======================COMPONENTS_MAGNETIC====================== B = uH V = N*A*delta_B/delta_time enegry = C*V^2/2 =i^2*L/2 ^ B /_\ | ________ B = u*H H*L =N*I | _-- _-- |/ / V = N*delta_Phi/delta_time / / /| / L = N*delta_Phi/delta_I ________/_|__/_________\ H / | / / Phi =B*Area u =u_0*u_r Phi = Flux B = Flux density H = Magnetic field u = permeablity m_r = 2000-> 6000 machine materials __\_ H | / | L_cm _______________|_____________ |\ --> I | \ W_cm \ \_____________|______________\ \|____________\|/______________| T_cm | V |_/_ L_uH = 0.002*L_cm*( ln(2*L_cm/( W_cm +T_cm ) +.5 ) <--L_inch----> __ __ __ _/\ \/\ \/\ \___ ^ |__/\ \/\ \/\ \__| | R_inch \_\ \_\ \_\ SELF INDUCTANCE Coil (L_cm,R_cm, N_turns) L_uH (N_turns*R_inch)^2/(9*R_inch + 10*L_inch) <-Dia_cm--> __________ ______ | | __ | | -|-|-_| | | | |____| | |________| L_nH= 8.5*Dia_cm*N_turns^(5/3) N_turns ->set 15 Dia_cm ->set =0.01/2.54 L_nH = 8.5*B15*B14^(5/3) The inductance (I), in microhenrys. N number of turns and I inductance in microhenrys. L and R distances in inches. 0 0 0 0 0 0 ^ _________ | R | | | Single Layer air-core Coil |<---L--->| V within 1% or 2% | | I_uH = R^2*N^2/( 9*R + 10*L) |_________| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ^ _________ | R | | | |<---L--->| V Multiple Layer Coil | | I_uH = 0.8*R^2*N^2/(6*R +19*L +10*B) |_________| 0 0 0 0 0 0 ^ B 0 0 0 0 0 0 | 0 0 ^ _ | R | | | | | V CASE 3: Single layer single row Layer Coil | | I_uH = 0.8*R^2*N^2/( 8*R + 11*B) |_| 0 ^ B 0 | <-Dia_cm--> __________ ______ | | __ | | -|-|-_| | | | |____| | |________| L_nH = 8.5*Dia_cm*N_turns^(5/3) <--L_inch----> __ __ __ _/\ \/\ \/\ \___ ^ |__/\ \/\ \/\ \__| | R_inch \_\ \_\ \_\ L_uH= (N_turns*R_inch)^2/(9*R_inch + 10*L_inch) _ _ Dia_inch | | | | _| | | |_ / __| |__ \ / / ^ \ \ R_inch/Dia_inch > 2.5 / / /|\ \ \ | | | | | | | R_inch | | \ \ / / \ \__ __/ / \_ --- _/ ------- L_uH =(R_inch/100)*(7.353*log(16*R_inch/Dia_inch)-6.386) ------------Self_Inductance---------------- about 9nH for small wire.. __\_ | / | _______________|_____________ ()_____________\|/____________) | V |_/_ \ <--L----> _/\\/\\/\\___ ^ |__/\\/\\/\\__| | R in inches \\ \\ \\ L = n^2*( r^2/ (9*r+10*l) ) microhenies L = FormF*D*n^2 in micro henries D in inches FormF = 0.025*(D/L) ---------------------------- <---D--> __________ ______ | | __ | | -|-|-_| | | D in cm | |____| | |________| L = 85e-10*D*N^(5/3) n = number turns D in cm on chip modeled a 2.8nH with a Q of 12.5 Mutual Inductance __ 1X + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ L1 = L1a+L1b L2 = L2a+L2b Turn Ratio =1:1 L2a _ _ _ L2b _ _ _ K = L1b/L1 = L2b/L2 /*\/ \/ \ /*\/ \/ \ VL1b M=K*sqrt(L1*L2) __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| 1X 0 0 \___/ |__| + VL2b - VL1 = (dI1/dt)*L1 + (dI2/dt)*M K = coupling coeffecient VL2 = (dI2/dt)*L2 + (dI1/dt)*M Typical Transformer __ P =10 + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | (P/S)*VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ L1 = L1a+L1b L2 = L2a+L2b Turn Ratio =P:S L2a _ _ _ L2b _ _ _ K=L1b/L1=L2b/L2=99% /*\/ \/ \ /*\/ \/ \ (S/P)*VL1b __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| S=100 0 0 \___/ |__| + VL2b - M= K*sqrt(L1*L2) VL1 = (dI1/dt)*L1 + (dI2/dt)*M*(P/S) K = coupling coeffecient VL2 = (dI2/dt)*L2 + (dI1/dt)*M*(S/P) VL1/VL2 = P/S CAPACITOR_IMPEDANCE_Ohms 100 .................................... | C . . . | . . L . | . . . | C . L . | . . . 