Parent Category: 2018 HFE

*By Firooz Faili, Julian Anaya Calvo, Thomas Obeloer and Daniel Twitchen*

RF resistors able to operate above 8 GHz while handing >100 W are critical for successful operation of phased array radar and 5G wireless infrastructure. Fabrication of high power resistors able to operate above S-Band requires reducing its parasitic electrical characteristics to a minimum. In this work it is demonstrated that this cannot be achieved with traditional substrates (AlN and BeO), but would be achievable by using CVD diamond. This will be illustrated primarily through the evaluation of resistor parameter ‘capacitance per watt’. Comparison of the performance of the different substrates for high power resistors using a model of a 75 W Wilkinson divider operating at 10 GHz, will be presented as well.

**Introduction**

The millimeter wave market demands solutions that offer GHz performance at high output power levels. With the designation of the operating spectrum for 5G at above 6 GHz [1,2], and high-performance phased arrays radars operating in the X and Ku bands [3], there is significant drive for passive components able to handle high power density at higher frequencies.

To date beryllium oxide (BeO) and aluminum nitride (AlN) have been the preferred substrates for high power RF resistors. These ceramic materials have relatively high thermal conductivity and enable resistors to handle tens to hundreds of watts when operating at L and S bands (1 4 GHz). However, when operating from X band up to Ku band (8 30 GHz), the trade-off between maximizing the dissipated power and reducing resistor parasitic effects leads to a diminished ability of dissipating few watts when using BeO or AlN substrates. This limitation in management of power at higher frequency will become a bottleneck for extending high power applications above S-band. What is proposed here is an enabling solution for RF resistors capable of operating above 8 GHz while handing over 100 W by using CVD diamond as the resistor substrate.

**Substrates for GHz Resistive**

Table 1 summarizes the values of the key parameters affecting performance for the different high thermal conductivity substrates used in RF resistors. It is evident that AlN, with the highest permittivity and the lowest thermal conductivity will perform worse than BeO, and diamond having the best combination of low permittivity and highest thermal conductivity would excel as a high frequency resistive substrate. Diamond’s permittivity is ~15-35% lower than those of BeO and AlN respectively and remains stable with changes in frequency and temperature, varying by only 5% from low frequencies up to tens of GHz, and only shifting by 730 ppm/°C from room temperature up to few hundreds of °C (Fig. 1-a) [4].

Table 1 • Resistive Substrates Properties (permittivity, loss tangent, thermal conductivity and thermal expansion).

Temperature is also important when considering the thermal conductivity. At 125°C the thermal conductivity values for AlN and BeO are reduced by 30-40% from room temperature values. Thermal conductivity of the purest single crystal diamond may exceed AlN and BeO by a factor of ~10-15, which roughly would means that a resistor using diamond should be able to handle 10-15 times more power. When considering polycrystalline diamond as a resistive substrate with thermal conductivity ranging from 1000 W/mK to 1800 W/mK, a 4-8x improvement in performance over that of AlN and BeO could be realized

ε_{r}tan δ **κ **(W/mK)α (ppm/K)

AlN8.88^{8}3.5x10^{-3}188^{9}3.55^{12}

(8.5GHz)(8.5GHz)^{8}

BeO6.75^{8}4x10^{-4}260-300^{10}6.48^{12}

(8.65GHz)(8.7GHz)^{8}

Diamond5.72^{7}5x10^{-5}>2000^{11}1.79^{12}

(>1GHz)^{7}

**Figure of Merit (Capacitance/Watt)**

To show the impact of the parasitic capacitance and inductance at GHz frequencies on the resistor’s performance we used a standard lumped model of a thin resistor [4,6]. This includes the parasitic inductance of the resistor metallic film and contacts, and the parasitic capacitance of the structure.

Typically the deviation from an ideal resistor is given by the voltage standing wave ratio (VSWR) which for a resistor is calculated as:

VSWR = max(Z_{0},Z(ν))/min(Z_{0},Z(ν)),

with Z_{0} the ideal resistance and Z(ν) the impedance calculated from the resistor equivalent circuit.

