Transducers, Power Amplifiers, and Energy Converters Transducer: a low energy device that receives an input signal of one form and delivers another form of output signal relative to the input signal in a specified way Power Amplifier: a device with a relatively low energy input port that receives information that determines the bulk energy transfer from an integral power supply through the output port Energy Converter: a device which provides, between the two access ports, reversible exchange of bulk energy that does useful work without a separate power supply

Black Box Diagram   P1P1 P2P2 +2-+2- +1-+1- InputOutput may be different types

Pressure Transducer Typical Construction uses a Diaphragm with a strain gauge RfRf q +P-+P Kpc R +v-+v- i +PC-+PC- CrCr Fluid Side Electric Side Ideally, R f = 0 C f = 0 Ideally, R f = 0 and C f = 0 They account for resistance to flow causing a pressure drop and C accounts for the change in the diaphragm

Power Amplifier Stereo ii ii +v2-+v2- +v1-+v1- w mw ex: -CD player -Tape -Radio ex: Servomotor +v1-+v1- ii Field Controlled Servomotor Power Supply I A = constant armature current Mechanical Load P2P2 P1P1 w  Field Terminals JmJm Mech. Load  R L +v1-+v1- ii P1P1 P2P2 BmBm +w-+w- mm KmiKmi ex: -tape drive motor -floppy disk drive motor -CD drive motor electrical port input (low power) mechanical port output (high power)

Ideal two-port subsystem Interfaces Sending Subsystem Ideal Interface Receiving Subsystem +1-+1- +2-+2- 11 11 P1P1 P2P2 P 1 =  1  1 = P 2 =  2  2 (since ideal power in = power out) Ex: * electric - electric * eletro - mechanical * rotational - linear

Ideal Two-Port Subsystem Interfaces Transformer Type Gyrator Type 11 22 11 22 = = a 11 22 22 11 = = P P & a may or may not have dimensions depending on the interface subsystems +v1-+v1- ii +v2-+v2- ii a : 1 +1-+1-  +2-+2-  +1-+1-  +2-+2-  P Generalized Electrical

Dependent-source Models of the Ideal Transformer & Gyrator +1-+1-  +2-+2-  a : 1 +1-+1-  +2-+2-  P +1-+1-  +2-+2-  P +1-+1-  +2-+2-  P +1-+1-  +2-+2-  +1-+1-  +2-+2- 

Electric Transformer N 1 Turns N 2 Turns +v1-+v1- ii P1P1 +v2-+v2- ii P2P2

Gear Train P2P2   1 w 1  2 w 2 P1P1 N 1 Teeth N 2 Teeth

Lever l1l1 l2l2 u2u2 f2f2 f1f1 u2u2 P1P1 P2P2

Hoisting Drum  1 w 1 r f2f2 P2P2 P1P1 r = mean radius of drum

Armature Controller Motor +v1-+v1- ii w  K = torque constant P1P1 P2P2

+v-+v-  +-+-  +u-+u- f 1 : r +w-+w- Kmi Kmw M Rotational to Translational Interface Ideal Motor kv 2 Km f rok

Ideal +v1-+v1- ii w  +v-+v- i +w-+w-  Km : 1 +v-+v- i +w-+w-  a : K mi K mw v1v1 v2v2 v3v3  w  = K w + k vi = w 

More Realistic JmJm L +v1-+v1- BmBm KmiKmi +-+- R  KmwKmw i +w-+w- JmJm L +v1-+v1- BmBm R  i +w-+w-