Switching Power Supply

Transcription

1 Switching Power Supply Submitted to: Professor Joseph Picone ECE 4522: Senior Design II Department of Electrical and Computer Engineering Mississippi State University Mississippi State, Mississippi April 28, 2003 Submitted by: Team Leader: F. Runnels Team Members: T. Carpenter, C. Jones, D. Lenoir, and J. Stevens Faculty Advisor: Dr. Noel Schulz Department of Electrical and Computer Engineering Mississippi State University {flr1, tjc1, djl4, ECE 4522 April 28, 2003

2 SWITCHING POWER SUPPLY DOCUMENTATION TABLE OF CONTENTS 1. PROBLEM 1 2. OBJECTIVES Delivering Constant Voltage with Varying Input Voltage Performance In Varying Weather Conditions Efficiency And Circuit Protection FCC and IEC Regulations Size and Cost 4 3. APPROACH Surge Protection Input Rectification Switching Flyback Transformer Output Rectification Feedback Network Controller Circuitry TEST SPECIFICATIONS Pspice Cadence Oscilloscope High Voltage Lab Heat Chamber ESD Simulator EPOCH-10 Multi-Amp Spectrum Analyzer TEST CERTIFICATION Pspice Cadence Oscilloscope High Voltage Lab 31

3 SWITCHING POWER SUPPLY DOCUMENTATION 5.5. Heat Chamber ESD Simulator EPOCH-10 Multi-Amp Specturm Analyzer SUMMARY AND FUTURE WORK ACKNOWLEDGEMENTS REFERENCES APPENDIX 40

4 SWITCHING POWER SUPPLY DOCUMENTATION EXECUTIVE SUMMARY Power supplies are being used more and more in industries throughout the world. Companies want more efficient and better-designed power supplies to meet their specifications. Traditional switching power supplies can only handle input voltages ranging from 90 to 265 VDC. The companies that need to use a wider range of input voltages have to spend more money for additional power supplies to compensate for this wider range of voltages. There needs to be a switching power supply that is capable of handling a wider range of input voltages and more efficient than the commercial power supplies available. Mississippi Power Company (MPC) has carefully designed a switching power supply of this caliber; however, they have some problems with their design. The main problems with their design were the PCB layout, the MOSFET overheating, the voltage spikes on the output, and extremely high noise emission levels. The first approach considered to correct these problems was to design a filter that would filter out any unwanted harmonics in the circuit, but this approach proved to be ineffective. Soft switching was also considered, but it is difficult to implement because the circuit has to be tuned precisely before implementation can be done. Designing a snubber circuit and a new PCB layout proved to be the best approach to meet the design constraints. The snubber circuit consists of a resistor, capacitor, and a diode. The ringing frequency was measured from the MOSFET. This value was used to calculate the value of the capacitor (720 pf). The value of 1kΩ was chosen for the resistor, and the diode is a MUR 1100E. This caused the MOSFET to stop overheating as well as produced less voltage spikes on the output. The new PCB layout has shorter, fatter traces that helped to reduce the noise emission level. The power supply that MPC designed had voltage spikes that ranged from 6 to 8 V. The redesigned power supply only has voltage spikes that range from 0.7 to 1.2 V. MPC s design only had a constant 13.5 VDC on the output. After designing the snubber circuit and the new layout, the redesigned power supply met the design constraint of 13.5 VDC on the output. In higher power level power supplies, the snubber circuit usually causes the power supply to be less efficient; however, the efficiency of this design stayed the same. The power supply that MPC designed was 85% efficient, and the redesigned power supply was 84.9% efficient. One of the other constraints was to have 40 Watts of output power. The power supply produces 41 Watts of output power at full load. At full load, the resistance is about 4.44 Ω and the output current is 3.04 A. The redesigned power supply, will allow Mississippi Power to be able to do away with their conventional power supplies. Since Mississippi Power currently has to use three power supplies, the newly designed power supply will be more cost efficient. Similar switching power supplies exist, but there range of input voltages does not meet Mississippi Power s requirements. There are only a few switching power supplies that can handle an input voltage of 310 VAC. Those power supplies are rated for a smaller range of input voltages, and do not have some the capabilities of the power supply that was redesigned.

