Non-Ideal Behavior of Components Todd H. Hubing Dept. of Electrical and Computer Engineering Clemson, University Clemson, SC 29634 USA email: hubing@clemson.edu Telephone: 1-864-656-7219
Circuit Schematics Global EMC University 2007 IEEE International Symposium on EMC 2
Resistors Global EMC University 2007 IEEE International Symposium on EMC 3
Resistance R = l σ A ohms Global EMC University 2007 IEEE International Symposium on EMC 4
Quiz Question The D.C. resistance of a 5-cm trace on a printed circuit board is, a.) about 100 ohms b.) about 100 milliohms c.) less than a milliohm Global EMC University 2007 IEEE International Symposium on EMC 5
DC Resistance of a Printed Circuit Board Trace Trace length = 5 cm Trace width = 0.25 mm Trace thickness = 0.034 mm σ cu = 5.7 x 10 7 S/m. 0.05m R = = 0.10 ohms 7 3 3 ( 5.7 10 S / m )( 0.25x10 m )( 0.034x10 m ) Global EMC University 2007 IEEE International Symposium on EMC 6
Skin Depth High-frequency electric fields and currents decay exponentially with distance from the surface of a good conductor. J ( x) = J S e x πfμσ Global EMC University 2007 IEEE International Symposium on EMC 7
Skin Depth δ = 1 π f μσ meters Global EMC University 2007 IEEE International Symposium on EMC 8
Resistance per unit length of a cable At 60 Hz δ 60Hz 1 = = 8.6 mm π 7 7 ( 60)( 4π 10 )( 5.7 10 ) 1 1 Rinnerconductorat60Hz = = = 22.3m Ω /m 2 σ A 5.7 10 0.5 10 7 3 ( ) π ( ) 1 1 Routerconductorat60Hz = = = 5.6 m Ω / m 7 3 3 σ A 5.7 10 2 5 10 0.1 10 ( ) π ( )( ) total = 22.3 + 5.6 = 28 m Ω / m Global EMC University 2007 IEEE International Symposium on EMC 9
Resistance per unit length of a cable At 100 MHz δ 100 MHz 1 = = 0.0066 mm π 8 7 7 ( 10 )( 4π 10 )( 5.7 10 ) 1 1 Rinnerconductorat100MHz = = = 832m Ω /m 7 3 6 σ A 5.7 10 2 0.5 10 6.6 10 ( ) π ( )( ) 1 1 Routerconductorat100MHz = = = 85m Ω /m 7 3 6 σ A 5.7 10 2 4.9 10 6.6 10 ( ) π ( )( ) total = 832 + 85 = 917 m Ω / m Global EMC University 2007 IEEE International Symposium on EMC 10
Capacitors Global EMC University 2007 IEEE International Symposium on EMC 11
Capacitance C = Q V farads. Q E = 0 2 a 4πε0r < < r r r r volts/m. Q Q 1 1 4πε0r 4πε0 ra rb b 0 0 Vab = dr = volts. r 2 a b C ab Q 4πε 0 0 = = Vab 1 1 r a r b farads. Global EMC University 2007 IEEE International Symposium on EMC 12
Absolute Capacitance Cabs = limcab = 4πε 0ra farads. b Global EMC University 2007 IEEE International Symposium on EMC 13
Self and Mutual Capacitance Global EMC University 2007 IEEE International Symposium on EMC 14
Self and Mutual Capacitance Global EMC University 2007 IEEE International Symposium on EMC 15
Inductors Global EMC University 2007 IEEE International Symposium on EMC 16
Inductance Inductance is a property of current loops! Ψ = S B ds webers L Ψ = I henries Global EMC University 2007 IEEE International Symposium on EMC 17
Inductance L circle N 2 8R Rμ ln a 2.0 henrys L square loop w w N 2 2μ 0 ln 0.774 π a henrys Global EMC University 2007 IEEE International Symposium on EMC 18
Quiz Question The inductance of a 2-cm wide, 10-cm long ground strap is, a.) about 10 nanohenries b.) about 100 nanohenries c.) undefined Global EMC University 2007 IEEE International Symposium on EMC 19
Loop Inductances Global EMC University 2007 IEEE International Symposium on EMC 20
Mutual Inductance L 21 Ψ = I 21 1 henries. Global EMC University 2007 IEEE International Symposium on EMC 21
