#### INTRODUCTION

High-power microwave (HPM), radio frequency (RF), directed energy weapons (DEWs) provide the Warfighter with several advantages over conventional kinetic energy weapons. Due to a relatively wide beam, HPM DEWs can engage multiple targets at the speed of light and with a high probability of hit. They can produce a range of effects that vary from long-term electronic upset to permanent damage, depending upon the target’s vulnerability level and range. Most importantly, they have a relatively unlimited supply of “low-cost ammo” (i.e., a “deep magazine of RF/microwave pulses”), limited only by the power and fuel capacity of the host platform/vehicle, which can lead to less logistics and costs.

The first step in evaluating the feasibility of an HPM DEW concept is to determine how much power is required for the weapon system to produce the desired effect at the desired range. Once we know the power required, we can compare this to the power available on the weapon platform to see if it is within its limits.

HPM DEWs can engage multiple targets at the speed of light and with a high probability of hit.

This article is divided into two basic sections. The first section describes the methodology, physics, and mathematics required to calculate the power requirements of an HPM DEW system. The process and equations described herein have further been integrated into an easy-to-use Excel™-based tool known as the Radio Frequency, Directed Energy Weapon Design Tool (RFDEDT). The second section of this article walks through a fictional example using the RFDEDT. The RFDEDT allows a user to specify the power density required at the target for an effect (i.e., the target effect/vulnerability level) and range, and the tool computes the effective radiated power (ERP) required for an HPM DEW system. The tool then computes the peak transmitter power required based on other user inputs, such as the antenna size and efficiency. The tool works backward to compute the total prime power required for the weapon system based on user inputs for the modulation needed to affect the target (i.e., pulse width and pulse repetition frequency [PRF]) and the efficiencies of the transmitter, modulator, and prime power supply. Once the user knows the total power required for the HPM DEW, he or she can compare the power available from the host platform/vehicle to determine if the HPM DEW concept is feasible from a power standpoint.

#### METHODOLOGY

The overarching approach to develop an HPM DEW system is shown as a five-step block diagram in Figure 1 [1]. The first step is to define the targets of interest and desired engagement range for those targets. Second, HPM power density required on the target to produce an effect, either electronic upset or damage, must be estimated. Third, the power/system requirements are developed. Fourth, the HPM DEW system is designed. And finally, the HPM DEW system is built and tested.

Given the desired targets and engagement range, we then need to estimate the required target effect level from our HPM DEW system. HPM typically enters a target through some port of entry and travels to the critical components. If the power at the component is greater than the component’s effect level, then there is a probability of effect. Ideally, if the target system is available for HPM effects experiments, we should determine the target effect level distribution based on experimental data and use the data to develop probability of target effect curves as a function of the incident HPM power density on the target. However, if this is not possible, we can roughly estimate the target effect level, *S*, by estimating the power required for component effect, *P _{c}*, the effective area of the HPM

*POE*,

*A*, and the HPM loss along the path from

_{e}*POE*to the component, as shown in Figure 1 and equation 1.

Figure 1: Methodology for Developing an HPM DEW System (Source: SURVICE Engineering Company).

*S = P _{c} / A_{e} L. (1)*

Once we know the target effect level, *S*, and the desired engagement range, *R*, we can compute the HPM DEW’s peak *ERP*, *ERP _{p}*, required to produce a target effect, as shown in equation 2.

*ERP _{p} = 4πR^{2} S. (2)*

This equation is a variation on the transmission equation and assumes that the HPM DEW is irradiating into free space and experiences no atmospheric losses. For frequencies from 1 to 10 GHz, this is a reasonable assumption unless the range is very large (i.e., tens of kilometers). The *ERP* is defined as the product of the transmitter’s power, *P*, and antenna gain, *G*, as shown in equation 3.

*ERP = PG. (3)*

Therefore, based on this equation, we can compute the transmitter power required for the HPM DEW by dividing the ERP by the antenna’s gain.

HPM DEWs typically need very high gain antennas to direct the HPM at the target and reduce the amount of power out of the transmitter. For RF/ microwave frequencies, this means the antennas need to be large compared to the wavelength of the radiation they are transmitting. Typically, antennas that can handle high power use a circular of rectangular aperture that is large relative to the radiation wavelength. The gain of an aperture-type antenna is based on the physical area of the aperture,* A*, its antenna efficiency, *N*, and the radiation wavelength, *λ*, as shown in equation 4.

*G = 4πAN/ λ ^{2}. (4)*

HPM DEWs typically need very high gain antennas to direct the HPM at the target and reduce the amount of power out of the transmitter.

For a circular aperture, with diameter, *D*, the gain is given by *G = (πD/λ) ^{2} N.*

Related to an antenna’s gain is its beam width. The half power beam width in degrees, *B*, of a circular aperture antenna with a radius, *D*, in meters is given in equation 5.

