Thermal Frequency Drift of 3D Printed Microwave Components

: Fabrication of microwave slot array antennas and waveguide bandpass and notch ﬁlters using 3D printing has signiﬁcant advantages in terms of speed and cost even for parts with high mechanical complexity. One disadvantage of Stereolithography (SLA) 3D printed, copper plated microwave components is that some SLA resins have a high Coe ﬃ cient of Thermal Expansion (CTE), quoted in micrometers per meter per degree or 10 − 6 per degree. Compared to typically used metals such as aluminum (CTE 24 × 10 − 6 · K − 1 ) and copper (CTE 17 × 10 − 6 · K − 1 ), SLA resin can have CTE above 100 × 10 − 6 · K − 1 . Resonant structures experience signiﬁcant frequency drift with temperature changes on the order of 10–50 ◦ C. The issue of 3D printed microwave structures changing frequency characteristics signiﬁcantly with temperature shift has not been addressed or reviewed in current literature. We measured and simulated the e ﬀ ect of temperature change on a slot array, cavity notch ﬁlters, and post loaded waveguide bandpass ﬁlters. We tested several types of SLA resin, di ﬀ erent plating techniques, and also Direct Metal Laser Sintering (DMLS) and Binder Infusion metal 3D printing. Performance as a function of temperature is presented for these alternatives.


Introduction
Microwave slot array antennas and bandpass and notch filters can be produced quickly and inexpensively using 3D printing [1][2][3]. The high CTE of SLA resins causes frequency drift with temperature to be notably worse than solid metal structures [4]. Somos Taurus SLA resin [5] has CTE of 105.3 × 10 −6 ·K −1 over the temperature range 0-50 • C. Choosing lower CTE resin, strengthening metal coatings using multiple layers of nickel and copper, and switching to 3D metal printing with DMLS or binder infusion improves frequency dependence on temperature. In this paper, the frequency dependence with temperature is presented for multiple SLA resins, multiple metal coatings, and 3D metal printed structures. Theoretical fits to expected temperature variation are presented to confirm the predictability of performance. Armed with these predictions and results, requirements for temperature stability can be applied to make decisions regarding the materials and processes to use for 3D printed fabrication of microwave devices.
It is possible to achieve metal CTE characteristics with 3D printing using DMLS. The AlSi10Mg alloy used for DMLS 3D printing has a CTE of 20.5 × 10 −6 ·K −1 [20] and σ = 11.3 × 10 6 S/m [21], which is better CTE than pure aluminum. There are a range of CTE values from 53 × 10 −6 ·K −1 to 145 × 10 −6 ·K −1 available for a desktop SLA 3D printer [22]. Electroplating can also use layers of copper and nickel to strengthen the metal coating and resist the expansion of plastic. Relatively broad band structures such as slot arrays and bandpass filters are not as badly affected by frequency drift as narrow band notch filters.

Materials and Methods
We measured the effect of temperature change on a slot array, cavity notch filters with single and multiple cavities, and post loaded waveguide bandpass filters. We tested several types of SLA resin, different plating techniques, and also DMLS and Binder Infusion metal 3D printed structures.
Analytical predictions of frequency shifts with temperature and calculation of effective CTE are estimates based on bulk scaling of resonators. Analytical scaling and HFSS bulk scaling results are consistent. Mechanical complications of the expansion of the structure causing it to expand in a more complicated way than bulk scaling cannot be simulated analytically or with HFSS. Metal coatings decrease the effect of plastic expansion. Quoted commercial CTE values for 3D printed resin are assumed to be accurate, and their quoted values change with temperature ranges. There is no quoted CTE for the binder infusion metal. The DMLS metal CTE is based on a publication. Measurements present the actual frequency drift performance of each device. Calculations and predictions offer a way to know the impact of material and construction choices.
The oven used for temperature testing was a Test Equity model 107, with temperature range −42 to +130 • C. The network analyzer used in the measurements was a Keysight N5242A. Commercial waveguide to coaxial transitions were used to test both filters and a slot array antenna.
