VIEWS: 15 PAGES: 5 CATEGORY: Education POSTED ON: 4/28/2010
Electronics Electronic Components • most instruments work on either analog or digital • Resistors: resists the flow of electron through a signals circuit • we will discuss circuit basics – units of Ohms (Ω) with symbol = – parallel and series circuits • Capacitors: resists changes in the voltage of a – voltage dividers circuit (capacitive reactance) – filters – high-pass, low-pass, band-pass filters – units of Faradays (usually μF or nF) – with symbol = OR • the main purpose of this chapter is to get you to • Inductors: resists changes in the current of a understand the electronic filters circuit (inductive reactance) – they help to reduce electronic noise – units of Henry’s (H) with symbol = – less noise = a clearer signal (more on this in Chapt 5) Resistors and Basic Circuit Laws Basic Circuits • a few Laws to provide equations • series batteries – (V = voltage, I = current, R = resistance) – voltage adds to produce a – Ohm’s Law: V=IR higher voltage – Power Law: P = IV OR P = V 2/R • Kirchoff’s Laws – current law: the algebraic sum of the current • parallel batteries around any point in a circuit is zero – currents add to add a higher – voltage law: the algebraic sum of the voltages current capacity around a closed electrical loop is zero Basic Circuit Voltage Dividers • series resistors • since the same current goes – resistance add directly through each RT= R1 + R2 + ... resistor, there is – same current through each different voltage drop across each • parallel resistors – resistance add as reciprocals • the total voltage 1/RT= 1/R1 + 1/R2 + ... divides across the series – same voltage drop across each 1 Example : a Voltage Divider Example : a Voltage Divider • Calculate the magnitude of the voltages across • Calculate the magnitude of the voltages across each resistor each resistor • Steps to solve • Steps to solve V = 100. V – calc. RT – calc. RT R1 = 50. Ω R2 = 150. Ω – calc. IT – calc. IT R3 = 250. Ω – calc. each V V = 100. V – calc. each V R1 = 50. Ω RT = 450. Ω R2 = 150. Ω V = IT R T RT= R1 + R2 + R3 R3 = 250. Ω or IT = V/RT RT= 50+150+250 RT=450 Ω IT = 100. V/450. Ω IT = 0.222 A Example : a Voltage Divider Current Dividers • Calculate the magnitude of the voltages across • since the voltage is the same across each each resistor resistor, the current across each is different V = 100. V R1 = 50. Ω • the total current is divide across each parallel V 1 = IT R 1 R2 = 150. Ω path V1 = (0.222 A)(50. Ω) R3 = 250. Ω V1 = 11.1 V = 11 V RT = 450. Ω •scan fig 2-3 on page 24 IT = 0.222 A V 2 = IT R 2 V2 = (0.222 A)(150. Ω) V2 = 33.3 V V 3 = IT R 3 V3 = (0.222 A)(250. Ω) V3 = 55.5 V Example : a Current Divider Example : a Current Divider • Calculate the magnitude of the current through • Calculate the magnitude of the current through each loop and the total current each loop and the total current V = 100. V R1 = 50. Ω • Steps to solve V = 100. V R1 = 50. Ω I1=V/R1=100.V/50. Ω=2.0 A R2 = 150. Ω – calc. each I R2 = 150. Ω – calc. IT I2=V/R2=100.V/150. Ω=0.667 A R3 = 250. Ω R3 = 250. Ω I3=V/R3=100.V/250. Ω=0.400 A 2 Example : a Current Divider Loading Error • Calculate the magnitude of the current through • making a measurement causes an uncertainty each loop and the total current in the measurement (analogous to the Heisenburg Uncertainty Principle) VM − Vx Er = × 100% Vx V = 100. V − RS R1 = 50. Ω IT = I1+ I2 + I3= 2.0 + 0.667 + 0.400 A Er = × 100% R2 = 150. Ω IT = 3.066 A = 3.1 A RM + RS R3 = 250. Ω Loading Error AC Circuits 0 -10 • % Error -20 • Chopping (AAS) -30 -40 • electrochemistry -50 1,000 100,000 10,000,000 • electrochemistry R M (Ω ) • The error drops as the internal resistance of the meter increases Inductors/Capacitors RC Calculations • Capacitors: resists changes in the voltage of a • reactance: the capacitor's equivalent to circuit (capacitive reactance) resistance – units of Faradays (usually μF or nF) – there is a frequency dependence – with symbol = OR 1 1 XC = = • Inductors: resists changes in the current of a 2πfC 2ωC circuit (inductive reactance) • impedance: the total “resistance” in an RC – units of Henry’s (H) with symbol = circuit – there is a frequency dependence • AC signals are constantly changing, so 2 ⎛ 1 ⎞ including these components in the circuit Z = R + X = R +⎜ 2 2 C⎜ 2πfC ⎟ 2 ⎟ affects the signal ⎝ ⎠ 3 RC Filters RC Filters • At high freq. the capacitor becomes • since this circuit is a voltage practically a wire divider • its reactance goes down and no – the voltage across the resistor is voltage is dropped across it R R R VR = V × =V × =V × RT Z 2 ⎛ 1 ⎞ 100% ⎜ 2πf C ⎟ R2 + ⎜ Voltage (% of input) ⎟ VR ⎝ ⎠ 75% VC – the voltage across the capacitor is 50% ⎛ 1 ⎞ • as f ↑, VR ? ↑ ⎜ ⎟ ⎜ 2 πf C ⎟ 25% X ⎝ ⎠ • as f ↑, VC ? ↓ VC = V × C = V × 0% Z 2 • as f ↓, VR ? ↓ ⎛ 1 ⎞ 10 100 1,000 10,000 2 ⎜ R +⎜ ⎟ ⎟ • as f ↓, VC ? ↑ Signal Frequency (Hz) ⎝ 2 πf C ⎠ RC Circuit Distortion RC Filters • Distortion is dependent on the size of RC • See homework problems RC Circuits RC Circuits • the capacitor cause a time lag in the voltage • the phase shift is frequency dependent, (phase shift) dV ⎛ 1 ⎞ decreasing as the frequency increases i=C ⎜ 2 πf RC ⎟ φ = arc tan ⎜ ⎟ dt ⎝ ⎠ Phase Shift (degrees) 12 R = 1 kΩ C = 1 nF 8 ⎛ 1 ⎞ 4 ⎜ 2 πf RC ⎟ φ = arc tan ⎜ ⎟ ⎝ ⎠ 0 100 10,000 1,000,000 100,000,000 Signal Frequency (Hz) 4 Electronics Definitions Other Components • resistance ≡ how a resistor effects a circuit • diode ≡ allows current to flow in only one direction; used in regulators • reactance ≡ how a capacitor or inductor effects • transitors ≡ can act as an amplifier or switch a circuit – replaced the vacuum tube • transformer ≡ converts one AC voltage to others • impedance ≡ the combination of resistance and reactance • rectifier & filter ≡ converts AC to DC • regulator ≡ prevents surges in current from changing the voltage of a power supply • oscilloscope ≡ a device to read and analyze signal and circuits 5