*B = kλ/D, (5)*

where *k* is a factor which varies depending on the shape of the reflector and the illumination pattern of the antenna feed. For a uniformly illuminated parabolic reflector, *k* is typically about 57 (the number of degrees in a radian). For a “typical” parabolic antenna without uniform illumination, *k* is approximately 70.

The radiation spot size (diameter), *d*, at a target is related to the antenna’s beam width, *B*, and target range, *R*, as shown in equation 6.

*d = 2R tan (B/2). (6)*

Another important parameter for an antenna is its far field boundary, which is defined as the distance from an antenna at which the RF radiation is essentially a plane wave and the power density from an HPM DEW decreases proportional to the inverse square of the distance. The minimum far field boundary of an antenna, *FF*, depends upon the largest dimension of the antenna aperture, *D*, and the wavelength being radiated, *λ*, as shown in equation 7.

*FF = 2D ^{2} / λ. (7)*

Once we know the gain of the antenna, we can compute the peak transmitter power,* P _{p}*, required for an HPM DEW by dividing the peak

*ERP*by the antenna gain, as shown in equation 8.

*P _{p} = ERP_{p} /G. (8)*

Since we are eventually interested in determining the total average prime power required for the HPM DEW, we convert the peak transmitter power required to average power,* P _{a}*, by multiplying the peak power by the HPM source’s pulse width,

*τ*, and

*PRF*,

*f*, as shown in equation 9.

_{r}*P _{a} = P_{p} τ f_{r}. (9)*

The product of the pulse width and *PRF* is known as the duty cycle of the HPM DEW system.

Unfortunately, transmitters are typically not 100% efficient due to internal losses, so some of the input power (power provided by the modulator) does not produce HPM radiation and is wasted as heat. The wasted power for a transmitter, *P _{TW}*, can be estimated by equation 10.

*P _{TW} = P_{a} (100 – E_{T})/100, (10)*

where *P _{a}* is the average input power of the transmitter and

*E*is the transmitter’s efficiency. Here, we define the transmitter’s efficiency as the transmitter’s output power divided by the input power.

_{T}Now that we know the total average power required for the transmitter, *P _{a}*, and the transmitter’s efficiency, we can compute the output power required from the modulator to drive the transmitter,

*P*, as follows:

_{M}*P _{M} = P_{a} / E_{T}. (11)*

As with the transmitter, modulators are typically not 100% efficient due to internal circuit losses, so some of the power is wasted in the form of heat. The power wasted in the modulator, *P _{MW}*, can be estimated by equation 12.

*P _{MW} = P_{M} (100 – E_{M})/100, (12)*

where *E _{M }*is the efficiency of the modulator.

Once we know the modulator power, *P _{M}*, we can compute the power required of the prime power system,

*P*, to drive the modulator as follows:

_{PR}*P _{PR} = P_{M} /E_{M}, (13)*

where* E _{M } *is defined as the efficiency of the modulator.

Prime power supplies for an HPM DEW are also not 100% efficient and waste some of the power. The total power needed to produce HPM, *P _{HPM}*, is given by equation 14.

*P _{HPM} = P_{PR} / E_{PP}, (14)*

where *E _{PP}* is defined as the efficiency of the prime power supply.

The power wasted by the prime power supply, *P _{PPW}*, is given by equation 15.

*P _{PPW} = P_{RF} (100 – E_{PP})/100. (15)*

Equation 14 represents the total prime power required for the HPM DEW to produce sufficient power at the target for an effect, but it is not the total prime power required for the HPM DEW system. Since the HPM DEW has other subsystems requiring power, we must include them in our power budget calculations. For example, an HPM DEW will most likely use vacuum tubes for the high-power transmitter, such as magnetrons and klystrons. These tubes require power for their filament and high-voltage power supplies. This is known as the transmitter’s “house-keeping power,”* P _{H}*. Further, the transmitter may require a vacuum pump to prevent voltage breakdown within the tube; this also requires power,

*P*. Finally, the HPM DEW will probably need power for the antenna control system,

_{VP}*P*(to point the antenna toward the target), power for a sensor to detect the target,

_{AC}*P*, and power for other auxiliary subsystems,

_{s}*P*.

_{AUX}

Prime power supplies for an HPM DEW are also not 100% efficient and waste some of the power.

Therefore, the total power required for an HPM DEW system, *P _{Total}*, is given by the sum of the power required for each of the subsystems as follows:

*P _{Total} = P_{HPM} + P_{H} + P_{VP} + P_{AC} + P_{AC} + P_{AUX} . (16)*

The total wasted power that must be removed by the thermal management cooling,* P _{TotalW}*, is the sum of the waste power from each of the major HPM DEW subsystems as given by equation 17.

*P _{TotalW} = P_{TW} + P_{MW} + P_{PPW}. (17)*

#### USING THE RFDEDT

All the equations discussed in the Methodology section have been built into the RFDEDT to quickly compute the total power required for a notional HPM DEW system. Figure 2 shows the main screen for the RFDEDT, along with fictional example values. In this section, we will walk through a fictional example to demonstrate use of the RFDEDT. All the numbers used in the example are totally fiction and meant only to demonstrate how to use the tool.