An 18 GHz slot array was cycled in temperature from −10 to +60 • C six times in 24 h intervals. Only S 11 was measured. After six cycles, there was visible warping of the structure. The S 11 minimum changed permanently after each cycle, so there was a hysteresis effect with a 70 • C temperature excursion. Our theory is that the plastic expanding during heating pushes the metal plating, and when the plastic shrinks during cooling, the metal does not return exactly to its original position.
As shown in Figure 1, the minimum S 11 was −20.047 dB at 18.07 GHz on the first cycle, −33.16 dB at 18.12 GHz after the second cycle, −32.11 dB at 18.13 GHz after the third cycle, −28.94 dB at 18.14 GHz after the fourth cycle, −22.19 dB at 18.15 GHz after the fifth cycle, and −27.36 dB at 18.14 GHz after the sixth cycle.
Metals 2020, 10, x FOR PEER REVIEW 2 of 12 better CTE than pure aluminum. There are a range of CTE values from 53 × 10 −6 ·K −1 to 145 × 10 −6 ·K −1 available for a desktop SLA 3D printer [22]. Electroplating can also use layers of copper and nickel to strengthen the metal coating and resist the expansion of plastic. Relatively broad band structures such as slot arrays and bandpass filters are not as badly affected by frequency drift as narrow band notch filters.

Materials and Methods
We measured the effect of temperature change on a slot array, cavity notch filters with single and multiple cavities, and post loaded waveguide bandpass filters. We tested several types of SLA resin, different plating techniques, and also DMLS and Binder Infusion metal 3D printed structures.
Analytical predictions of frequency shifts with temperature and calculation of effective CTE are estimates based on bulk scaling of resonators. Analytical scaling and HFSS bulk scaling results are consistent. Mechanical complications of the expansion of the structure causing it to expand in a more complicated way than bulk scaling cannot be simulated analytically or with HFSS. Metal coatings decrease the effect of plastic expansion. Quoted commercial CTE values for 3D printed resin are assumed to be accurate, and their quoted values change with temperature ranges. There is no quoted CTE for the binder infusion metal. The DMLS metal CTE is based on a publication. Measurements present the actual frequency drift performance of each device. Calculations and predictions offer a way to know the impact of material and construction choices.
The oven used for temperature testing was a Test Equity model 107, with temperature range −42 to +130 °C. The network analyzer used in the measurements was a Keysight N5242A. Commercial waveguide to coaxial transitions were used to test both filters and a slot array antenna.
An 18 GHz slot array was cycled in temperature from −10 to +60 °C six times in 24 h intervals. Only S11 was measured. After six cycles, there was visible warping of the structure. The S11 minimum changed permanently after each cycle, so there was a hysteresis effect with a 70 °C temperature excursion. Our theory is that the plastic expanding during heating pushes the metal plating, and when the plastic shrinks during cooling, the metal does not return exactly to its original position.
As shown in Figure 1, the minimum S11 was −20.047 dB at 18.07 GHz on the first cycle, −33.16 dB at 18.12 GHz after the second cycle, −32.11 dB at 18.13 GHz after the third cycle, −28.94 dB at 18.14 GHz after the fourth cycle, −22.19 dB at 18.15 GHz after the fifth cycle, and −27.36 dB at 18.14 GHz after the sixth cycle.    The maximum frequency excursion was 80 MHz, which is a 0.44% permanent change. The −10 dB bandwidth did not change from 100 MHz or 0.55%. A 70 • C temperature shift, a minimum of −10 • C and a maximum of +60 • C cause permanent damage to a 3D printed, copper plated microwave slot array. An obvious alternative that would avoid hysteresis and damage is metal 3D printing. Metal 3D printing with DMLS becomes expensive for part dimensions greater than six inches.
