CHARACTERIZING AND INTEGRATING RESISTIVE INK FOR USE IN RF 
COMPONENTS 

By 

Koltin Grammer 

A THESIS 

Submitted to 
Michigan State University 
in partial fulfillment of the requirements   
for the degree of 

Electrical and Computer Engineering – Master of Science  

2025 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ABSTRACT 

Aerosol jet printing (AJP) is gaining attention in additive manufacturing as a method that 

can be used to fabricate small and precise radio frequency (RF) components. Although work has 

been done to prove the usefulness of this manufacturing method up to D-band, most of that work 

has been done using highly conductive inks for transmission lines and radiators. Currently, no 

reliable method exists to fabricate resistive components for use in high-frequency circuits. The 

work presented here undergoes the process of characterizing commercially available ink for that 

purpose. It will be shown that resistors can be fabricated small enough and with low enough 

resistance to be used in RF components. A Wilkinson power divider that operates in Ka band as 

well as one that operates in V band are fabricated. A set of loaded microstrips are fabricated to 

show how the printed resistors operate when they act as terminations.

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This thesis is dedicated to my wife Emily. 
Thank you for the unwavering support from the beginning. 

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ACKNOWLEDGEMENTS 

This work is funded in part by the Department of Energy’s Kansas City National Security 

Campus, operated by Honeywell Federal Manufacturing & Technologies, LLC under contract 

number DE-NA0002839. 

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TABLE OF CONTENTS 

CHAPTER 1: Introduction .......................................................................................................... 1 
1.1 Aerosol Jet Printing ............................................................................................................ 1 
1.2 How AJP Works .................................................................................................................. 2 

CHAPTER 2: Ink Selection ......................................................................................................... 6 
2.1 Clevious FE T ...................................................................................................................... 6 
2.2 Mixed Materials................................................................................................................. 15 
2.3 Metalon JR-038 ................................................................................................................. 16 

CHAPTER 3: Characterizing Metalon Resistive Ink ............................................................. 17 

CHAPTER 4: Fabricating RF Devices ..................................................................................... 25 
4.1 Load Terminated Microstrip ........................................................................................... 25 
4.2 Wilkinson Power Divider.................................................................................................. 30 

CHAPTER 5: Conclusions and Future Work .......................................................................... 43 
5.1 Altering Ink Resistivity ..................................................................................................... 43 
5.2 Power Testing .................................................................................................................... 44 
5.3 Additional Circuits ............................................................................................................ 44 

WORKS CITED.......................................................................................................................... 46

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CHAPTER 1: Introduction 

1.1 Aerosol Jet Printing 

The rapid proliferation of radio frequency (RF) components calls for advanced 

manufacturing techniques that are capable of high precision fabrication, miniaturization, and 

customization. One such technique is aerosol jet printing (AJP). AJP stands out for its ability to 

print over a wide range of length scales, with previous work showing its ability to print down to 

10µm [1], [2], as well as its ability to print functional components in Ka, W, and D band [3], [4], 

[2]. AJP is an additive process, unlike many of the currently utilized processes, which are 

subtractive in nature and therefore generate significant amounts of material waste and dangerous 

chemical waste (hydrofluoric acid). The current semiconductor processes require mask 

fabrication and lithography, where the AJP process can quickly customize designs and adjust 

fine feature sizes as needed leading to a reduction in non-reoccurring engineering (NRE). AJP 

has proven successful in the field of packaging with its ability to print broadband, low-loss 

interconnects [5]. Additionally, AJP as the ability to print over conformal surfaces [4], as well as 

across multiple layers [6]. 

While previous work has shown the utility of AJP, little research has gone into using this 

manufacturing technique to fabricate structures other than dielectrics (polyimide, 

benzocyclobutene) or conductors (silver). The few attempts at fabricating resistive components 

have produced components that were either too resistive [7], too large [8], or required extremely 

high levels of process control relative to the methods shown in this thesis [7], [8], [9]. RF devices 

typically require resistive components that have relatively low resistive values (100Ω for 

Wilkinson power divider). RF devices require resistive components to be much smaller than a 

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wavelength to be considered lumped (one-sixth being a rule of thumb [10]), and high levels of 

process control can make resistor fabrication and repeatability difficult. 

The work in this thesis will explore various resistive ink options and rule out less 

desirable inks. It will be shown possible to print resistors that are physically small, relatively low 

resistance, and repeatable using a commercially available carbon-based ink. The characterization 

process will show how to fabricate resistors of a given size and resistance as well as how curing 

effects device geometry. The I-V characteristics of the fabricated resistor will show that the 

resistor has ohmic behavior. Finally, RF devices will be fabricated using the printed resistor to 

prove their effectiveness in actual components. 

1.2 How AJP Works 

Figure 1.1: Aerosol jet printer at Michigan State University 

Aerosol jet printing is a direct writing method and happens in four basic stages: ink 

preparation, ink atomization and transport, ink deposition, and post processing. 

During the ink preparation stage, the material that is to be printed may need to be altered 

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to be compatible with the printer. The most important aspect is the ink viscosity. If the material 

is too viscous, it will not be able to be atomized and transported to the deposition stage. Both the 

polyimide and the silver that are used to fabricate the RF devices in chapter 4 are altered during 

the ink preparation stage. The carbon ink that is used to fabricate the resistor does not require any 

ink preparation. 

Two methods are used for ink atomization: pneumatic atomization (PA) and ultrasonic 

atomization (UA). PA is typically used for more viscous inks, such as the polyimide used to form 

the dielectric layers. UA is used for less viscous ink such as silver, and carbon. 