10 |..........C.........L............... | . . . | . C L . . | . . . | . R . . | . R . . 1|___________________________________. 1MHz 10MHz 100MHz FREQUENCY _______\_____ I <--- | / | ____________|____ | | \ | _____ /|\ \ \|/ H Field \ | __\__ | \ | _____ | \ | \ | \ ---> I \ | AREA in SPACE DEFINES \____________\ | INDUCTANCE | | |______/______| \ Remember, Current always flows in loops.. Even for transismision lines like below. ------------------------------------------------------------- _ _ _ /*\/ \/ \ __ | () () | | |__| 100uH |__ |__| | | | /| |_/\ _____| _|_/ | \/ 300 | | | | 8 ohm speaker __ | |___| | | |_____________| | \ | |__| | \| ------------------------------------------------------------- _ _ _ /*\/ \/ \ __ | () () | | |__| 100uH |__ |__| | | | /| |_/\ _____| _|_/ | \/ 500 | | | | 16 ohm speaker __ | |___| | | |_____________| | \ | |__| | \| ------------------------------------------------------------- _ _ _ /*\/ \/ \ __ | () () | __ | |__| .65uH |__| | |__| | | |__| |_/\ __| \/ 3ohms Ferrite Bead ________ / \ \ ______/_ \ \_______ ()_______) | |_______) \ / / \_/______/ ------------------------------------------------------------- Lp_Leak Lsec_Leak _ _ _ _ _ _ RL*(Np/Ns)^2 __ Rp / \/ \/ \ / \/ \/ \ Rs __ | |_ /\_| () () |____| () () |_ /\___| |_ |__| \/ | | | _ _ _ \/ | |__| | _|_ Rc / | / \/ \/ \ _|_ / Cp ___ core \ |_| () () | Cs ___ \ __ | loss / K*Lprime | | __ / | |______|_______|____________|______|_| |_| |__| |__| L Ip*Np Is*Ns Vp/Np Vs/Ns Rp winding resistance primary Lp winding reactance primary Rs winding resistance secondary Ls winding reactance secondary Rc core heating LK*Lp magnetic current ------------------------------------------------------------- ------------------------------------------------------------- Motors V N*delta_Phi/delta_time w*N*Phi*sin(wt) Torque K*I *sin(wt) ------------------------------------------------------------- _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) L_cm __ L_cm > D_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) ------------------------------------------------------------- ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | if L1 = L2 =M __ | () () | | | |__| |_____| then Lb=0 |__| __ | |__ _____ |__| | | | La = L1 + L2 +2*M |*() () | | if L1 = L2 =M \_/\_/\_/ L1 | then Lb=4*L La M _ _ _ | / \/ \/*\ L2 |K =((La-Lb)/4)/sqrt(L1*L2) __ | () () | | K = M/sqrt(L1*L2 | |__| |_____| |__| __ __ | |__ <-L-> __| | K = coef of coupling |__| | | |__| K = M/sqrt(L1*L2) | () () | \_/\_/\_/ L1 K = sqrt(1-Lclose/Lopen) M _ _ _ Lopen = L1*K / \/ \/ \ L2 Lclose =L1*(K^2 -1)*K __ | () () | __ | |__| |__| | if K=1 then M=sqrt(L1*L2) |__| |__| Lopen = L1 and Lclose =0 ------------------------------------------------------------- _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) L_cm __ L_cm > D_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) L _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ C __ | __ | |_________________|____| | |__| |__| Will ring where Impedance_L = Impedance_C 2*PI()*Freq*L = 1/(2*PI()*Freq*C) Q_factor =( Impedance_L )/R Q_factor = cycles to settle ------------Self_Inductance---------------- ----------------------Inductor--------------------------- __ 1X + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ Mutual Inductance L2a _ _ _ L2b _ _ _ /*\/ \/ \ /*\/ \/ \ VL1b __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| 1X 0 0 \___/ |__| + VL2b - L1 L1a+L1b L2 L2a+L2b Turn Ratio 1:1 K coupling coeffecient L1b/L1 = L2b/L2 M Mutual Inductance K*sqrt(L1*L2) VL1 (dI1/dt)*L1 + (dI2/dt)*M VL2 (dI2/dt)*L2 + (dI1/dt)*M ------------------------------------------------------------- __ P =10 + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | (P/S)*VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ Typical Transformer Turn Ratio =P:S L2a _ _ _ L2b _ _ _ K = L1b/L1 = L2b/L2 = 99% /*\/ \/ \ /*\/ \/ \ (S/P)*VL1b M = K*sqrt(L1*L2) __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| S=100 0 0 \___/ |__| + VL2b - L1 L1a+L1b L2 L2a+L2b Turn Ratio P:S K coupling coeffecient L1b/L1 = L2b/L2 = 99% M Mutual InductanceK*sqrt(L1*L2) VL1 (dI1/dt)*L1 + (dI2/dt)*M*(P/S) VL2 (dI2/dt)*L2 + (dI1/dt)*M*(S/P) VL1/VL2 P/S _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) ------------------------------------------------------------- __-----__ / d_inch \ Impedances inside coax / ___ \ | / ^ \ | | | |_ |__\| \ \___/ // \ D_inch/ \__ __/ ----- L_R_C Coaxial(D_inch,d_inch) Z_ohms = sqrt(L/C) = 138*log(D_inch/d_inch)/sqrt(E) C_pf/ft = 7.36*E/log(D_inch/d_inch) L_uH/ft = 0.14*log(D_inch/d_inch)) Delay_ns/ft = 1.016*sqrt(E) Propagation_%_c = 100/sqrt(E) CutOffFreq_Ghz = 7.5/( sqrt(E)*(D_inch+d_inch) ) ------------------------------------------------------------- Dielectric Constant E TFE 2.1 ethylene propylene 2.24 polyethylene 2.3 cellular polyethylene 1.4-2.1 silicone rubber 2.08-3.5 polyvinylchoride 3-8 _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) ------------------------------------------------------------- ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | Lb = 0 if (L1 = L2 = M) __ | () () | | | |__| |_____| |__| Voltage dropping current \ -----> \ \____\ \______\ \ \ \ \ \ \ _ \ _ ->E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V Voltage \ |_/ \ __/_ \ Pulse \ __/_ |_/ \ \ \ |_/ \ | _V | voltage \ \ - + \ \____\ \______\ \ \ \ \ \ ---> \ _ \ _ | E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V \ |_/ \ __/_ \ __/_ ->E |_/ \ \ |_/ \ \|/ | | v H \ \ \ \____\ \______\ \ \ \ \ current <------ Voltage increasing -----------------SimTransmissionLines-------------------- ___\__ --> I _______ ______|___/__|______________| | ->()___________\|/_____________| | |_/____| _/___ |50 Ohms| ________\_______|_\___|_____| | <-()_____________________|_____| | <-- I |___\_| |_______| / ------------------------------------------------------------------ 