5 SWITCHING POWER SUPPLY: DOCUMENTATION Page 1 of PROBLEM The traditional AC to low voltage DC power supply used in the electric utility industry typically has a fixed input voltage rated at 120VAC or 130VDC. Past applications tended to be telemetry and other electronic equipment located within substation environments where 120VAC station service or 130VDC station battery service was available. At almost all residential/commercial/small industrial customer service points, the only active component has been the energy meter. However, over the past 10 years the need for telemetry data from industrial and commercial customer service points has increased. With this increased demand for data has came the demand for low voltage DC to power communications as well as other microprocessor based monitoring equipment [1]. Within the electric utility environment, voltage at the meter point depending upon service type may range from 66VAC to 310VAC phase to ground, which is a wide range for the linear power supplies used in the past. Vendors have attempted to compensate by adding multiple input voltage taps. The linemen had to then select what input voltage would be used by the power supply either by wiring the input voltage to a particular terminal appropriate for the applied voltage or the selection of the input voltage via a slide switch. In practice, Mississippi Power Company Metering Services has experienced an approximate 5% failure by trained employees who failed to select the correct tap when installing these type power supplies. Assuming a commercially power supply cost of $100, 0.5 hours to replace the failed unit, and a $65 per hour labor rate, the cost of each failure is $ With a wide range switching power supply, these losses could be eliminated [2]. At present switching power supplies are available with input voltages ranging from 90 to 265VAC [3]. Since the utility companies also routinely use 277VAC services, this range is not adequate. Therefore, the utility companies are forced the stock several different power supplies or instrument transformers that can be used to match the service voltage to that of the power supply. In 1995 Bryan Seal, a senior engineer at Mississippi Power, led a team of engineers to build power supply that would address the problems they had with the conventional power supplies. The team designed a switching power supply and then installed it in about a hundred various units. However, the power supplies have some problems. The main problem is that the power supplies are electronically too noisy. The output signal had several transients on it. These transients would spike up to 3 volts higher than the intended output voltage of 13.5 volts. Mississippi Power asked for analysis of their current power supply and for a more efficient power supply design [3]. The power supply that Mississippi Power needs should be able to accept an input voltage anywhere from 90 to 310 VAC. They need a continuous DC output voltage of 13.5 volts, with a tolerance of +/- 5%. The power supply also needs to supply 40 watts of power. Mississippi Power also requires that noise level be below 200 mv peak-to-peak. The power supply should be constructed for less than $100, since to be competitive with conventional power supplies [2]. ECE 4522 April 28, 2003

6 SWITCHING POWER SUPPLY DOCUMENTATION Page 2 of 45 Since the input voltage will so wide, the utility companies will not have to stock other power supply types and instrument transformers. Therefore the equipment inventory for the utility companies will be reduced. Also there will be the benefit of increasing inventory turn over and lowering handling cost. An additional benefit is the reduction in training time necessary for single type power supply installation over various other linear and switching power supply designs [2]. 2. OBJECTIVES The main problem with the original power supply that Mississippi Power Company (MPC) designed was that it had several voltage spikes on the output signal ranging from 6.5 to 8.5 VAC (pk-pk). These spikes caused the device that was being powered to reset. Another problem with MPC s design was that the electromagnetic interference (EMI) created by the power supply was interfering with the cellular transmissions of their equipment. The objectives of the redesigned power supply consist of five technical requirements and five real world constraints. The major concerns of the new design are output noise reduction, EMI reduction, and operating efficiency improvement. The new design will achieve 13.5 VDC +/- 1.5% output with enough power to supply a small 40- watt radio transmitter. The EMI of the new power supply will be reduced to conform to FCC class 15 emissions. 1. Performance: The design will achieve 13.5 VDC output with a ripple voltage of less than 0.2 VAC rms. 2. Performance: The design will be able to operate between the temperature ranges of -20 to 60 C (-4 to 120 F). 3. Performance: The power supply will withstand stray voltages from lightning strikes of up to 10 times the maximum input voltage value. 4. Performance: The operating efficiency of the new design will range from 68% at no load to 85% at full load. 5. Performance: Fault protection will be added to reset the device in 10 milliseconds if a ground fault is connected to the output. 6. Performance: The device will be able to accept input voltages ranging from 90 to 310 VAC rms. 7. Power: The new power supply will provide 40 watts of power to the load at a full load current of 3 amps. 8. Standards: The system will conform to FCC class 15 emissions and IEC950 surge standards.