During pneumatic atomization nitrogen enters the system though the atomizer inlet gas 

nozzle at the top of the pneumatic atomizer and is directed into the jar. Inside the bottom of the 

jar is a jet that directs the nitrogen into the jar and atomizes the ink. The difference in pressure 

then carries the nitrogen-ink mixture to the mist output port. The exhaust is in line with the mist 

output and removes access air from the system. A pictorial representation of the pneumatic 

atomizer is given in figure 1.2. 

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Figure 1.2: Pneumatic atomizer [11] 

Ultrasonic atomization operates in a similar fashion; however, the vial of ink is 

suspended in a water bath that has a transducer at the bottom. The transducer vibrates the water 

which transfers the vibration into the ink resulting in a small amount of ink atomization. 

Nitrogen enters the system and carries away the ink droplets. There is no exhaust during 

ultrasonic atomization. 

The deposition head is the same for both PA and UA. The nitrogen-ink mixture is 

delivered to the deposition head that uses a nitrogen sheath gas to focus the mixture into a 

focused stream prior to leaving the system. Once the ink leaves the system it is deposited onto 

the print stage where the part is being fabricated. To temporarily stop deposition during this 

process a shutter is used to temporarily cover the nozzle when needed. A pictorial representation 

of the deposition head is given in figure 1.3. 

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Figure 1.3: Deposition head [11] 

The post processing step is dependent on the material that was being printed. Silver and 

carbon undergo cures in an oven with no change in atmosphere. Polyimide undergoes cure in a 

vacuum oven with atmosphere pumped out and nitrogen pumped in. Some inks are cured using 

ultra-violet (UV) light, but none of those were used in this work.

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CHAPTER 2: Ink Selection 

2.1 Clevious FE T 

The first ink evaluated was Clevious FE T, manufactured by Heraeus. This ink is a 

Poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT: PSS) based mixture. The 

PEDOT component of this mixture contributes to its electrical conductivity. The sulfonate 

component contributes to water solubility. This mixture has a reported sheet resistance range of 

80-500 

𝛺

𝑠𝑞

 [12], which could make it an ideal candidate for resistor fabrication. Additionally, 

some groups have had success using aerosol jet printing with this ink to print ultra-wide band RF 

components [13]; However, the characterization and printing procedure was not explored in 

detail. PEDOT: PSS mixtures have also been used in the ink-jet printing process [14], [15], [16]. 

In [14] the authors used a mixture of ink-jetting and capillary channels to control the deposition 

of the PEDOT: PSS ink. In [16] patterning was used to control the deposition. While these 

methods are valid, they require a significant amount of preparation and pre-processing of the 

print area. The goal of this thesis is to discover a method that eliminates those pre-processing 

steps and only utilizes AJP. 

The Clevious FE T has a reported viscosity of 50-70 mPA-s [12]. Due to its viscosity, the 

pneumatic atomizer was used to print resistive test structures. These test structures would be 

used not only to test its electrical capabilities but determine also how it reacted mechanically to 

the print and curing process. The printed test structure is given in figure 2.1. 

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(a) 

(b) 

Figure 2.1: Two different test structures: (a) 1.5mm x 1mm (b) 100µm x 100µm 

The test structures were printed using the following recipe: 1000 standard cubic 

centimeters per minute (SCCM) PA mass flow rate, 850 SCCM exhaust flow rate, tip speed 2 

mm/s and 300µm tip. The curing profile was 100°C for 30 minutes in accordance with [12]. 

While the initially printed test structures looked promising, problems with the curing profile 

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were immediately evident. Table 2.1 gives the height of the test structures before cure and after 

cure. 

Table 2.1: Shrinkage profile of Clevious devices 

Before Cure Height (µm) 
13.07 
18.42 
30.88 
41.22 
55.14 
148.90 
132.80 
179.66 
152.70 

After Cure Height (µm) 
5.53 
5.90 
6.83 
6.18 
11.36 
34.49 
45.87 
35.83 
35025 
The largest change in the height from pre-cure to post-cure was an 85% change in 

Shrinkage (%) 
58 
68 
78 
85 
79 
77 
65 
80 
77 

structure height. The reported change in structure height given in [12] is greater than 98%, 

therefore, the material was not reacting mechanically as expected. 

Figure 2.2 shows two attempted prints that were fading in and out during deposition. This 

problem was prolonged and extended across numerous attempts to print simple square structures. 

While investigating the cause behind the fading prints, it was discovered that the ink reacted 

poorly to the AJP process. The ink was clogging the printer machinery during the process. some 

of the clogging examples are given in figure 2.3. 

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(a) 

(b) 

Figure 2.2: Continuous prints that fade during printing 

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(a) 

(b) 

Figure 2.3: Clevious FE T drying out in machinery parts during printing 

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Figure 2.3 shows that the ink drying out inside the printer’s virtual impactor during the 

printing process. The nitrogen flow that carries the ink from the PA to the deposition nozzle was 

most likely flashing off the solvents in the ink. This led to poor print consistency and would 

make fabricating a given geometry difficult. This drying is also likely a cause for the poor 

shrinkage performance during the cure. Less solvents remain in the ink when deposited, 

therefore, there is less solvent to flash off during the cure and as a result, less shrinkage occurs. 

This was tested and verified by using a dropper to drop the ink onto a glass slide and measuring 

the pre-cure and post-cure height. This experiment results in a curing profile that was closer to 

that reported in the data sheet but would make it impossible to reliably fabricate resistors of a 

predetermined geometry without significant preparation. 

To make matters worse, similar issues were discovered inside the PA print jar that holds 

the ink during print. Inside the jar is a metal ball that is used to slowly stir the ink while the 

machine is in operation. The ink is very acidic, and the ions in the ink tend to react with the 

metal. This reaction can change the ink chemical properties as well as cause the ink to congeal 

inside the jar. This issue was discovered when cleaning the ink jar to correct the fading print 

issues. Proof of the congealed ink is given in figure 2.4. 

