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Output signal alternates between on and off within specified period Controls power received by a device The voltage seen by the load is directly proportional to the source voltage 2 PWM PULSE WIDTH MODULATION

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6 Magnetomotive force is a quantity appearing in the equation for the magnetic flux in a magnetic circuit, sometimes known as Hopkinson's law: where Φ is the magnetic flux and R is the reluctance of the circuit. Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating electric energy it stores magnetic energy

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7 1. ℱ = NI where N is the number of turns in the coil and I is the electric current through the circuit 2. ℱ = ΦR where Φ is the magnetic flux and R is the reluctance 3. ℱ = HL where H is the magnetizing force (the strength of the magnetizing field) and L is the mean length of a solenoid or the circumference of a toroid

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9 Introduction and definitions Types of PWM Methods of generation Characteristics of PWM Applications and examples

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Duty Cycle: on-time / period V low is often zero 10

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Pulse center fixed, edges modulated Leading edge fixed, tailing edge modulated Tailing edge fixed, leading edge modulated Pulse Width constant, period modulated 11

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Analog PWM signals can be made by combining a saw- tooth waveform and a sinusoid 13 PWM output is formed by the intersection of the saw-tooth wave and sinusoid Analog Generation of PWM

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Digital: Counter used to handle transition Delta : used to find the PWM at a certain limit Delta Sigma: used to find the PWM but has advantage of reducing optimization noise 14

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Output signal compared with limits Every time limits reached, changes state 15

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PWM signal generated by Delta method Error = output – reference Error integrated State changes when integration reaches limits Advantage Circuit simpler Reduces quantization noise by high pass filter 16

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17 The voltage supplied to a DC motor is proportional to the duty cycle Both brushed and brushless motors can be used with PWM Both analog and digital control techniques and components are available

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3 different AC currents at different phases Phase: 120 degrees apart Creates constant power transfer Rotating magnetic field Pulses substitute for AC current 18

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Used for three-phase AC motors Convert DC current to AC current Gates turned on/off at different intervals 3 PWM created 19

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Average value proportional to duty cycle, D Low power used in transistors used to switch the signal Fast switching possible due to MOSFETS and power transistors at speeds in excess of 100 kHz Digital signal is resistant to noise Less heat dissipated versus using resistors for intermediate voltage values 21 Advantages of PWM

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22 Cost Complexity of circuit Radio Frequency Interference Voltage spikes Electromagnetic noise Disadvantages of PWM

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23 Introduction and definitions Types of PWM Methods of generation Characteristics of PWM Applications and examples

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In the past, motors were controlled at intermediate speed by using resistors to lower delivered power Electric stove heater Lamp dimmers Voltage regulation – convert 12 volts to 5 volts by having a 41.7% duty cycle Sound production: PWM controlled signals give sound effects similar to a chorus Power transfer: PWM used to reduce the total power given to a load without relying on resistive losses 24 Applications of PWM

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Commonly used in toys Lowpass filter smooths out transients from harmonic effects Frequency values of harmonics doesn’t change, but the amplitude does, which adjusts the analog output signal 25 PWM used with D/A conversion

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26 Clock signal is found “inside” PWM signal More resistant to noise effects than binary data alone Effective at data transmission over long distance transmission lines PWM used to transmit data in telecommunications

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Ripple is the noise in the output signal Appropriate PWM controllers can minimize these effects 27 Concerns: Ripple of PWM Signal

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1.Must be at least 10 times higher than the control system frequency 2.Higher than 20kHz – audible frequency of sounds to avoid annoying sound disturbances, caused by magnetostriction 3.If too low the motor is pulsed, not continuous, because the motor’s inductance can not maintain the current 4.Inverse of frequency should be much less than the motor/load time constant 5.Higher error from ripple voltages Frequency of the PWM Signal Upper Limits Lower Limits 1.If too high the inductance of the motor causes the current drawn to be unstable 2.MOSFET transistor generates heat during switching 3.Limited by resolution of controller 4.Eddy currents generated in electromagnetic coils which lead to adverse heating 5.Heat losses in electromagnetic materials is proportional to frequency squared 10/29/2009 28

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Potentiometer is used to adjust the duty cycle 30 Example: PWM with 555 Timer

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1.Maxon EC-16 brushless motor, Time constant = 8.75 ms 2. Want to avoid audible frequencies f ≥ 20 kHz 3. PID control loop running at 150 Hz f ≥ 10 ∙ 150 Hz Requirements 31 Example: Specifying circuit elements

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Set f to 25 kHz to add in a factor of safety Choosing C 1 to be 100 nF, R 1 is 576 Ω ~ 500 Ω Recalculating with these values f = 28.8 kHz This circuit has a PWM frequency according to: ≥ 117 Hz ≥ 20 kHz ≥ 1.5 kHz f Check constraints 32 Example: Specifying circuit elements

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18 kHz frequency Continuous 28 amps $55.95 Where can I buy a PWM controller? Texas Instruments Digikey Mouser Electronics Critical Velocity Motor Control Texas Instruments TAS5508B 8-Channel Digital Audio PWM Processor 64 pin chip, max 192 kHz frequency $7.25 120 amps, used for hybrid vehicles $469.00 SMALL BIGGER HUGEHUGE 33

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34 SAMPLE PWM CIRCUITS

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