Three slot arrays were simulated with CTE of 50 × 10 −6 ·K −1 to examine the effects of temperature change on gain and S 11 parameters. A 315 × 323 mm array designed to operate at 18.4 GHz showed an S 11 minimum at 18.375 GHz, with S 11 = −30.52 dB with no temperature offset. The -10 dB S 11 width was from 18.3 to 18.44 GHz (140 MHz bandwidth). With a 20-degree temperature offset, the minimum S 11 shifted to 18.356 GHz (∆f = −19 MHz), with S 11 = −30.78 dB. The −10 dB S 11 width was from 18.28 to 18.43 GHz. With a 50-degree temperature offset, the minimum S 11 shifted to 18.330 GHz (∆f = −45 MHz), with S 11 = −35.5613 dB. The −10 dB S 11 width was from 18.25 to 18.40 GHz. The temperature scaling is shown in Figure 2. This array used a four-point corporate network, so it had a wide bandwidth (145 MHz or 7.9%). The realized gain at the design frequency of 18.4 GHz was 34.16 dB with no temperature offset, and reduced to 33.92 dB with a 20-degree temperature offset and to 33.53 dB with a 50-degree temperature offset (−0.62 dB). This is due to the shift in optimum S 11 .
Metals 2020, 10, x FOR PEER REVIEW 3 of 12 The maximum frequency excursion was 80 MHz, which is a 0.44% permanent change. The −10 dB bandwidth did not change from 100 MHz or 0.55%. A 70 °C temperature shift, a minimum of −10 °C and a maximum of +60 °C cause permanent damage to a 3D printed, copper plated microwave slot array. An obvious alternative that would avoid hysteresis and damage is metal 3D printing. Metal 3D printing with DMLS becomes expensive for part dimensions greater than six inches.
Three slot arrays were simulated with CTE of 50 × 10 −6 ·K −1 to examine the effects of temperature change on gain and S11 parameters. A 315 × 323 mm array designed to operate at 18.4 GHz showed an S11 minimum at 18.375 GHz, with S11 = −30.52 dB with no temperature offset. The -10 dB S11 width was from 18.3 to 18.44 GHz (140 MHz bandwidth). With a 20-degree temperature offset, the minimum S11 shifted to 18.356 GHz (Δf = −19 MHz), with S11 = −30.78 dB. The −10 dB S11 width was from 18.28 to 18.43 GHz. With a 50-degree temperature offset, the minimum S11 shifted to 18.330 GHz (Δf = −45 MHz), with S11 = −35.5613 dB. The −10 dB S11 width was from 18.25 to 18.40 GHz. The temperature scaling is shown in Figure 2. This array used a four-point corporate network, so it had a wide bandwidth (145 MHz or 7.9%). The realized gain at the design frequency of 18.4 GHz was 34.16 dB with no temperature offset, and reduced to 33.92 dB with a 20-degree temperature offset and to 33.53 dB with a 50-degree temperature offset (−0.62 dB). This is due to the shift in optimum S11. A 301 × 319 mm array designed to operate at 10.73 GHz had a minimum S11 at 10.7305 GHz, with S11 = −20.26 dB with no temperature offset as shown in Figure 3. The −10 dB S11 width was from 10.69 to 10.76 GHz (70 MHz bandwidth). With a 20-degree temperature offset, the minimum S11 shifted to 10.721 GHz (Δf = −9.5 MHz), with S11 = −20.1103 dB. The −10 dB width was from 10.6842 to 10.7530 GHz. With a 50-degree temperature offset, the minimum S11 shifted to 10.705 GHz (Δf = −25.5 MHz), with S11 = −20.87 dB. The −10 dB S11 width was from 10.67 to 10.74 GHz. This array was coaxial fed in the center of a centered feeding waveguide. The realized gain at the design frequency of 10.73 GHz reduced from 28.42 dB with no temperature offset to 28.45 dB with a 20-degree temperature offset and 28.13 dB with a 50-degree temperature offset (−0.29 dB). 