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(a) 

(b) 

Figure 2.4: (a) Congealed ink in PA jar. (b) Result of filtering ink (c)Ink congealing around 
metal stir ball 

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Figure 2.4 (cont’d) 

(c) 

When testing the electrical characteristics of the few successfully printed structures, the 

Clevious could finally be eliminated as a candidate for an ink that could be used reliability. The 

I-V characteristics of the structure did not show consistent ohmic behavior but rather showed 

evidence of non-linear behavior. The I-V characteristics of the printed test structure are given in 

figure 2.5. 

Figure 2.5: Test structure I-V characteristics (100µm x 100µm structure) with varying height 

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Over the range from -1 to 1 volt, the current does not increase linearly. The curve is 

linear when less than -0.4 volts, between -0.4 and 0.4 volts, and above 0.4 volts; however, the 

slope of these regions is not consistent. This behavior was repeated with similar results but with 

the diode behavior starting and stopping at different points based on test structure geometry. 

Figure 2.6 shows another test of the same nature but on different test structures that are 

significantly larger.  

Figure 2.6: Test structure I-V characteristics (1.5mm x 1mm test structure) 

Some tests were done that involved mixing additional solvents in with the ink prior to 

printing. It has been reported that mixing in solvents can help lower the resistivity of the ink 

[17]. It was possible that loading in additional solvents could help counterbalance the jamming 

issue by giving a larger buffer for solvent evaporation in the printer. These methods were 

attempted; however, were ultimately unsuccessful. 

For the above reasons, Clevious ink was ruled out as a reliable candidate for AJP resistor 

printing applications. 

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2.2 Mixed Materials 

The work presented in [5] shows that it is possible to mix a highly conductive ink (silver) 

with other less conductive inks (graphene, carbon nanotubes, and carbon black nanoparticles). 

This work utilized both the pneumatic and ultrasonic atomizers simultaneously to mix ink in 

process. The ratio of carbon materials to silver was varied from 0% to 1% The resulting change 

in resistivity varied from roughly 10-5 Ω-cm to 10 Ω -cm. While this range would include 

resistivity values that would be useful for small RF components, there is a range that is six orders 

of magnitude within an exceedingly small change in carbon content. The inks were mixed during 

the printing process using a "Y" type connector that connected both the PA and UA. Process drift 

could make achieving a small variance in resistance for a given device difficult without high 

levels of process controls. 

Opting to mix carbon nanotubes with various solvents prior to use in the UA was 

attempted in [7]. This removes some of the difficulty associated with process drift and 

controlling two different printer flows. Instead that high degree of process control is needed in 

the form of weighing inks and mixing with high degrees of precision. Ensuring a uniform 

mixture of carbon to solvents is important. To mitigate that issue a centrifuge was used. This 

would require specialized equipment and could still prove difficult to have a low variance in 

resistor values for a given device. 

Resistive carbon paste can be diluted to meet the viscosity requirements of AJP. It was 

shown that this diluted carbon paste solution can successfully print resistors [8]. The resistors 

printed in [8] were small enough to use for low frequency RF applications, so continuation of 

this work could have proved fruitful; however, this process involves precisely diluting highly 

viscous carbon paste to create a solution that can be printed, and this is an added layer of 

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difficulty beyond printing. The paste used in [8] is manufactured for screen printing and it was 

noted in [8] that the particle size could lead to problems when using this method for AJP. 

It is for the reasons above that diluting carbon paste to formulate a new ink was ruled out 

as a candidate for AJP resistor printing. 

2.3 Metalon JR-038 

The ink that was chosen for characterization and device fabrication is Metalon JR-038 

manufactured by Novacentrix. This ink is designed specifically for use in the AJP process and 

can be printed onto both porous (polyimide) and non-porous (glass) substrates. The ink has a 

reported resistivity of 8000 Ω-µm [18]. During the initial testing, this ink proved to be easy to 

print, had reliable resistivity values, and did not require any pre-processing. 

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CHAPTER 3: Characterizing Metalon Resistive Ink 

The end goal of the resistive ink is for use in various RF components which are normally 

mounted on a dielectric substrate, therefore, to best match the final mounting environment during 

testing, a glass slide (3"x2") was spin coated with the same polyimide that would be used in 

component fabrication. This layer of polyimide will provide a surface for Metalon ink to adhere 

to, substantially lowering the potential for delamination. A silver test structure was designed that 

would provide area for the resistor as well as provide convenient probe landing locations. The 

printed resistor would be placed in a gap between the two halves of the silver. This makes it 

possible to vary resistor length by adjusting the size of gap. The gap was made the same size as 

the gap that would be needed for a Wilkinson power divider that operates in Ka band. The gap 

was made 100µm long (space between silver) and 250µm wide. The test structure with and 

without the resistive ink is given in Fig 3.1. 

(a) 

Figure 3.1: Resistor test structures 

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Figure 3.1 (cont’d) 

(b) 

This test setup will also ensure that any resistance at the interface between the silver and 

the carbon will be included in any measurements that are taken, assuming the amount of overlap 

between the two materials remains constant. The overlapping region is important to the operation 

of the device, most importantly, the amount of overlap that exists. If the overlap is too low, then 

the I-V characteristics of the resistors can be unpredictable, likely due to the weak connection 

between the materials. It was found that an overlap of 40µm was sufficient for this application; 

however, no detailed studies were done to prove that there is anything unique about this value. 