The frequency at which the VSWR of the resistor reaches 1.25 (-19 dB); a common metric for the quality of a resistor; is shown in Fig. 1-a as a function of the parasitic capacitance. This figure illustrates how the parasitic capacitance affects the behavior of the resistor. As an example for a 50 Ω resistor operating at X-band, a parasitic capacity lower than 0.4 pF is needed to achieve a VSWR equal or lower than 1.25. If the frequency is increased to K-band, the capacitance needs to be half this value. Expectedly increasing the resistance requires even lower capacitance values [4]. To calculate the capacitance of a single-sided, mounted resistor on a given dielectric we approximate the behavior of the thin film resistor to that of a very lossy transmission line [5]. For simplicity it is assumed that contacts and resistor area have similar width (W), and that “contact width” Wc (inset Fig. 1-b) is fixed to 0.2 mm. The aspect ratio W/L (L is the resistor length) of the resistor is also fixed to 0.5 for simplicity. With these simplifications calculating the capacitance of the geometry is straightforward from the optimized design equations derived for calculating capacitances in micro-strips [16].

Fig. 1 a). Frequency at which the VSWR of the resistor reaches 1.25 as a function of the parasitic capacitance for a 50 Ω and 100 Ω resistor and 0.1 nH. Inset: equivalent lumped circuit of a resistor. b) Calculated capacitances of a single-sided mounted resistor vs resistor area (0.5 aspect ratio) for different substrates. Inset: geometry of a resistor.

The total capacitance obtained for single-sided and mounted resistors on different substrates as a function of resistor area is plotted in Fig. 1-b. Comparing the three resistive substrate options with the same thickness (1mm) it is clear that diamond with its lower permittivity yields the smaller capacitance per unit area value. Even a further reduction in capacitance values would be achieved through use of thinner diamond substrates enabling an improved cost/performance metric for the diamond solution. Enabled by the values obtained from Fig. 1-b, in combination with the trending curves shown in Fig. 1-a, a set of design rules are developed to choose the correct area for a resistor ensuring the VSWR below 1.25 at a given frequency and keeping and the targeted maximum power without exceeding the 125 C temperature limit.

Using that set of design rules, a finite element model of the single-sided and mounted resistor was developed to evaluate the maximum power that can be handled by different substrates. For simplicity and without loss of generality the size of the dielectric (which acts as a heat spreader) remained constant when reducing the size of the resistor (Fig. 3, top sketch).

Fig. 2 • Top: sketch of the finite element simulation domain. a) Power per capacitance of the resistors with different substrates at a maximum peak temperature of 125°C. Note that diamond substrate is 0.3 mm (1 mm for AlN and BeO), the red dash line sets the 100 W limit. b) Maximum frequencies for a 50 and 100 resistor dissipating 100 W to operate below 1.25 VSWR. C), power per capacitance normalized to the resistor on AlN.

The results of this benchmark between substrates are summarized in Fig. 3-a. In this figure the maximum power dissipated in the resistor per capacitance and not exceeding 125 ˚C is presented for different substrates. Furthermore the results are directly correlated with operational frequencies in Fig. 3-b where it follows that for a 50 resistor able to dissipate 100 W (not exceeding 125 ˚C) on AlN or BeO the frequency cut-off is limited to S-band (<5 GHz). In contrast, the use of diamond means that the operational frequency for a similar resistor exceeds 10 GHz for all the analyzed diamond grades which is the theoretical limit in the K band. It is worth nothing that these theoretical results are in very good agreement with measurements on real resistors reported elsewhere [17]. Finally, the power per capacitance normalized to the resistor on AlN is shown on figure Fig. 3-c.

Fig. 3 • Top: Typical representation of an RF Wilkinson divider and its equivalent representation using lumped ideal elements. For 10 GHz central frequency R=50 , L1=1.125 nH, C1=0.225 pF and C3=2C1. a) |S11| vs frequency of the Wilkinson divider using 100 resistors on different substrates. Inset VSWR of the Wilkinson dividers in which the 1.25 VSWR region has been highlighted. b) |S21| vs frequency of the Wilkinson divider using 100 W resistors on different substrates.