7 SWITCHING POWER SUPPLY DOCUMENTATION Page 3 of Physical Packaging: The new design will be packaged in a molded plastic container measuring 3 high, 6 wide, and 9 deep. 10. Cost: The cost for the new design will not exceed $100 excluding the cost of having the board manufactured. The above constraints are a set of goals that MPC would like to have accomplished with the new design. However, the main goal is to focus on redesigning MPC s power supply to have a 13.5 VDC output at a noise level less than 0.2 VAC rms. Once this goal is accomplished, the other constraints will be investigated if time permits Delivering Constant Voltage with a Varying Input Voltage The power supply will be used to power a 40-watt voltage-sensitive cellular transmitter that requires 13.5 VDC. Since the transmitter is voltage sensitive, it is important to make sure that voltage used to supply it has a ripple voltage less than 0.2 VAC rms. If the ripple voltage is higher the transmitter may not operate properly. The new power supply will be able to accept an input voltage ranging from 90 to 310 VAC rms [2] and convert it to a constant 13.5 VDC +/- 1.5% at 40 watts Performance In Varying Weather Conditions MPC will install the power supplies outside where varying temperatures and weather could affect performance. Because of this, the power supply will be designed so that it is able to withstand temperatures from -20 to 60 C. The new design will also reject stray voltages up to 3,100 VAC rms (8800 Vpk-pk) from lightening strikes that could potentially cause failure to the power supply Efficiency And Circuit Protection The efficiency of the power supply will range from 68% at no load to 85% at full load. These numbers are based on typical switching power supplies that usually have an efficiency rate between 70% and 85% [1]. The power supply will protected from ground faults such as a short circuit. If an overcurrent or ground fault occurs, the power supply will reset within 10 milliseconds; therefore, protecting the circuitry of the unit. If the fault occurs continuously for 5 reset cycles, the power supply will shut off FCC and IEC Regulations FCC class 15 emission standards state that no devices can emit, intentionally or nonintentionally, frequencies that will interfere with established communication organizations operating in the area [4]. Due to the lack of proper equipment, the power supply cannot be tested at this university. MPC can test the power supply by sending it to a FCC testing facility. By reducing the noise and increasing the efficiency, the power supply is more likely to pass the FCC class 15 emissions. IEC 950 specifies rules

8 SWITCHING POWER SUPPLY DOCUMENTATION Page 4 of 45 regarding construction, insulation, and safety features of electronic equipment. Basically this standard specifies the minimum distance different components can be spaced on a PCB. The power supply layout will conform to this standard Size and Cost The size of the new power supply will be no larger than the old prototype. Since MPC will be mounting the power supplies on utility poles, they want the size to be as small as possible. The power supply should be no larger than 3 x 6 x 9. The cost of power supplies on the market today is about $100. Therefore, the component cost of the new power supply should not exceed this value. The cost of board manufacturing is excluded from this cost because MPC will negotiate this price with the board manufacturer. 3. APPROACH The traditional approach to designing a switching power supply is shown in Figure 3.1 [1]. In redesigning Mississippi Power s prototype, a slightly different approach was taken. First, the values of components used in the prototype used by Mississippi Power had to be verified. The block diagram of a typical switching power supply is shown in figure 3.2. In the redesign process, some components were changed to achieve a more optimal design. Two major design changes were the addition of a snubbing circuit on the MOSFET switch and a new PCB layout. Figure 3.1. Traditional Approach to Designing a Switching Power Supply

9 SWITCHING POWER SUPPLY DOCUMENTATION Page 5 of 45 VAC Surge Protection Input Rectification Switching Flyback Transformer Output Rectification VDC Controller Feedback Figure 3.2. Block Diagram of a Switching Power Supply 3.1. Surge Protection For simple design purposes, a MOV and a fuse were used for surge protection at the input of the power supply. The MOV was used because it will shunt voltage spikes of 3kV or higher to ground. The fuse was used because it will blow in case of over currents. An MOV and a zener diode was also added to the output of the power supply to protect from any electro-static discharge that the power supply may encounter by personnel touching the output connectors Input Rectification The input rectification stage will be able to convert input voltages that range from 90 to 310 VAC and convert them to DC voltages. The rectification stage consists of a common mode inductor (used to isolate the circuit), a full bridge rectifier, and capacitors. An important consideration in this stage is to choose diodes that are capable of handling the high input voltages. Figure shows the PSpice schematic that was used to simulate the input rectification stage. The equation used to calculate the correct input capacitance values for the rectification circuit is shown in equation [1]. C in 0.3* P in( avg ) = (3.2.1) f * V * V in in(min) ripple( pk pk )