Sixteen test structures, including the resistor, were fabricated utilizing the 40µm carbon-

silver overlap. The print recipe was as follows: 75 standard cubic centimeters per minute 

(SCCM) sheath flow, 25 SCCM ultrasonic atomizer flow, 200µm tip, and 1 

𝑚𝑚

𝑠

 tip speed. The 

resistors were cured at 100°C for 30 minutes. The resistors were printed to an arbitrary height 

and the cross-sectional area of the printed resistor would be measured using a Keyence optical 

profilometer, therefore, all geometric properties of the resistor will be known. The I-V 

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characteristics of the resistor were measured using a four-point probe. Determining the resistivity 

of the material (after cure) is then possible using the relationship given in equation 3.1. With the 

resistivity of the material known, it could be possible to tailor the resistor values and geometry to 

the needs of the application. 

𝑅 = ρ

𝑙𝑒𝑛𝑔𝑡ℎ
𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

(3.1) 

The resistivity value cited for this curing profile is 8000Ω - µm [18]. The resistivity 

values that were measured and calculated are given in figure 3.2. 

Figure 3.2: Measured resistivity of 16 printed resistors 

The resistivity of 15 of the 16 resistors is around the cited value, but there is some 

significant deviation. This deviation could make it difficult to fabricate components with high 

degrees of precision. The 16th resistor is an outlier and is the result of a printing error. 

To control the resistivity value more precisely, the curing profile was changed to match 

the curing profile of silver, 180°C for 5 hours. This curing profile was used during the 

fabrication of the 30 GHz power divider (section 4.2.2) since the resistor would be subjected to a 

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final silver cure. The hotter and longer cure did aid in increasing the precision of the resistivity 

values. Changing the curing profile both increased the precision of the resistor resistivity and 

lowered the average resistivity value. This will be beneficial for trying to make low resistance 

components. The results of the new curing profile on resistivity can be seen in figure 3.3. 

Figure 3.3: Component resistivity with long, hotter cure 

A sample of the I-V curves for the printed resistor are given in figure 3.4. An ideal curve 

would be linear and increasing. This would show that the current through the resistor is directly 

and proportionally related to the voltage applied across the resistor. This is indicative of ohmic 

behavior; therefore, the resistor follows ohms law (equation 3.2). 

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Figure 3.4: Device I-V curve 

𝑅 =

𝑉
𝐼

(3.2) 

Equation 3.1 shows that the resistance of a device is determined by both the resistivity 

and cross-sectional area of the device. This can pose a problem during fabrication since the 

geometry of the device (cross sectional area) will change during cure as the solvent in the carbon 

ink is flashed off. This makes it important to understand how a given cure profile will affect the 

geometry of the printed device. With the curing profile established to be 180°C for 5 hours, the 

geometrical change in cross sectional area is shown for all sixteen devices in figure 3.5. 

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Figure 3.5: Change of resistor cross-sectional area due to cure 

The amount that the resistor geometries change during the cure is relatively consistent 

and predictable. The slope of the linear line of best fit is a good approximation for how the 

resistor cross-sectional area changes during the cure. With this shrinkage profile, it is possible to 

modify equation 3.1 to give an equation that can be used to determine resistor geometry before 

cure. The benefit being that the user can get closer to desired resistance values with less print 

steps. The modified equation to account for the change in cross-sectional area is given in 

equation 3.3. 

𝑅 = ρ

0.3 𝑙𝑒𝑛𝑔𝑡ℎ
𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

(3.3) 

Note that the device length does not change, as this is determined by the separation of the 

silver conductors. Additionally, the resistivity does not change since that is a material property of 

the ink. 

Equation 3.3 is an approximation and is only true when a given set of conditions are 

satisfied. The most notable of those conditions concerns the cross-sectional area of the resistor. 

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In equation 3.3 cross − sectional  area  =  resistor  width  × resistor  height, and there is a 

limit to how large either the width or height for a given device can be. Put into the extreme, the 

width can not be infinitely large or the height infinitely high and produce a device of 0Ω 

resistance. To prove this case, a microstrip was fabricated and numerous print runs were 

performed to build the height of the resistor to be extremely tall. The resistor was measured to 

have a resistance of 147Ω, then more layers were added on and measured again, the resistance 

was unchanged. This proved that there is an upper limit to the width and height. The conceptual 

reasoning behind this is shown in fig 3.6. 

(a)  Resistor with narrow width 

(b) Resistor with large width 

Figure 3.6: Electric field lines in different size resistors (conceptual) 

To further prove this concept a simulation was run using Ansys HFSS to visualize 

the electric field in a printed resistor. The simulation is shown in figure 3.7. The red 

portion is the conductor. The green portions of the resistor are where the electric field is 

strongest, and the blue is where the electric field is the weakest. The electric field quickly 

dies off as distance from the conductor is increased. 

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Figure 3.7: Electric field strength inside printed resistor 

This shows that when the resistor width is narrow, the field lines from one 

conductor to the other are confined and utilize the entire width of the resistor. This forces 

the charge carries to move through the resistive material that constructs the entire resistor. 

In this case equation 3.3 is accurate; however, when the resistor has a large width the 

electric field lines do not use all the resistive material, and the charge carriers are not 

forced through the entire resistor. This makes the utilized width smaller than the physical 

width and equation 3.3 is no longer accurate. The same logic holds true for increasing the 

height of the device beyond a certain point. The observation made throughout this project 

is that if the height of the resistor is larger than the separation of the conductors, the I-V 

characteristics no longer behave as expected. The width of the resistor should not exceed 

2 times the width of the conductors. These rules of thumb were discovered and used 

throughout; however, no rigorous experimentation was done. 

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CHAPTER 4: Fabricating RF Devices 

4.1 Load Terminated Microstrip 

Terminated microstrip transmission lines play a large role in various RF circuits such as: 

hybrid couplers, quarter wave directional couplers, and rat race couplers. These examples 

represent four port devices where one port acts as an input port, two ports are outputs, and the 

final port is simply terminated with a matched load. These couplers typically offer a simple 

method to split/combine a signal and achieve various phase shifts. However, these devices can be 

constrained to lower frequencies if the load resistor is unable to be scaled to a small size. The 

goal for fabricating loaded microstrips was to determine whether it was possible to fabricate 

small resistors, and if possible, quantify its ability to absorb a signal and minimize reflections. 