18.4 GHz Slot Array Temperature Scaling  A 448 × 420 mm array designed to operate at 8.18 GHz showed an S11 minimum at 8.171 GHz, with S11 = −30.11 dB with no temperature offset as shown in Figure 4. The −10 dB S11 width was from 8.13 to 8.22 GHz (90 MHz bandwidth). With a 20-degree temperature offset, the minimum S11 shifted to 8.161 GHz (Δf = −10 MHz), with S11 = −32.42 dB. The −10 dB S11 width was from 8.12 to 8.21 GHz. With a 50-degree temperature offset, the minimum S11 shifted to 8.147 GHz (Δf = −24 MHz), with S11 = −35.4 dB. The −10 dB S11 width was from 8.11 to 8.19 GHz. The array used a center feeding waveguide fed from the end, which is why it has smaller bandwidth. The realized gain at the design frequency of 8.18 GHz was 29.84 dB with no temperature offset, reduced to 29.81 dB with a 20 °C offset, and reduced to 29.66 dB with a 50-degree temperature offset (−0.18 dB).  Given that all three arrays lose less than one dB of realized gain with a 50 °C temperature increase, slot array performance is apparently not significantly affected by operating at high temperatures. The effect of temperature variation is much less pronounced than it is for narrow band notch filters and to a lesser degree bandpass filters. On the other hand, a high enough temperature will cause permanent changes to the array, and with a high enough temperature, visible damage.  Given that all three arrays lose less than one dB of realized gain with a 50 • C temperature increase, slot array performance is apparently not significantly affected by operating at high temperatures. The effect of temperature variation is much less pronounced than it is for narrow band notch filters and to a lesser degree bandpass filters. On the other hand, a high enough temperature will cause permanent changes to the array, and with a high enough temperature, visible damage.
A microwave notch filter can be created by coupling a single or multiple resonant cavities to a waveguide [23]. The cavity resonance causes a dip in S 21 , notching the frequency out of the passband. Not only do the resonant cavity dimensions grow with increasing temperature, but the coupling apertures will also increase in size, which also decreases the resonant frequency assuming that the cavity was originally under-coupled.
The resonant frequency of a TE 101 rectangular cavity is given by For a resonant frequency of 10 GHz based on WR-90 waveguide (a = 0.9 inches = 22.86 mm), the guide wavelength is given by where λ c is the cutoff wavelength given by two times the waveguide width 'a.' At 10 GHz, λ 0 = 29.979 mm and λ g = 39.707 mm. The length of a TE 101 cavity is exactly λ g /2 so d = 19.854 mm. As temperature increases, cavity dimensions change according to the following formulas: The resonant frequency as a function of temperature and CTE is shown in Figure 5 below.

Equation (1) combined with Equations
For a TE 101 notch filter centered at 15.7 GHz, using the same analytical scaling, CTE of 20 × 10 −6 ·K −1 produces a slope of −300 kHz·K −1 , a CTE of 50 × 10 −6 ·K −1 produces a slope of −800 kHz·K −1 , and a CTE of 100 × 10 −6 ·K −1 produces a slope of −1.6 MHz·K −1 . For a DMLS 3D printed cavity filter made with AlSi10Mg, with a notch at 15.644 GHz, with CTE published as 20.5 × 10 −6 ·K −1 , we measured −16 MHz shift for a temperature range from 23 to 55 • C, corresponding to −500 kHz·K −1 . Measurement of S 21 at 20, 23, 35, 40, 45, and 50 • C was followed by plotting the S 21 null versus temperature and applying a linear fit to the data. An analytical fit to this frequency change corresponds to a CTE of 32 × 10 −6 ·K −1 . An image of the single cavity DMLS metal 3D printed notch filter is shown in Figure 6.  [24] in the cured state is 119 × 10 −6 ·K −1 , so the stronger metal coating did have an effect. The heated plastic expands, but a stronger metal coating more strongly resists this expansion. In the limit where the metal coating was very thick, it is obvious that the plastic would be completely prevented from expanding. Returning to 20 °C, the S21 null was −29.89 dB (−13.85 dB change) at 15.939 GHz (Δf = +6 MHz). There was some hysteresis effect.