**Wilkinson Divider/Combiner**

The performance of a single stage Wilkinson divider has been chosen to illustrate the impact of the high frequency behavior of the resistors with different substrates (Fig. 4, sketch). A Wilkinson divider/combiner is a well-known and omnipresent circuit able to provide isolation between the output ports while maintaining a matched condition for all the ports [18]. However keeping this ideal behavior relies on the isolation resistor, which should satisfy the relation= 2Z_{0}, with Z_{0} the impedance of the line (fixed at R=50 Ω). Hence any deviation of the resistor impedance (ideally 100 Ω) will result in a deviation from the ideal characteristics of the divider. The performance of the divider is typically given thorough the S_{11} and S_{21} parameters of its scattering matrix, which give information about the reflection coefficient in port 1 and the transmission coefficient between ports 1 and 2 [19]. For an ideal device at the design frequency |S_{11}| is 0 and |S_{21}|=|S_{31}|=0.5 (-3 dB) [19]. These ideal characteristics have been calculated for a 10 GHz (X band) device following the derivation made by Cohen in [20] and the results are shown in Fig. 4. When the deviation from the ideal impedance is included in the isolation resistance of the Wilkinson divider model [20], the |S_{11}| and |S_{21}| characteristics shown in Fig. 4-a and Fig. 4 b are obtained for each substrate. From these results it follows that resistors using good quality diamond are able to offer excellent performance at 10 GHz; |S_{11}| is at least -20 dB at the frequency design showing a bandwidth of 9 GHz (|S_{11}|< 15 dB, black dotted line in Fig. 4-a). On the other hand, for these particular frequency and power conditions the use of low grade diamond as a resistor substrate represents the lower limit to ensure a good performance for the chosen Wilkinson divider (|S_{11}|≈-15 dB). In comparison Wilkinson dividers making use of resistors on AlN and BeO substrates show very poor characteristics around the design frequency with |S_{11}| well above -10 dB and |S_{21}| widely deviating from the optimal -3 dB (Fig. 4-b).

**Conclusions**

It has been demonstrated that by switching the substrate of high power RF resistors from AlN and BeO to CVD diamond it is possible to extend their operative frequency range well above X-band whilst handling powers above 100 W. This could offer a step change improvement towards minimizing distortion and complexity of high power electronics in 5G communications and military millimeter-wave devices operating in X-band and above.

**About the Authors**

Firooz Faili, Julian Anaya Calvo, Thomas Obeloer and Daniel Twitchen are with Element Six Technologies.

**References**

[1] NGMN Alliance, 5G White Paper, *https://www.ngmn.org/*

[2] OFCOM, *Spectrum above 6 GHz for future mobile communications,* https://www.ofcom.org.uk.

[3] E. Brookner, *Phased-Array and Radar Breakthroughs, *2007 IEEE Radar Conference, Boston, MA, 37-42, (2007)

[4] A.Ibarra et al, *Wide frequency dielectric properties of CVD diamond, *Diamond and Related Materials, 6, 856-859 (1997).

[5] R.S. Johnson et al. *Frequency response of thin film chip resistor,* Proc. of the 25th CARTS USA 2005: 136-141. (2005)

[6] K. Steinberg et al, J.Appl.Phys. *Microwave inductance of thin metal strips* 108, 096102 (2010)

[7] Z. Wang, J. Deen and A. Rahal, *Accurate Modelling of Thin-Film Resistor up to 40 GHz,* Solid-State Device Research Conference, 2002. Proceeding of the 32nd European, pp. 307-310, (2002).

[8] E.Bogatin, *Design rules for microstrip capacitance, *IEEE Transactions on components, hybrids, and manufacturing technology 11.3, 253-259, (1988).

[9] M. Bailly *Diamond Rf ™ Resistive the answer to high power and low capacity,* Microwave Journal 53.11 94-100, (2010). [10] G.P. Akishin et al. *Thermal conductivity of berylli16um oxide ceramic.* Refractories and Industrial Ceramics 50.6 465-468, (2009).

[10] E.J. Wilkinson, *An N-way Power Divider,* IRE Trans. on Microwave Theory and Techniques, 8, 116-118, (1960).

[11] L. G. Maloratsky, *Chapter 8 -Dividers and Combiners, *In Passive RF & Microwave Integrated Circuits, Newnes, Burlington, Pages 165-203, (2004).

[12] S. B. Cohn, *A class of broadband three-port TEM-mode hybrids.* IEEE Transactions on Microwave Theory and Techniques 16.2 110-116, (1968).

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