To understand the theory of operation, it will be assumed that the point where the 

microstrip meets the printed resistor is at x = 0. The signal is generated by a source that is located 

at some point before this point. Therefore, the signal is travelling from the source to the load in 

the $+x$ direction, but at the microstrip to resistor interface, there will be some reflections that 

generate a wave travelling in the direction from the resistor back to the source. The sum of these 

waves gives the total voltage on the microstrip and is given in equation 4.1. The voltage is 

related to the current via the impedance using equation 4.2. 

𝑉(𝑥) = 𝑉0

+𝑒−𝑗β𝑥 + 𝑉0

−𝑒𝑗β𝑥

𝐼(𝑥) =

𝑉0

+𝑒−𝑗β𝑥
𝑍0

−

𝑉0

−𝑒𝑗β𝑥
𝑍0

(4.1) 

(4.2) 

The impedance of the load can be found by divider equation 4.1 by 4.2 at the point x = 0. 

This is given in equation 4.3. 

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𝑍𝐿 =

𝑉(0)
𝐼(0)

=

𝑉0
𝑉0

−
+ + 𝑉0
− 𝑍0
+ − 𝑉0

(4.3) 

Finally, the reflection coefficient, Γ, can be determined by rearranging to find the ratio of 

the forward travelling signal and the backward travelling signal. The reflection coefficient can be 

found strictly in terms of the load and characteristic impedance. See equation 4.4. 

Γ =

𝑍𝐿 − 𝑍0
𝑍𝐿 + 𝑍0

(4.4) 

Equation 4.4 shows that if the load impedance is well match to the characteristic 

impedance, reflections can be minimized. This can be highly desirable since reflections can 

result in poor performance of RF parts. Minimizing reflection also makes it possible to isolate 

the RF circuits from unwanted signals, as will be done when fabricating the V-band Wilkinson 

power divider in section 4.2.2. 

Fabrication of the loaded microstrips started with mechanically removing the oxide on a 

molybdenum-copper (MoCu) carrier plate that is 1"x1" in size. This carrier plate acts as a stage 

onto which the AJP parts will be fabricated and will also act as the ground plane for the 

microstrip lines. Polyimide was deposited to serve as the dielectric substrate layer upon which 

the silver will be printed. The width of the silver to obtain a characteristic impedance of 50Ω was 

50µm, which is not wide enough to print a resistor that has an impedance that low for the reason 

that is shown in figure 3.5. To overcome this challenge, a small set of flanges were added either 

side of the resistor, a pictorial representation is shown in figure 4.1. It is important that these 

flanges remain small when compared to the wavelength, otherwise, they could have a negative 

effect of circuit performance when it begins to act as a distributed element. In this situation the 

flanges were made to be 200µm long and 40µm wide. 

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Figure 4.1: Microstrip flanges to increase resistor width 

This process was repeated 12 times over to fabricate 12 individual microstrips. The 

resistors were then printed to a varying height with an increasing number of layers. For example, 

the first loaded microstrip only has a single layer of carbon printed for the resistor, the second 

microstrip has 2 layers of carbon, and the final loaded microstrip has 12 layers of carbon printed 

for its resistor. This resulted in a range of resistance values from as high as 206Ω to as low as 

45Ω. The printed microstrip and its resistor is shown in figure 4.2, and the resistance 

measurement for each resistor is given in figure 4.3. 

Figure 4.2: Two loaded microstrips 

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Figure 4.3: Resistance measurement of each loaded microstrip resistor 

These microstrips were measured through W-band to determine how this device operates 

at both low and high frequencies. To convert equation 4.3 into something that can be directly 

measured, the reflection coefficient can be used to determine the return loss, which is directly 

measured. Equation 4.5 converts the reflection coefficient into a return loss. 

𝑅𝐿 = −20𝑙𝑜𝑔(Γ)𝑑𝐵

(4.5) 

Based on equations 4.3 and 4.4 it is expected that as the resistance of the printed resistor 

approaches the characteristic impedance, the return loss will improve. The measured DC 

resistance value, the calculated reflection coefficient, and the calculated return loss are given in 

table 4.1. These calculations were done using measured resistance as the load impedance. Figure 

4.4 shows the measured results of all the loaded microstrips. Figure 4.5 compares four measured 

and simulated microstrips. 

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Table 4.1: Calculated return loss using measured resistance values 

Device 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 

ZL 
206 
136 
98 
83 
72 
72 
78 
53. 
54 
71 
47 
45 

Z0 
50 
50 
50 
50 
50 
50 
50 
50 
50 
50 
50 
50 

Γ 
0.61 
0.46 
0.32 
0.25 
0.18 
0.18 
0.22 
0.03 
0.04 
0.17 
0.03 
0.05 

RL (dB) 
4.3 
6.7 
9.8 
12.1 
14.9 
14.9 
13.2 
30.7 
28.3 
15.2 
30.2 
25.6 

Figure 4.4: VNA measurements of the loaded microstrips 

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Figure 4.5: Measured VS Simulated loaded microstrips 

In total, the loaded microstrips operate acceptably well when compared to the simulated 

values; however, the performance could be better. This degraded performance could be for a 

couple major reasons: The characteristic impedance is not perfectly 50Ω, the resistance of the 

printed carbon is changing at RF frequencies due to the skin effect, and parasitic inductance and 

capacitance may dominate in higher frequency ranges. Even with these potential issues, the 

return loss of the resistors that are within 5% of the characteristic impedance is better than 10 dB 

at all frequencies up to 110 GHz. 