Images of SLA 3D printed, copper plated single cavity notch filters using WR-42 and WR-62 waveguide are shown in Figure 7.   [24] in the cured state is 119 × 10 −6 ·K −1 , so the stronger metal coating did have an effect. The heated plastic expands, but a stronger metal coating more strongly resists this expansion. In the limit where the metal coating was very thick, it is obvious that the plastic would be completely prevented from expanding. Returning to 20 • C, the S 21 null was −29.89 dB (−13.85 dB change) at 15.939 GHz (∆f = +6 MHz). There was some hysteresis effect.
Images of SLA 3D printed, copper plated single cavity notch filters using WR-42 and WR-62 waveguide are shown in Figure 7.
have an effect. The heated plastic expands, but a stronger metal coating more strongly resists this expansion. In the limit where the metal coating was very thick, it is obvious that the plastic would be completely prevented from expanding. Returning to 20 °C, the S21 null was −29.89 dB (−13.85 dB change) at 15.939 GHz (Δf = +6 MHz). There was some hysteresis effect.
Images of SLA 3D printed, copper plated single cavity notch filters using WR-42 and WR-62 waveguide are shown in Figure 7.   A three-cavity filter at 17.2 GHz was fabricated using binder infusion metal 3D printing. In this process, a binder is printed on tungsten powder and infused with bronze [25]. The percentage of tungsten is 50-55%. For a TE101 notch filter centered at 17.2 GHz, using the same analytical scaling, CTE of 20 × 10 −6 ·K −1 produces a slope of −343 kHz·K −1 , a CTE of 50 × 10 −6 ·K −1 produces a slope of −859 kHz K −1 , and a CTE of 100 × 10 -6 ·K −1 produces a slope of −1.71 MHz·K −1 . The binder infusion three cavity notch filter measured a frequency shift of 3 MHz over a temperature range from 23 to 50 °C, corresponding to −111.11 kHz·K −1 . Compared to analytical scaling, this corresponds to an effective CTE of 6.5 × 10 −6 ·K −1 . Since bronze has CTE of 17 × 10 −6 ·K −1 and tungsten has CTE of 4.5 × 10 −6 ·K −1 , assuming 50% of each one should expect overall CTE of 10.75 × 10 −6 ·K −1 . An image of the binder infusion metal 3D printed notch filter is shown in Figure 9.  Taurus Resin Copper Plated Notch Filter A three-cavity filter at 17.2 GHz was fabricated using binder infusion metal 3D printing. In this process, a binder is printed on tungsten powder and infused with bronze [25]. The percentage of tungsten is 50-55%. For a TE 101 notch filter centered at 17.2 GHz, using the same analytical scaling, CTE of 20 × 10 −6 ·K −1 produces a slope of −343 kHz·K −1 , a CTE of 50 × 10 −6 ·K −1 produces a slope of −859 kHz K −1 , and a CTE of 100 × 10 −6 ·K −1 produces a slope of −1.71 MHz·K −1 . The binder infusion three cavity notch filter measured a frequency shift of 3 MHz over a temperature range from 23 to 50 • C, corresponding to −111.11 kHz·K −1 . Compared to analytical scaling, this corresponds to an effective CTE of 6.5 × 10 −6 ·K −1 . Since bronze has CTE of 17 × 10 −6 ·K −1 and tungsten has CTE of 4.5 × 10 −6 ·K −1 , assuming 50% of each one should expect overall CTE of 10.75 × 10 −6 ·K −1 . An image of the binder infusion metal 3D printed notch filter is shown in Figure 9.