Figure 2: Screen Shot of the RFDEDT With Fictional Values Shown (Source: SURVICE Engineering Company).

We start with the “Target” block shown on the lower right of the main screen. The inputs to the tool are shown in green and the calculated values shown in black. For the Target block, the user inputs are the target effect level required and the target range. Based on equation 2, the tool calculates that we would need 50 GW of *ERP *to affect a target at 2000 m, with a target effect level of 0.1 W/cm². Next, we input the HPM DEW’s pulse width, *PRF*, and the dwell time on target for effect. For an HPM DEW that produces 1-μs pulses at 100 Hz, the duty cycle would be 1 X 10^{-4}. The average ERP required to affect the target would be 5 MW.

Next, we go to the “Antenna” block shown in the upper right corner of the main screen. Here, we calculate the antenna gain based on the user inputs of antenna size/diameter, the antenna efficiency, and the HPM frequency/ wavelength. Based on equations 4 and 5, we see that a circular, 3-m diameter antenna with an efficiency of 60% and radiating at a frequency of 1000 MHz would provide a gain of 592 (or 27.7 dB). Further, the antenna’s beam width would be about 7 degrees, producing a beam spot size diameter of 236 m at the target range of 2000 m. The far field boundary for such an antenna is estimated to be about 60 m.

The “Transmitter” block to the left of the Antenna block will calculate the peak and average transmitter power required for the HPM DEW to affect the target. Based on equation 3, the peak transmitter power required to produce a peak *ERP* of 50 GW is 85 MW. With this peak power, the average transmitter output power would be about 8.5 kW, based on the duty cycle assumed. The primary user input for the Transmitter block is the efficiency of the transmitter. For our example, we have assumed a transmitter efficiency of about 50%, which is a reasonable number for very high-power tubes [2]. Based on equation 11, we see that for a transmitter with an efficiency of 50% to produce 8.5 kW of average power, the modulator must provide at least 17 kW into the transmitter. Since not all the transmitter’s input power is converted to HPM, based on equation 10, the wasted power is estimated to be about 4 kW.

The “Modulator” block will determine how much power is required from the modulator to drive the transmitter. For the modulator, the primary user input is the efficiency. For our example, we have assumed a modulator efficiency of 75%, which is a typical efficiency for a modulator based on a pulse-forming network made from inductors and capacitors [2]. With a modulator efficiency of 75%, the prime power required to drive the modulator is estimated to be about 23 kW, with a waste power of about 4 kW.

Finally, we go to the “Prime Power Supply” block on the main screen. For the prime power supply, the primary user input is the efficiency of the prime power supply. For our example, we have assumed a prime power supply efficiency of 90%, which is reasonable for prime power supplies such as generators [3]. Based on equation 14, the total prime power required for an HPM DEW to affect the target is estimated to be about 25 kW. Since we assumed that we must irradiate the target for a dwell time of 3 s, this means we must have at least 75 kJ of energy.

It must be emphasized that this is the power/energy needed just to produce the HPM energy necessary to affect the target at range. We must also consider the power requirements for other parts of the HPM DEW system. For our example, we have assumed that we will need about 56 W of filament power for the transmitter, 10 kW for the antenna control system, 1 kW for the sensors, and 1 kW for the vacuum pumps to prevent voltage breakdown in the tube. Therefore, the total power required to drive the HPM DEW system is estimated to be about 37 kW, and the total waste power is estimated to be about 10 kW.

At this point, the user can compare the total power estimated to be required for an HPM DEW concept to the power available from the proposed platform. If the power required is less than the available power, the concept may be feasible from a power budget standpoint. If the power available is less than the power required, then the concept may not be feasible or require a larger prime power generator.

#### CONCLUSION AND FUTURE PLANS

The RFDEDT tool is meant to only provide an estimate of the total power required for an HPM DEW and is very dependent upon the user inputs and assumptions. For an actual HPM system design, one should add a safety power margin to the computed value to ensure that the weapon has a high probability of target effect.

To fully evaluate the feasibility of an HPM DEW concept, it is also important to perform a technology survey to determine if there is commercially available equipment that meets the HPM DEW requirements or whether new technology must be developed. To assist in this problem, the RFDEDT also has subscreens for the transmitter, the modulator, and the prime power supply that provide some of the available commercial equipment. In the future, we hope to add size and weight for each of the subsystems to estimate the total size, weight, and power (and cooling) required for an HPM DEW concept. In the interim, we hope this design tool will be useful to HPM weapon concept developers to quickly and easily determine the power requirements. It has been reviewed to ensure correct calculations for the inputs used, but it is not a commercial application. HPM concept developers should follow the basic design methodology that has been presented and are encouraged to take advantage of the RFDEDT. Please contact the author for more information and/or to obtain a copy of the RFDEDT.