4.2 Wilkinson Power Divider 

4.2.1 Background/Theory 

The Wilkinson power divider is an N-port device that is used to split power equally N-

ways and was originally introduced in 1960 by E.J. Wilkinson [19]. In this divider two quarter 

wave transformers are connected to a common input port and two separate output ports. 

Separating the output arms of the power divider is an isolation resistor that has a value of 2Z0, 

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where Z0 is the characteristic port impedance. The quarter wave transformer is used to 

impedance match the port with the isolation resistor and minimize the resulting reflections. 

When power is incident on the input port it is equally split between each quarter wave 

transformer.  Since the device is symmetrical, when the signal reaches the resistor both arms 

have a signal that is equal in both phase and magnitude, therefore, there is no potential difference 

across the resistor and current does not move through it. Each output port would receive half the 

power and measure at roughly -3dB. In this case, the device is acting as a divider. If two signals 

that were equal and in phase where incident on the output ports, the device would have the same 

operation in reverse and would be acting as a combiner. 

When power is incident on a single output port that signal travels through two quarter 

wave transformers to reach the opposite output port, therefore, the signal has a phase offset of 

180 degrees across the resistor. This corresponds to the largest potential across the resistor and as 

a result the largest current through the resistor. The power being consumed inside the resistor is 

in accordance with P = IV and isolates the output ports from each other. 

The resistor plays a large role in the performance of the Wilkinson power divider and its 

ability to isolate signals and reflection. For this reason, a Wilkinson power divider was chosen to 

act as a test bed for the printed resistor. 

4.2.2 Ka-Band Wilkinson Power Divider 

The Wilkinson power divider has port impedance of 50Ω, this value is chosen since it is 

both industry standard and is the port impedance of the PNA-X that was used to measure its 

performance. The resistor separating the output arms was 100Ω. To ensure that the resistor did 

operate as a lumped element device its largest aspect ratio was kept to less than one-tenth the 

wavelength. The wavelength of the signal can be calculated using equations 4.6 and 4.7 [20]. 

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ϵ𝑒 =

ϵ𝑟 + 1
2

+

ϵ𝑟 − 1
2

1

√1 + 12

𝑑
𝑤

λ =

𝑐

𝑓√ϵ𝑒

(4.6)

(4.7) 

The dielectric for the divider is made from PI-2611, manufactured by HD microsystems, 

diluted with N-Methyl-2-Pyttolidone (NMP) at a ratio of 2:3 by volume. The dielectric constant 

for this dielectric mixture has been found experimentally to be roughly 3.5. This is consistent 

with other works done that used similar materials [21]. The conductor used for the power divider 

is Clariant silver ink diluted with distilled water at a ratio of 1:3 by volume, respectively. It has 

been found that this mixture after cure has a conductivity, σ, in the range of 20% - 40% the 

conductivity of bulk silver. 

The narrowest portion of the silver traces was along the quarter wave transformer. This 

portion of the conductor was the limiting factor that helps determine the height of the dielectric, 

since the dielectric height directly affects the microstrip width needed to achieve a given 

impedance value. The impedance along the quarter wave transformer was √2𝑍0, or 70.7Ω. The 

design equations used to determine the ratio between the width of the microstrip line and the 

height of the dielectric are given in equations 4.8 and 4.9. Both can be found in [20]. These 

equations are only valid when 

W

d

> 2, which will be the case for this device. 

𝐵 =

377π
2𝑍0√ϵ𝑟

𝑊
𝑑

=

2
π

[𝐵 − 1 − 𝑙𝑛(2𝐵 − 1) +

ϵ𝑟 − 1
2ϵ𝑟

(𝑙𝑛(𝐵 − 1) + 0.39 −

0.61
ϵ𝑟

)]

(4.8) 

(4.9) 

Based on the above equations, the target height for the dielectric was chosen to be 

roughly 40µm. This dielectric height would result in a theoretical trace width of 108µm and 

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64µm for a characteristic impedance of 50Ω and 70.7Ω, respectively. These widths were 

optimized in HFSS, and the target widths will be 100µm and 50µm, which is near the theoretical 

values. 

To determine the maximum allowable size of the resistor the wavelength must be known. 

The wavelength of the signal can be found using equation 4.10, 4.11 [22]. 

𝑣𝑝 =

1

√ϵ0ϵ𝑟μ

𝑐

√ϵ𝑒

=

𝑐

λ =

𝑣𝑝
𝑓

=

√ϵ𝑒𝑓

(4.10) 

(4.11) 

This yields a wavelength of 4.4mm. One-tenth of this is 0.44mm or 440µm, which is the 

largest that the resistor should be. This is well within the capabilities of the AJP process. The 

final resistor dimensions are 250μm  × 100μm. The HFSS model of the Wilkinson power 

divider is given in fig 4.6. 

Figure 4.6: HFSS model of Ka-band Wilkinson power divider 

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A molybdenum-copper (85% molybdenum and 15% copper) carrier plate is used as the 

ground plane. This mixture of MoCu is used to match the coefficient of thermal expansion of 

group III-V semiconductors (this is not a concern for this device and any good conductor would 

have been sufficient). The carrier plate was mechanically sanded and polished using a Dremel 

and sanding disks up to 10000 grit. The sanding process helps remove any surface oxide and 

preps the surface for the application of adhesion promoter. The adhesion promoter is 0.1% VM-

651, manufactured by HD Microsystems) diluted with 99.9% deionized water. The adhesion 

promoter is used to ensure the polyimide substrate adheres strongly to the ground plane and 

minimizes the chance of delamination during the curing steps. polyimide was applied in 10µm 

thick layers using the pneumatic atomizer. The recipe for this print consisted of a sheath gas 

mass flow rate of 80 SCCM, 800 SCCM pneumatic atomizer mass flow rate, 775 SCCM exhaust 

mass flow rate, a 300µm tip and speed of 1 

mm

s

The part then placed on a hot plate to soft bake up 

to 200°C. The soft bake help flash off solvents in the polyimide in the bottom layers prior to 

adding further layers. This minimizes the potential for delamination and bubble formation in the 

substrate. The final hard cure was 300°C for three hours. The final dielectric height was 41.5µm 

(not accounting for surface roughness). The measurement results are given in Fig 4.7. 

