolation resistor 34. Isolation resistor 34 distributes the active phased antenna feed network signal into two equal-amplitude and in-phase transmit signals and outputs them to matching stripline 45. Isolation resistor 46 distributes the signal into four equal-amplitude and in-phase transmit signals and outputs them to stripline 27. Then, through interlayer transition structure 438, the signal is output to microstrip line 49. Finally, through microstrip line 439, the signal is interconnected with the microstrip line of the active phased antenna feed network.
[0056] When receiving microwave signals, the signal enters the microstrip line 39 of the synthesizer through the microstrip line of the active phased antenna feed network, enters the stripline 37 through the interlayer transition structure 38, and is combined into two equal-amplitude and in-phase received signals through the isolation resistor 36 and output to the matching stripline 35. The two equal-amplitude and in-phase received signals are combined into one received signal through the isolation resistor 34 and output to the matching stripline 33. Then, it is output to the microstrip line 31 through the interlayer transition structure 32, and then interconnected with the microstrip line of the active phased antenna feed network through the output of the microstrip line 31.
[0057] The synthesizer body 1 is composed of 14 dielectric layers and 6 circuit layers stacked together. From top to bottom, the 6 circuit layers are located in the first, fifth, ninth, thirteenth, seventeenth and twentieth layers of the synthesizer body 1, respectively. Among them, the first, ninth and seventeenth layers are shielding ground layer circuits, the fifth and thirteenth layers are stripline circuit layers, and the twentieth layer is used as a shared layer for microstrip line circuit layers and shielding ground layer circuits.
[0058] The dielectric layer is made of low-temperature co-fired ceramic K05, with a dielectric constant of 5.2 and a thickness of 0.096 mm after sintering of a single dielectric layer.
[0059] The microstrip line 21 of the twentieth layer in the first beamforming module 2 is connected to the stripline 27 of the fifth layer by the interlayer transition structure 22, and the microstrip line 29 of the twentieth layer in the first beamforming module 2 is connected to the stripline 27 of the fifth layer by the interlayer transition structure 28.
[0060] The microstrip line 31 of the twentieth layer in the second beamforming module 3 is connected to the stripline 37 of the thirteenth layer by the interlayer transition structure 32, and the microstrip line 49 of the twentieth layer in the second beamforming module 3 is connected to the stripline 37 of the thirteenth layer by the interlayer transition structure 48.
[0061] Microstrip line 1 (21), microstrip line 2 (29), microstrip line 3 (31), and microstrip line 4 (39) all adopt a 50-ohm characteristic impedance. The formula for calculating the characteristic impedance Z0 of microstrip line 1 (21), microstrip line 2 (29), microstrip line 3 (31), and microstrip line 4 (39) is as follows:
[0062] Z0=87 / r+1.41ln5.98H / (0.8W+T)
[0063] Where r is the dielectric constant, H is the dielectric thickness, W is the conductor width, and T is the conductor thickness.
[0064] The interlayer transition structure 1 22, interlayer transition structure 28, interlayer transition structure 32, and interlayer transition structure 4 38 are all designed with a 50-ohm characteristic impedance. The formula for calculating the characteristic impedance Z0 of the interlayer transition structure 1 22, interlayer transition structure 28, interlayer transition structure 32, and interlayer transition structure 4 38 is as follows:
[0065] Z0 = [60 / √εr] × Ln(b / a)
[0066] Where b is the inner diameter of the outer conductor of the coaxial grounding via, a is the outer diameter of the coaxial signal via, and εr is the relative permittivity of the insulating medium between the conductors.
[0067] The impedance of stripline 27 and stripline 37 is 50 ohms. The impedance of matching stripline 23, matching stripline 25, matching stripline 33, and matching stripline 35 is transformed from the characteristic impedance of 50 ohms to... The characteristic impedance Z0 of a stripline structure is calculated using the following formula:
[0068] Z0=[60 / sqrt(Er)]ln{4H / [0.67π(T+0.8W)]}
[0069] Where H is the distance between the two reference planes, W is the line width, T is the copper thickness of the trace, H is the distance from the trace to the reference plane, and Er is the dielectric constant of the dielectric material.
[0070] The above description is merely a preferred embodiment of the present invention and is illustrative rather than restrictive. Those skilled in the art will understand that many changes, modifications, and even equivalents can be made within the spirit and scope defined by the claims of the present invention, all of which will fall within the protection scope of the present invention.
Claims
1. A dual-beam combiner for an active phased array antenna in the Ku, K, and Ka bands, comprising a combiner body, a first beam combining module, and a second beam combining module, characterized in that, The first beamforming module and the second beamforming module are respectively disposed on both sides of the synthesizer body; Both the first and second beamforming modules are used for signal synthesis.