10 SWITCHING POWER SUPPLY DOCUMENTATION Page 6 of 45 Where: f in is the frequency from the supplied voltage V in is the minimum peak rectified value of the AC line V ripple is the peak to peak droop in voltage desired across the input capacitor Diodes were chosen from calculations of maximum input current and voltage. The minimum input was calculated using the input voltage of 90 VAC, and maximum input voltage was specified as 310 VAC. Equations 3.2.2, 3.2.3, and were used to select the correct input rectification diodes [1]. VR 1.414* Vin( pk pk)(max) (3.2.2) I 1.5* I (3.2.3) I F FSM in( DC)(max) 5* I (3.2.4) F Figure PSpice Schematic of Input Rectification Stage The PSpice simulation results are shown in figure These results were consistent with the results of the actual circuit. Figure is an oscilloscope picture that shows the actual results from the breadboarded prototype. The theoretical simulations are very close to actual results.

11 SWITCHING POWER SUPPLY DOCUMENTATION Page 7 of 45 Figure Simulation Results from Input Rectification Circuit Looking closely at the picture of the oscilloscope readout, figure 3.2.5, you can see the voltage measured on the input rectification is 161 VDC which is close to the simulated voltage, figure 3.2.4, of 165 VDC with a 2 V pk-pk ripple voltage. Figure Measured Output of the Input Rectification Stage

12 SWITCHING POWER SUPPLY DOCUMENTATION Page 8 of 45 Figure shows the actual circuit that was constructed on a breadboard. The breadboard prototyping was found to be insufficient for higher voltage produced from this circuit. Arch-over was noted by high-pitched popping noises from the breadboard. At the time of arch-over, the rectified voltage was noted to drop significantly. Due to the noted arch-over, further design was implemented on the original PCB. Figure Breadboard Prototype of Input Rectification Stage 3.3. Switching The switch used in the original prototype was researched and verified to be a reliable switch for the voltage and current ratings specifications for the power supply. Other MOSFET switches were researched, but the price was higher for most and others did not meet voltage and current requirements. Noise was the major problem in Mississippi Power Company s original prototype switching power supply; therefore, the main focus was to reduce the noise from the switch. Figure shows the waveform on the drain of the MOSFET switch. Noise from ringing occurs when stray inductance is between the switch and flyback transformer. This ringing can be seen as an exponentially decaying sine wave on the switch waveform.

13 SWITCHING POWER SUPPLY DOCUMENTATION Page 9 of 45 Figure Waveform at the Drain of the MOSFET Switch without Snubber This ringing propagates through the power supply and can be seen as voltage spikes of 5 to 10 volts on the output signal. Some of the voltage spikes were captured using the oscilloscope. Figure shows one of the voltage spikes spread out so the peak-to-peak voltage could be measured. Figure Noise Measured on the Output Signal without Snubber

14 SWITCHING POWER SUPPLY DOCUMENTATION Page 10 of 45 To reduce noise from the switch, various options were considered. The first option investigated was a soft-switching technique. Soft switching basically allows the MOSFET switch to turn on or off slowly to reduce the instantaneous switch in voltage [9]. Soft switching was quickly abandoned due to the complexity of tuning the power supply. The power supply we are designing here has a wide range of input voltages, which would make soft switching unfeasible in this case. Filtering can reduce some of the output noise, but will not reduce stress of ringing on the switch [11]. At first filtering was briefly researched, but snubbing circuits were the first choice for noise reduction. Snubber circuits are used to modify the switching waveforms of controllable switches [10]. There are several different types of snubbers that we researched to use in the power supply. We decided on two different snubbers to use in the power supply. The first snubber acted as a voltage clamp. When the MOSFET switches on and off, the voltage across the transformer can jump up to over twice the input voltage. Therefore, a snubber was placed across the transformer to reduce the voltage spikes [12]. A second snubber was implemented across the MOSFET in order to eliminate the stress on the switch. The snubber allowed the power from the MOSFET to be dissipated through an R-C tank [10]. The following equation shows the equation used to approximate the snubber resistor and capacitor values: f ringing 1 =. (3.3.1) R* C Because snubber circuits are hard to calculate, this equation is only an approximation. The snubber must be fine tuned through actual trial and error on the breadboard. Lower resistor values produced higher power losses but reduced the ringing significantly. Higher resistor values produced lower power losses, but there was more ringing left on the drain. A compromise between power loss and snubbing was reached after numerous combinations of resistors and capacitors. First, the ringing from the MOSFET was measured from the oscilloscope across the drain to ground. This frequency was measured to be approximately 3 MHz. After various values of resistance and capacitance were used to design the snubber, a final value of approximately 1 kω and 760 pf was used. A MUR1100E fast-switching diode was selected for the snubber diode since this diode is commonly used in switching power supplies. Figure shows the actual RCD snubber attached across the drain and source of the MOSFET to reduce switching noise. Figure shows the waveform from the drain of the MOSFET with the snubber implemented. You can see from the picture that the snubber circuit has significantly reduced the ringing. The excess energy from ring is dissipated through the snubber diode. The values of the snubber resistor and capacitor determine the ringing or snubbed frequency.