Figure 4.7: Polyimide height measurement 

To minimize the electrical losses in the silver, the target thickness of the silver is chosen 

to be multiple times larger than the skin depth. The skin depth can be calculated using equation 

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4.12 [22]. 

δ = √

2
ωμσ

(4.12) 

Where ω is the frequency of the signal in radians per second, µ is the conductivity or 

permeability of silver, and σ is the conductivity of silver(ω = 2 × π × freq, μ =

4 × π × 10−7 × 0.9998, σ = 6.173 × 107 × 0.2). This gives a skin depth of 0.8µm. The skin 

dept represents the value at which a signal is attenuated to 

1
 of its initial value. The thickness of 

e

the silver should be at least three times this value. The silver was deposited using the ultrasonic 

atomizer with a recipe of 75 SCCM sheath gas flow, 30 SCCM ultrasonic atomizer flow, 

$200\mu m$ tip and tip speed of 1 

mm

s

. All silver cures were subject to a hard cure of 180°C for 5 

hours. The measurement results for the silver are given in figure 4.8. 

Figure 4.8: Ka-band divider silver measurement 

The silver thickness is much more than the needed 2.4µm. The widths of the 50Ω and 

70.7Ω traces are 105µm and either 51µm or 49µm, these correspond to values within 5%. A gap 

was left in the quarter wave transformer during the initial silver print. This gap allows for 

measurement of the isolation resistor during fabrication. The power divider at this point in 

fabrication is given in figure 4.9. 

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Figure 4.9: Ka-band divider prior to resistor fabrication 

The isolation resistor was fabricated in four stages. Following each stage the resistor was 

value was measured using a 4-point probe. The first stage was printed to an arbitrary height, then 

measured. This made it possible to ensure that the resistor properties, resistivity, and resistance, 

were tracking as expected during fabrication. The following three stages were printed with the 

intention of getting closer to the desired resistance value (100Ω) without going under. Between 

each print step the part was cured in 180°C for five hours. This curing profile was selected 

because it is the curing profile of silver, and a final silver cure would still be needed to connect 

the quarter wave transformer. Curing the carbon at these temperatures helped ensure that the 

carbon ink could mechanically withstand these temperatures as well as minimize unwanted 

additional cures during the silver cure that connects the quarter wave transformers together. The 

carbon print recipe was as follows: 75 SCCM sheath gas flow, 25 SCCM ultrasonic atomizer 

flow, 200µm tip, and a speed of 1 

mm

s

. Following resistor fabrications, the quarter wave 

transformers were connected with a silver jumper. The divider following the resistor fabrication 

is given in figure 4.10. The measured resistance values between each print stage are given in 

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figure 4.11. The measured resistivity values between each print state is given in figure 4.12. 

Figure 4.10: Ka-band divider after resistor fabrication 

Figure 4.11: isolation resistor resistance values during fabrication 

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Figure 4.12: Resistivity of isolation resistors during fabrication 

The resistance value drops as the cross-sectional area is increased; however, the 

resistivity remains relatively constant regardless of cross-sectional area. This is the expected 

behavior of the resistive ink. It is simple to add more ink, but no good method of ink removal 

was tested, this is why multiple steps were used. The final resistance value was 106Ω, which is 

within 10% of the theoretical value. Additionally, this resistor is 250µm wide and 100µm long. 

This is smaller than available packaged thick film resistor and removes the requirement to mount 

a thin film resistor. This Wilkinson power divider was made homogeneously using aerosol jet 

printing, no additional forms of manufacturing or external parts were needed. The completed 

Wilkinson power divider is shown in Fig 4.13. 

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Figure 4.13: Completed Ka-band Wilkinson power divider 

The power divider was then tested using three ground-signal-ground (GSG) probes, 

manufactured by GGB Industries INC, and a 4-port network PNA-X manufactured by Keysight 

(N5245B). The network analyzer was calibrated using a short-open-load-transmit 

(SOLT) method on a CS-5 calibration substrate. This brings the reference plane to the probe tips. 

Because the three ports were measured simultaneously, 90-degree bends on the calibration 

substrate were used for the thru standard between ports 1 and 2 and ports 1 and 3. The 

measurement results are given in Fig 4.14. 

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Figure 4.14: Ka-band Wilkinson power divider results 

Measurements show that the power divider operates within common performance limits 

across a range of 15-35 GHz. Within that range, the input match (S11) is below -10 dB, the output 

port isolation (S32) is below -10 dB. The output port isolation is related to the performance of the 

printed isolation resistor. S22 and S33 are less than -20 dB in this range. The added insertion loss 

is less than 0.7 dB beyond the nominal 3 dB power splitting in the 15-25 GHz range and less 

than 0.9 dB from 15-35 GHz. The output ports are well balanced with less than 0.1 dB difference 

between S21 and S31 at a given frequency. This proves the effectiveness of the printed resistor in 

a common RF component for applications at least up to Ka band. 