2. The dual-beam combiner for Ku, K, and Ka band active phased array antennas as described in claim 1, characterized in that, The first beamforming module includes a microstrip line 1, an interlayer transition structure 1, a matching stripline 1, an isolation resistor 1, a matching stripline 2, an isolation resistor 2, a stripline 1, an interlayer transition structure 2, and a microstrip line 2. The first microstrip line is used as the input of the active phased antenna feed network signal. A set of interlayer transition structures is connected to the second microstrip line, a set of matching striplines is connected to the first interlayer transition structure, and a set of isolation resistors is connected to the first matching stripline. The active phased antenna feed network signal entering through the first microstrip line enters the first isolation resistor through the first interlayer transition structure and the first matching stripline. The two sets of matching striplines are respectively connected to the two input and output terminals of the isolation resistor. Each input and output terminal of the matching stripline is connected to a set of isolation resistors. The two sets of striplines are respectively connected to the two input and output terminals of the isolation resistor. Each input and output terminal of the stripline is connected to a set of interlayer transition structures. Each input and output terminal of the interlayer transition structure is connected to a set of microstrip lines.
3. The dual-beam combiner for Ku, K, and Ka band active phased array antennas as described in claim 1, characterized in that, The second beamforming module includes microstrip line three, interlayer transition structure three, matching stripline three, isolation resistor three, matching stripline four, isolation resistor four, stripline two, interlayer transition structure four, and microstrip line four; The microstrip line three is used for the input of the active phased antenna feed network signal. A set of interlayer transition structures three is connected to the microstrip line three, a set of matching striplines three is connected to the interlayer transition structure three, and a set of isolation resistors three is connected to the matching striplines three. The active phased antenna feed network signal entering through the microstrip line three enters the isolation resistor three through the interlayer transition structure three and the matching striplines three. The two sets of matching striplines four are respectively connected to the two input and output terminals of the isolation resistor three. Each input and output terminal of the matching stripline four is connected to a set of isolation resistor four. The two sets of striplines two are respectively connected to the two input and output terminals of the isolation resistor four. Each input and output terminal of the stripline two is connected to a set of interlayer transition structure four. Each input and output terminal of the interlayer transition structure four is connected to a set of microstrip lines four.
4. The dual-beam combiner for Ku, K, and Ka band active phased array antennas as described in claim 1, characterized in that, The synthesizer body 1 is composed of 14 dielectric layers and 6 circuit layers stacked together. From top to bottom, the 6 circuit layers are located in the first, fifth, ninth, thirteenth, seventeenth and twentieth layers of the synthesizer body 1, respectively. Among them, the first, ninth and seventeenth layers are shielding ground layer circuits, the fifth and thirteenth layers are stripline circuit layers, and the twentieth layer is used as a shared layer for microstrip line circuit layers and shielding ground layer circuits.
5. A dual-beam combiner for an active phased array antenna in the Ku, K, and Ka bands as described in claim 1, characterized in that, The dielectric layer is made of low-temperature co-fired ceramic K05, with a dielectric constant of 5.2 and a thickness of 0.096 mm after sintering of a single dielectric layer.
6. The dual-beam combiner for Ku, K, and Ka band active phased array antennas as described in claim 1, characterized in that, The microstrip line 1 of the twentieth layer in the first beamforming module is connected to the stripline 1 of the fifth layer by the interlayer transition structure 1, and the microstrip line 2 of the twentieth layer in the first beamforming module is connected to the stripline 1 of the fifth layer by the interlayer transition structure 2.
7. A dual-beam combiner for an active phased array antenna in the Ku, K, and Ka bands as described in claim 1, characterized in that, The microstrip line 3 of the twentieth layer in the second beamforming module is connected to the stripline 2 of the thirteenth layer by the interlayer transition structure 3, and the microstrip line 4 of the twentieth layer in the second beamforming module is connected to the stripline 2 of the thirteenth layer by the interlayer transition structure 4.
8. A dual-beam combiner for an active phased array antenna in the Ku, K, and Ka bands as described in claim 1, characterized in that, Microstrip line 1, microstrip line 2, microstrip line 3, and microstrip line 4 all adopt ohmic characteristic impedance. The formula for calculating the characteristic impedance Z0 of microstrip line 1, microstrip line 2, microstrip line 3, and microstrip line 4 is as follows: Z0=87 / r+1.41ln5.98H / (0.8W+T) Where r is the dielectric constant, H is the dielectric thickness, W is the conductor width, and T is the conductor thickness.
9. A dual-beam combiner for an active phased array antenna in the Ku, K, and Ka bands as described in claim 1, characterized in that, Interlayer transition structure one, interlayer transition structure two, interlayer transition structure four are all designed with ohmic characteristic resistors. The formula for calculating the characteristic impedance Z0 of interlayer transition structure one, interlayer transition structure two, interlayer transition structure four is as follows: Where b is the inner diameter of the outer conductor of the coaxial grounding via, a is the outer diameter of the coaxial signal via, and εr is the relative permittivity of the insulating medium between the conductors.
10. A dual-beam combiner for an active phased array antenna in the Ku, K, and Ka bands as described in claim 1, characterized in that, The impedance of stripline one and stripline two is ohms, and the impedance of matching stripline one, matching stripline two, and matching stripline four is transformed from a 50-ohm characteristic impedance to... The characteristic impedance Z0 of a stripline structure is calculated using the following formula: Z0=[60 / sqrt(Er)]ln{4H / [0.67π(T+0.8W)]} Where H is the distance between the two reference planes, W is the line width, T is the copper thickness of the trace, H is the distance from the trace to the reference plane, and Er is the dielectric constant of the dielectric material.