15 SWITCHING POWER SUPPLY DOCUMENTATION Page 11 of 45 Figure MOSFET Switch and Snubber Circuit Figure Waveform at the Drain of the MOSFET Switch with Snubber When a value of 1 kω is used on the snubber approximately 6 watts was dissappated. One 2 watt resistor could not handle the charging power of this RC tank. The final design of the snubber was made using a bank of four 2-watt resistors. The available values used were two 3.9 kω and two 4.3 kω which gives approximately 1 kω if all resistors are connected in parallel. A 750-pF capacitor was used for the snubbing capacitor. The noise on the 13.5 VDC output is shown in figure The noise spikes of 5 to 10 volts have been reduced to 0.5 to 1.5 volts. The snubber circuit is more efficient as the load is increased. The noise at full load is at minimum while it is at

16 SWITCHING POWER SUPPLY DOCUMENTATION Page 12 of 45 maximum with no load. The snubber circuit greatly reduced the ringing from the switch. Since the snubber did not completely eliminate the noise, more options for noise reduction had to be researched. Figure Noise Measured on the Output Signal with Snubber The next choice for noise reduction was PCB layout. A new circuit board with shorter wider traces to eliminate residual inductance was constructed. The shorter and wider traces give current a less resistive path to travel; therefore, reducing inductance and noise while increasing efficiency [13]. The new PCB layout was by far better than the original board. Ground planes were added throughout the board to help keep the inductance of the lines low. However, the new board did not do much for eliminating the noise problems. The next thing we tried to reduce the noise was adding an output low-pass filter to the circuit. A low-pass filter will only allow frequencies below the cutoff frequency to pass through it. The filter will reject any frequency above the cutoff frequency [15]. The cutoff frequency of the filter can be set by the following formula: f cutoff = 1/(2π LC) (3.3.2) The noise happened at every 100 khz and the ringing of the noise was at 7 MHz; therefore the filter was designed to have a cutoff frequency of 1 khz. A 25-µH torrid and a 470-µF electrolytic capacitor were used to create the filter. While this filter helped reduce the noise somewhat, it did not reduce it as much as was expected. After some discussion with faculty members, it was decided to try using an inline inductor with a ceramic capacitor. Logan also notes that inline inductors have better filtering characteristics [16].

17 SWITCHING POWER SUPPLY DOCUMENTATION Page 13 of Flyback Transformer Another important factor in designing a switching power supply is the transformer design. Different topologies of switching power supplies require different transformer designs. Most transformers are designed for forward mode operation. A typical transformer operating in forward mode has current flowing through both primary and secondary windings at the same time, but the topology chosen for the switching power supply required a flyback transformer because of the specified input voltages used and output power required for full load. Flyback transformers operate in the flyback mode, which describes the flow of current across the primary and secondary windings. The core material of the primary windings store energy until the MOSFET is switched off [17]. The energy that is stored in the primary core will transfer to the secondary core and windings. Any transformer can operate in flyback mode with a fast switching diode attached to the secondary; however, a properly designed transformer is need for highly efficient energy transfer and reduction of noise spikes. In the power supply design, Mississippi Power offered a transformer. Redesigning the transformer was briefly discussed; however, the turn around period in a custom wound transformer was found to be six weeks from Cramer Magnetics [8]. This long turn around time deterred the group from the redesign of the transformer. Table shows the different switching power supply topologies, voltage input range, and output power range. For the power supply required by Mississippi Power, two topologies were acceptable, the 1T forward and flyback topologies. The flyback topology has been proven to have efficiency on average of 2% higher than the 1T forward. Topology Power Range (W) V in(dc) Range Buck Boost Buck-Boost T forward Flyback Push-Pull Half-bridge Full-bridge Table Power and Voltage Range of Switching Power Supply Topologies Figure shows a schematic representation of the flyback converter used for the design of the switching power supply. Once the high voltage is switched on the primary side of the transformer, the secondary conducts. This flyback design also steps down the voltage 11 times. The flyback diode chosen was the MUR820 for the high power ratings and fast switching. The auxiliary windings shown in the schematic are isolated from the secondary windings for powering of the gate controller integrated circuit. We also investigated using a shottky diode for the flyback diode because shottky diodes have a smaller reverse recovery time. This would help to eliminate some of the noise problems