4.2.3 V-Band Wilkinson Power Divider 

A V-band Wilkinson power divider was fabricated using the same method that was used 

to fabricated the Ka-band power divider with one notable expectations. This difference concerns 

how the part would be measured. It is possible to measure all three ports of the Ka-band 

Wilkinson simultaneously; however, this would not be possible with the equipment available 

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when attempting to measure in V-band, so a method was needed to convert a three-port device 

into a two-port device. This transformation was done by fabricating two separate devices and 

placing a load resistor at one of the ports. One of the dividers terminated an output port, this 

allowed for measurements to be taken for S11 and S21. The other divider would have the input 

port terminated to allow for measurements of S32, the amount of isolation between the output 

ports. These measurements were then combined to interpolate the performance of a single device 

with no terminated ports. The V-band Wilkinson power divider is shown in figure 4.15. 

Figure 4.15: Both halves of V-band Wilkinson 

The left termination, right termination, left isolation, and right isolation resistors have 

values of 80Ω, 76Ω, 113Ω, and 115Ω, respectively. The isolation resistor values are within 15% 

of the desired 100Ω and should not affect the performance of the divider significantly, and any 

degradation in performance due to this would be observed as a degradation in output port 

isolation (S32). The left and right termination resistors are off their target of 50Ω by about 60 and 

52 percent, which does have the potential to significantly impact the device performance; 

however, as can be seen in figure 4.4, the return loss at these resistance values is slightly larger 

than 10 dB. This corresponds to nearly 90 percent of the signal getting attenuated, then in the 

case of the left device, that signal is further attenuated by the isolation resistor. This combination 

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ensured that while the resistor values are far from their target, they will still be functional and 

makes the risk of additional heat cycles not worth attempting. The performance of the V-Band 

power divider is given in figure 4.16. 

Figure 4.16: Measured and simulated results of V-band power divider 

This V-band power divider a high degree of isolation, S32 is less than -15 dB, starting at 

35GHz and continuing up to at least 67GHz. Any disturbance and/or reflection that occur at one 

of the output ports will have a small effect on the opposite output port. The return loss is low, 

more than 15 dB, at and above 45 GHz up to at least 67 GHz. Therefore, more than 97% of the 

power that is incident on the input port is transmitted into the system. The insertion loss for this 

system is 1 dB larger than the ideal 3 dB split in the frequency range 37.2 - 65.3 GHz. The 

insertion loss improves to being within 0.5 dB when the frequency range is further restricted to 

45.6 - 58 GHz. 

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CHAPTER 5: Conclusions and Future Work 

It was shown in this thesis that using commercially available carbon black ink can be 

used in the AJP process. The ink was characterized to determine its resistivity and geometrical 

properties. Knowing the resistivity value is what will give engineers the ability to customize the 

resistor value and geometry to the needs of a given application. An additional understanding of 

how the resistor changes during cure will allow those using AJP to print resistors reliably and 

with fewer tuning steps. This thesis has also shown that these printed resistors can be used in RF 

components and their effectiveness was shown up to V-band. Practical termination resistors were 

shown effective through W-band. This could have significant practical uses in both component 

fabrication and packaging as the world moves to utilize higher regions of the RF spectrum. 

While this thesis was a step in the right direction to prove the effectiveness of printing resistors, 

some work remains. 

5.1 Altering Ink Resistivity 

Resistor size was a significant obstacle throughout the course of this work. The best 

method that existed to decrease the resistance value of a given device was to attempt to increase 

height and/or increase the device width. It would be beneficial if there was a method to lower the 

resistivity of the ink. This could potentially be done in a few ways.  

Experiment with the curing process to see if there is a recipe that would lower resistance 

further without damaging the device. It was shown in chapter 3 that converting from the 100°C 

30-minute cure to the 180°C 5-hour cure did lower the resistivity value, but no work was done to 

find the optimal curing profile. The environment (atmosphere) that the resistors were cured in 

was never changed. While it was uncommon, there were instances where the resistive ink would 

crack during the curing process. Placing the device under vacuum during cure may help remove 

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excess air from the ink prior to the ink hardening. Removing this access air may help prevent 

cracking as well as make resistor less porous, leading to a lower resistivity. 

At no point in the course of this work was the ink recipe altered. It may be possible to add 

certain materials to the ink to change the ink's carbon-solvent ratio. Future work could focus on 

introducing water to the ink to lower the carbon-water ratio of the ink. This could lower the 

amount of carbon deposited using the same print while also lowering the viscosity and enabling 

more precise printing. Additionally, this work could be expanded past water and include studies 

on adding other materials with different resistivity values, such as adding small amounts of 

highly conductive ink. It is possible that mixing in lower resistivity materials may help lower the 

overall resistivity; however, it is also possible that small channels consisting of low resistivity 

materials form and bypass the less conductive ink. 

5.2 Power Testing 

Power testing the resistor would be beneficial. If the power handling capabilities of the 

ink were known, the limits of what is possible with the ink would similarly be known. This 

would be difficult given that power handling is heavily affected by resistor size and resistor size 

is variable using this fabrication process. The power testing would need to be done both at DC 

and RF. While this thesis did prove that the printed resistors worked in RF circuits, the power 

levels were extremely low. DC testing of the device was normally kept between -1 and 1 volt, 

and never more than 20mA across the resistor. 

5.3 Additional Circuits 

It would be beneficial to use this process in additional circuits to further test the abilities 

of the printed resistors. Devices such as attenuators could be made. Given that the resistance can 

be fabricated as desired, the resistance value can also be tuned, operators are no longer confined 

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to commercially available values. This could make attenuators that have attenuation values from 

0dB all the way to complete attenuation. Additionally, having the ability to control resistance 

could help fabricate resistive power dividers with various power splitting ratios. 

Fabricating termination resistors was also possible. This could have wide ranging uses in 

any device that requires termination resistors such as branch line couplers, rat race splitters, and 

terminated transmission lines. 

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[3]   K. Grammer, J. Albrecht, P. Chahal, M. Hodek and J. Papapolymerou, "Low-Power 

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