Partial Inductance L L L 21 21 Ψ = I = S2 21 1 Bids I 1 1 henries. ( A ) henries. ids L 12 L 11 1 A1 dl S2 2 21 = = i μi henries A1 = 1 dl / I1 I 4π R 1 webers m L21 μ dl idl 4π R = 1 2 henries Useful for computer modeling. Not useful for estimating inductance. L ij μ = 4 where I J π i = 0 i = 0 l ij l = ij segment i segment j dl idl i R ij j Global EMC University 2007 IEEE International Symposium on EMC 22
Partial Inductance (Branch Inductance) L loop = L trace + L via + L via + L plane Global EMC University 2007 IEEE International Symposium on EMC 23
Resistors Global EMC University 2007 IEEE International Symposium on EMC 24
Do Resistors Have Capacitance and Inductance? Global EMC University 2007 IEEE International Symposium on EMC 25
Impedance of a 50-Ohm Resistor 0.8 pf 20 nh 48 ohms 1000 Impedance in Ohms 100 10 1 10 100 1000 Frequency in MHz Global EMC University 2007 IEEE International Symposium on EMC 26
Types of Resistors Metal Film High precision, low cost Composite Medium precision, good transient immunity Wire Wound High power, high inductance Global EMC University 2007 IEEE International Symposium on EMC 27
Capacitors Global EMC University 2007 IEEE International Symposium on EMC 28
Do Capacitors Have Resistance and Inductance? 0.011 μf 2 nh 15 mohms Global EMC University 2007 IEEE International Symposium on EMC 29
Impedance of a 0.01-μF Capacitor 0.011 μf 2 nh 15 mohms 100 Impedance in Ohms 10 1 0.1 0.01 1 10 100 1000 Frequency in MHz Global EMC University 2007 IEEE International Symposium on EMC 30
What are ESR and ESL??!! Global EMC University 2007 IEEE International Symposium on EMC 31
SMT Capacitor Connection Inductance C = 3.4 nf B L = 5 nh BULK L = 2nH D C BULK = 1 μ F C = 10nF D Bare Board 100. 10. 1. Board with decoupling 0.1 0.1 MHz 1 MHz 10 MHz 100 MHz 1 GHz Global EMC University 2007 IEEE International Symposium on EMC 32
Types of Capacitors Ceramic Tantalum Other Electrolytic Mica Low cost, stable, good precision Polarized, good energy density Polarized, good energy density High-voltage applications Global EMC University 2007 IEEE International Symposium on EMC 33
Inductors Global EMC University 2007 IEEE International Symposium on EMC 34
Do Inductors Have Resistance and Capacitance? 160 pf 15 mohms 5 μh Global EMC University 2007 IEEE International Symposium on EMC 35
Impedance of a 5-μH Inductor 160 pf 15 mohms 5 μh 1000 Impedance in Ohms 100 10 1 0.1 1 10 Frequency in MHz Global EMC University 2007 IEEE International Symposium on EMC 36
Types of Inductors Ferrite Core Air Core High inductance in small package Linear behavior under high-current conditions Common-mode Impedes common-mode currents while passing differential-mode currents. Global EMC University 2007 IEEE International Symposium on EMC 37
Ferrites Fair-Rite 2643000701 Global EMC University 2007 IEEE International Symposium on EMC 38
Non-Ideal Behavior of Active Devices Currents on the lead frame of an RDR memory module at the third harmonic of the clock frequency. Global EMC University 2007 IEEE International Symposium on EMC 39
Summary All components (when connected to a circuit) have resistance, capacitance and inductance. The behavior of a component at high frequencies is usually much different than the nominal (low-frequency) behavior. The inductance of a low-inductance device is generally determined by the connection and is not a property of the device itself. Global EMC University 2007 IEEE International Symposium on EMC 40