process, a binder is printed on tungsten powder and infused with bronze [25]. The percentage of tungsten is 50-55%. For a TE101 notch filter centered at 17.2 GHz, using the same analytical scaling, CTE of 20 × 10 −6 ·K −1 produces a slope of −343 kHz·K −1 , a CTE of 50 × 10 −6 ·K −1 produces a slope of −859 kHz K −1 , and a CTE of 100 × 10 -6 ·K −1 produces a slope of −1.71 MHz·K −1 . The binder infusion three cavity notch filter measured a frequency shift of 3 MHz over a temperature range from 23 to 50 °C, corresponding to −111.11 kHz·K −1 . Compared to analytical scaling, this corresponds to an effective CTE of 6.5 × 10 −6 ·K −1 . Since bronze has CTE of 17 × 10 −6 ·K −1 and tungsten has CTE of 4.5 × 10 −6 ·K −1 , assuming 50% of each one should expect overall CTE of 10.75 × 10 −6 ·K −1 . An image of the binder infusion metal 3D printed notch filter is shown in Figure 9. One remedy for the temperature drift problem is to adjust the coupling aperture of a single cavity filter to be near critical coupling. This increases the resonant bandwidth. If the notch width is 150 MHz and the interfering signal has a bandwidth of 50 MHz or less, significant temperature drift One remedy for the temperature drift problem is to adjust the coupling aperture of a single cavity filter to be near critical coupling. This increases the resonant bandwidth. If the notch width is 150 MHz and the interfering signal has a bandwidth of 50 MHz or less, significant temperature drift can be tolerated while still attenuating the target signal. One problem with this technique is that it does not allow filtering of an interfering signal that is closer in frequency than the notch bandwidth.
The bandpass filter design that was 3D printed is a post loaded waveguide. The inductive posts form coupled resonant cavities. This filter was designed based on a technique described in [24]. The filter has openings along the center of the waveguide broad wall, following the technique described in [1] to enable internal electroplating of a 3D printed structure.
The SLA 3D printed, copper electroplated bandpass filter measured a passband shift of −549 kHz·K GHz (50 °C) as shown in Figure 10. The value of f for S21 = −15 dB at each temperature was plotted and a linear fit was used to characterize the overall temperature variation. The high temp SLA, copper plated bandpass filter measured a passband shift of −365.89 kHz·K −1 . The measured frequencies were 12.6742 GHz (20 °C), 12.6733 GHz (23 °C), 12.6708 GHz (35 °C), 12.6658 GHz (40 °C), 12.6650 GHz (45 °C), and 12.6642 GHz (50 °C). Images of the SLA and DMLS 3D printed, post-loaded, waveguide microwave bandpass filters are shown in Figure 11. Simulation with HFSS using bulk scaling of the structure corresponding to CTE of 20 × 10 −6 ·K −1 showed a frequency shift of −300 kHz·K −1 , very close to the measured value for DMLS with actual reported CTE of 20 × 10 −6 ·K −1 . The HFSS simulation result is shown in Figure 12 for ΔT = 0 to 50 °C.  Simulation with HFSS using bulk scaling of the structure corresponding to CTE of 20 × 10 −6 ·K −1 showed a frequency shift of −300 kHz·K −1 , very close to the measured value for DMLS with actual reported CTE of 20 × 10 −6 ·K −1 . The HFSS simulation result is shown in Figure 12 for ∆T = 0 to 50 • C.

Conclusions
Resins used for stereolithography 3D printing typically have high CTE. Microwave structures manufactured with 3D printing using SLA and copper plated can have strong frequency dependence on temperature. In particular, multi-cavity filters with narrow bandwidth are strongly affected by dependence of resonant frequency on temperature. This can preclude their usefulness if the frequency drift approaches the bandwidth of the device. Electroplating with layers of copper and nickel to strengthen the metal coating resists the expansion of plastic and reduces temperature dependence. Using DMLS metal printing approaches metal structure performance, so that metal 3D printed structures can approach temperature characteristics of solid metal structures. Single cavity notch filters printed with lower CTE resin can be useful if a wide enough notch bandwidth is used to accommodate frequency drift. One must choose the right 3D printing materials and processes to achieve the temperature stability required by the application.