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Maximum Power Delivered Delivered power Digilent Inc

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Maximum Power Delivered Delivered power Digilent Inc Powered By Docstoc
					              Lecture 12
                   (parts A & B)

•Review:
  •Source transformations
  •Maximum power transfer
•Derivation of maximum power transfer
•Thévenin theorem examples
•Operational Amplifiers
•Related educational materials:
  –Chapters 4.5, 4.6, 5.1-5.4
     Using Source Transformations in Circuit Analysis
• Any voltage source in series with a resistance can be modeled as a
  current source in parallel with the same resistance and vice-versa
             Maximum Power Transfer
• The load receives the maximum amount of power if
  RL = RTH




• Why?
     Maximum Power Transfer – Derivation
• Load voltage:           • Delivered power:
                                                           2
                                  2
                                  V    V 
                                        2
                                               RL      
                             PL  L
                                       OC
                                                      
                                  RL   RL  RL  RTH
                                          
                                                       
                                                       




                             PL
                  RL
    VL  VOC
               RL  RTH

                                               RL
                   Maximizing power
• Set derivative of power to zero:
  PL                2      RL      
       0           VOC            2
                                        0
  R L     RL           RL  RTH  
• Chain rule:
     ( RL  RTH )2  2 RL ( RTH  RL ) 
                                        0
    2
  V 
               ( RL  RTH )
   OC                        4
                                       
• Set numerator to zero:
        RL  RTH
           Maximum Power Delivered
• Delivered power:
                                 2
           V2
                    RL      
      PL   OC
                 
                 R R       
                             
           RL     L    TH   
• Letting RL = RTH:
              2
           VOC
      PL 
           4 RTH
        Example 1: Maximum power transfer
(a) Determine the load resistance, R, which absorbs the
    maximum power from the circuit.
(b) What is the maximum power delivered to the load?
Example 1(a): Load Design
Example 1(b): Power delivered
                        Example 2
• Determine the Norton equivalent of the circuit of example 1
                Operational Amplifiers
• So far, with the exception of our ideal power
  sources, all the circuit elements we have examined
  have been passive
   – Total energy delivered by the circuit to the element is
     non-negative
• We now introduce another class of active devices
   – Operational Amplifiers (op-amps)
   – Note: These require an external power supply!
        Operational Amplifiers – overview
• We will analyze op-amps as a “device” or “black
  box”, without worrying about their internal circuitry
   – This may make it appear as if KVL, KCL do not apply to the
     operational amplifier
   – Our analysis is based on “rules” for the overall op-amp
     operation, and not performing a detailed analysis of the
     internal circuitry
• We want to use op-amps to perform operations, not
  design and build the op-amps themselves
              uA741 op-amp schematic




• Source: RFIC Technologies web site
            Ideal Operational Amplifiers
• Typical circuit schematic symbol:

                ip +
        vp - vn = vin
               in -
• Three-terminal device (2 inputs, 1 output)
• Operation characterized by:
   – Voltage difference between input terminals (vin)
   – Currents into the input terminals (ip and in)
       Ideal Operational Amplifier “Rules”
• More complete circuit      • Assumptions:
  symbol
  • (Power supplies shown)      • ip = 0, in = 0


                                • vin = 0


                                • V - < vout < V +
           Notes on op-amp operation
1. Output current is generally not known (it is
   provided by external power supplies)
2. KCL at input nodes is generally a good starting
   point in op-amp circuit analysis
3. vin is multiplied by a large number to get vout


4. vout is limited by the external power supplies
              Op-amp circuit – example 1
• Find Vout
              Op-amp circuit – example 2
• Find Vout

				
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posted:9/25/2012
language:English
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