18 SWITCHING POWER SUPPLY DOCUMENTATION Page 14 of 45 that are being noted on the output. However, the shottky diodes do not have high enough power ratings to be used in the power supply. Figure Flyback Converter Schematic To reduce voltage spikes and noise from the flyback transformer, an interleaving winding technique should be used [8]. By investigating the properties of the transformer Mississippi Power supplied, the team noted that the correct interleaving technique was used. By investigating the prototype power supply through testing and simulation, the transformer was noted to be one of the main sources of noise and ringing across the MOSFET. A redesigned transformer may alleviate some of the voltage spikes and noise from the switch, but the RDC snubber was proven to work extremely well in ringing and noise reduction. Figure shows an interleaving and non-interleaving technique. Figure Transformer Winding Techniques 3.5. Output Rectification The design of the output stage perhaps has the greatest effect on the efficiency of the switching power supply than any other stage, since the majority of the losses within the

19 SWITCHING POWER SUPPLY DOCUMENTATION Page 15 of 45 power supply are seen in the output stage [1]. The output stage simply rectifies the signal. The wave coming off the secondary side of the transformer has voltage ripples and some distortion. The output stage, which is a resistive and capacitive network, simply rectifies the ripples. The switching power supply that Mississippi Power designed has a number of resistors and capacitors that makes up the output rectification stage. Mississippi Power chose different values for their resistors and capacitors to rectify the ripple voltage to a smooth, constant 13.5 VDC. There is also an inductor included on the output, but it is used to clamp the voltage spikes. Figure shows the output stage of Mississippi Power s design. Figure Output Rectification Schematic The picture on the previous page is the resistor and capacitor network of the output rectification circuit. The two resistors in series (R2 & R3) are there to help the capacitors to discharge. The LED (light emitting diode) indicates that the power supply is supplying the correct voltage. The capacitor (C1) and resistor (R1) are part of the feedback network and will be discussed further in the following section Feedback Network The first thing to consider when designing the voltage feedback network is whether or not it needs to be isolated. The feedback network needs to be isolated when the input voltage is considered lethal to the operator of the equipment [17]. Since the input voltage of the power supply will be as high a 310 VAC, the feedback network needs to be isolated so that the operator of the power supply will not be hurt. In order to isolate the feedback network an optoisolator must be used. However, using an optoisolator introduces some unwanted variations in the circuit. To minimize the drift effect of the optoisolator, an error amplifier is desired on the secondary side [1]. Figure shows the typical circuit for a voltage feedback network. Mississippi Power chose the TL431 chip to provide the feedback error amplification. After researching the data sheets for this chip, it was decided that this chip was a good choice for the feedback error amplifier. This chip

20 SWITCHING POWER SUPPLY DOCUMENTATION Page 16 of 45 needs a minimum of 1.0 ma current flowing into its output pin at +2.5 voltage for proper operation [1]. Figure Voltage Feedback Network The value of R1 can be found by calculating the value of resistance needed to get the proper voltage drop on the error amplifier. R1=(Vout-Vsense-Vdiodes)/I (4.6.1) R1=( )/6.0mA=1.6 kω The value of the sense resistor can be found using the following formula: R2= (Vout-Vsense)/Isense (4.6.2) R2= (13.7V 2.5V)/1mA = 11.2 kω The value of R4 should be calculated so that there will be a +2.5 V signal for the reference point on the TL431 chip. Simple voltage division can be used to calculate this value. Vsense=R4*Vout/(R4+R2) (4.6.3) This equation can be manipulated to find the value of R4: R4=(Vsense*R2/Vout)/(1-Vsense/Vout) (4.6.4) R4=(2.5V * 11.2kΩ/13.7V)/(1-2.5V/13.7V) R4=2.52 kω The next part to designing the feedback loop is to design the feedback loop compensation. This power supply has a single-pole output filter characteristic that is