40 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOOOOO O IIIOIIIIOIOIOIOI_ 5V O I OOOOO O I IIIOIII I O I O IOIOIOOO 10ns =1/100MHz ------------------------------------------------------------------ 50 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOIOIOIOIOI 5V O I O I IIIOIII I O I O IOIOIOOO 10ns 80 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOIOIOIOIOIO 5V IIIOIII OOOOOOO O I O I IIIOIII I O I O IOIOIOOO 10ns 50 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 50 \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 IIIOIOIOIOIOIO 2.5 I O I O IOIOIOOO 10ns 25 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 50 \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:2 IIIIIIOIOIOIOIOIO 3.33V = 5V*50/75 I O I O IOIOIOOOOOO 20ns = 2*1/100MHz 25 ___ _/\ __________ _________ ______________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ _ /_ 5V\+Vin _________ 25 \/ |__ Need cap /| | \ 25 _| |_ | _|_ \ |_| / __/\ __| |_________| |______/\ ___| ___1fF \____/ _|__ \/ | 25 \/ _|_ _|_ /5V_ \-Vin Z0:50 | /// /// /| | | \ Freq:100M | ___ \|_| | / L_norm:2 |____________| | \____/ |___| _|_ /// IIIIIIOIOIOIOIOIO 2.5V I O I O IOIOIOOOOOO 20ns = 2*1/100MHz IOIOIOIOOOOOO 2.5V I O I O IIIIIIOIOIOIOIOIO 20ns = 2*1/100MHz ------------Q_factor-------------------------- L _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ C __ | __ | |_________________|____| | |__| |__| ring freq where Impedance_L = Impedance_C 2*PI()*Freq*L 1/(2*PI()*Freq*C) Q_factor ( Impedance_L )/R cycles to settle _ | | _ | | | | _ | | | | | | _ PULSE RESPONSE | | | | | | | | _ | | | | | | | | | | _ |_|_|_|_|_|_|_|_|_|_|_|_____\ | | | | | | | | | |_| / Time | | | | | | | |_| | | | | | |_| | | | |_| | | | | |_| ------------------------------------------------------------- _______ / a \ Inductance inside coax / ___ \ | / ^ \ b | In inches | | |_|__\| \ \___/ // \ / \_______/ L = (a/100)*( 7.353*log(16*a/6) -6.386 ) uHenries C = 8.5*er*( ((b/a)+1)/((b/a)-1) ) pF per foot __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | if L1 = L2 =M __ | () () | | | |__| |_____| then Lb=0 |__| __ | |__ _____ |__| | | | La = L1 + L2 +2*M |*() () | | if L1 = L2 =M \_/\_/\_/ L1 | then Lb=4*L La M _ _ _ | / \/ \/*\ L2 | K = ((La-Lb)/4)/sqrt(L1*L2) __ | () () | | K = M/sqrt(L1*L2) | |__| |_____| |__| __ __ | |__ <-L-> __| | K = coef of coupling |__| | | |__| K = M/sqrt(L1*L2) | () () | \_/\_/\_/ L1 K = sqrt(1-Lclose/Lopen) M _ _ _ Lopen = L1*K / \/ \/ \ L2 Lclose =L1*(K^2 -1)*K __ | () () | __ | |__| |__| | if K=1 then M=sqrt(L1*L2) |__| |__| Lopen = L1 and Lclose =0 Lp_Leak Lsec_Leak _ _ _ _ _ _ __ Rp / \/ \/ \ / \/ \/ \ Rs __ | |_ /\_| () () |____| () () |_ /\___| |_ |__| \/ | | | _ _ _ \/ | |__| | _|_ Rc / | / \/ \/ \ _|_ / RL*(Np/Ns)^2 Cp ___ core \ |_| () () | Cs ___ \ __ | loss / K*Lprime | | __ / | |______|_______|____________|______|_| |_| |__| |__| L Q_factor QualityFactor cycles to settle ( Impedance_L )/R cycles to settle ring freq where Impedance_L = Impedance_C 2*PI()*Freq*L 1/(2*PI()*Freq*C) _ | | _ | | | | _ | | | | | | _ PULSE RESPONSE | | | | | | | | _ | | | | | | | | | | _ |_|_|_|_|_|_|_|_|_|_|_|_____\ | | | | | | | | | |_| / Time | | | | | | | |_| | | | | | |_| | | | |_| | | | | |_| L _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ C __ | __ | |_________________|____| | |__| |__| ------------------------------------------------------------- <-Dia_cm--> __________ ______ | | __ | | -|-|-_| | | | |____| | |________| L_nH = 8.5*Dia_cm*N_turns^(5/3) <--L_inch----> __ __ __ _/\ \/\ \/\ \___ ^ |__/\ \/\ \/\ \__| | R_inch \_\ \_\ \_\ L_uH= (N_turns*R_inch)^2/(9*R_inch + 10*L_inch) _ _ Dia_inch | | | | _| | | |_ / __| |__ \ / / ^ \ \ R_inch/Dia_inch > 2.5 / / /|\ \ \ | | | | | | | R_inch | | \ \ / / \ \__ __/ / \_ --- _/ ------- L_uH =(R_inch/100)*(7.353*log(16*R_inch/Dia_inch)-6.386) ----------------------Self_Inductance---------------- about 9nH for small wire.. __\_ | / | _______________|_____________ ()_____________\|/____________) | V |_/_ \ _______ / a \ Inductance inside coax / ___ \ | / ^ \ b | In inches | | |_|__\| \ \___/ // \ / \_______/ L = (a/100)*( 7.353*log(16*a/6) -6.386 ) uHenries C = 8.5*er*( ((b/a)+1)/((b/a)-1) ) pF per foot <--L----> _/\\/\\/\\___ ^ |__/\\/\\/\\__| | R in inches \\ \\ \\ L = n^2*( r^2/ (9*r+10*l) ) microhenies L = FormF*D*n^2 in micro henries D in inches FormF = 0.025*(D/L) ------------------------------------------------------ <---D--> __________ ______ | | __ | | -|-|-_| | | D in cm | |____| | |________| L = 85e-10*D*N^(5/3) n = number turns D in cm on chip modeled a 2.8nH with a Q of 12.5 ------------Resistor_Caps---------------- DALE , Metal film 0.06pf ___________________ / \ \ ________/ \ \_______ ()_______) | |_______) \ / / \_/_________________/ Beyschlog carbon film 0.25pF ____ ____ / \ \_________/ `` \ ________/ \ \ \\ \\ \\ \_______ ()_______) | | || || || |_______) \ / /____//__// // / \_/__/ \_,,_/ ALLEN Bradley 1/4W carbon composite 0.3pF ____________________ / \ \\ \\ \\ _______/__ \ \\ \\ \\_______ ()_________) | || || ||_______) \ / // // // \__/__________//_//_// FERRITE_BEAD _ _ _ /*\/ \/ \ __ | () () | __ | |__| .65uH |__| | |__| | | |__| |_/\ __| \/ 3ohms Ferrite Bead ________ / \ \ ______/_ \ \_______ ()_______) | |_______) \ / / \_/______/ _ _ _ /*\/ \/ \ __ | () () | | |__| 100uH |__ |__| | | | /| |_/\ _____| _|_/ | \/ 300 | | | | 8 ohm speaker __ | |___| | | |_____________| | \ | |__| | \| _ _ _ /*\/ \/ \ __ | () () | | |__| 100uH |__ |__| | | | /| |_/\ _____| _|_/ | \/ 500 | | | | 16 ohm speaker __ | |___| | | |_____________| | \ | |__| | \| Transmission_Line ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | Lb = 0 if (L1 = L2 = M) __ | () () | | | |__| |_____| |__| __ | |__ _____ |__| | | | La = L1 + L2 +2*M |*() () | | if L1 = L2 = M \_/\_/\_/ L1 | then Lb=4*L La M _ _ _ | / \/ \/*\ L2 |K =((La-Lb)/4)/sqrt(L1*L2) __ | () () | | K = M/sqrt(L1*L2 | |__| |_____| |__| Voltage dropping current \ -----> \ \____\ \______\ \ \ \ \ \ \ _ \ _ ->E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V Voltage \ |_/ \ __/_ \ Pulse \ __/_ |_/ \ \ \ |_/ \ | _V | voltage \ \ - + \ \____\ \______\ \ \ \ \ \ ---> \ _ \ _ | E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V \ |_/ \ __/_ \ __/_ ->E |_/ \ \ |_/ \ \|/ | | v H \ \ \ \____\ \______\ \ \ \ \ current <------ Voltage increasing Dielectric Constant E TFE 2.1 ethylene propylene 2.24 polyethylene 2.3 cellular polyethylene 1.4-2.1 silicone rubber 2.08-3.5 polyvinylchoride 3-8 _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) __-----__ / d_inch \ Impedances inside coax / ___ \ | / ^ \ | | | |_ |__\| \ \___/ // \ D_inch/ \__ __/ ----- L_R_C Coaxial(D_inch,d_inch) Z_ohms = sqrt(L/C) = 138*log(D_inch/d_inch)/sqrt(E) C_pf/ft = 7.36*E/log(D_inch/d_inch) L_uH/ft = 0.14*log(D_inch/d_inch)) Delay_ns/ft = 1.016*sqrt(E) Propagation_%_c = 100/sqrt(E) CutOffFreq_Ghz = 7.5/( sqrt(E)*(D_inch+d_inch) ) _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ C __ | __ | |_________________|____| | |__| |__| __ L_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| __ | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | if L1 = L2 =M __ | () () | | | |__| |_____| then Lb=0 |__| Lp_Leak Lsec_Leak _ _ _ _ _ _ __ Rp / \/ \/ \ / \/ \/ \ Rs __ | |_ /\_| () () |____| () () |_ /\___| |_ |__| \/ | | | _ _ _ \/ | |__| | _|_ Rc / | / \/ \/ \ _|_ / RL*(Np/Ns)^2 Cp ___ core \ |_| () () | Cs ___ \ __ | loss / K*Lprime | | __ / | |______|_______|____________|______|_| |_| |__| |__| L __\_ H | / | _______________|_____________ ()_____________\|/____________) R_cm --> I | V L_cm |_/_ \ __\_ H | / | L_cm _______________|_____________ |\ --> I | \ W_cm \ \_____________|______________\ \|____________\|/______________| T_cm | V |_/_ \ _ _ Dia_inch | | | | _| | | |_ / __| |__ \ / / ^ \ \ R_inch/Dia_inch > 2.5 / / /|\ \ \ | | | | | | | R_inch | | \ \ / / \ \__ __/ / \_ --- _/ ------- <--L_inch----> __ __ __ _/\ \/\ \/\ \___ ^ |__/\ \/\ \/\ \__| | R_inch \_\ \_\ \_\ <---D--> __________ ______ | | __ | | -|-|-_| | | D in cm | |____| | |________| _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) __ L_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | if L1 = L2 =M __ | () () | | | |__| |_____| then Lb=0 |__| __ | |__ _____ |__| | | | La = L1 + L2 +2*M |*() () | | if L1 = L2 =M \_/\_/\_/ L1 | then Lb=4*L La M _ _ _ | / \/ \/*\ L2 | K = ((La-Lb)/4)/sqrt(L1*L2) __ | () () | | K = M/sqrt(L1*L2) | |__| |_____| |__| __ __ | |__ <-L-> __| | K = coef of coupling |__| | | |__| K = M/sqrt(L1*L2) | () () | \_/\_/\_/ L1 K = sqrt(1-Lclose/Lopen) M _ _ _ Lopen = L1*K / \/ \/ \ L2 Lclose =L1*(K^2 -1)*K __ | () () | __ | |__| |__| | if K=1 then M=sqrt(L1*L2) |__| |__| Lopen = L1 and Lclose =0 Lp_Leak Lsec_Leak _ _ _ _ _ _ __ Rp / \/ \/ \ / \/ \/ \ Rs __ | |_ /\_| () () |____| () () |_ /\___| |_ |__| \/ | | | _ _ _ \/ | |__| | _|_ Rc / | / \/ \/ \ _|_ / RL*(Np/Ns)^2 Cp ___ core \ |_| () () | Cs ___ \ __ | loss / K*Lprime | | __ / | |______|_______|____________|______|_| |_| |__| |__| L _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ C __ | __ | |_________________|____| | |__| |__| _ | | _ | | | | _ | | | | | | _ PULSE RESPONSE | | | | | | | | _ | | | | | | | | | | _ |_|_|_|_|_|_|_|_|_|_|_|_____\ | | | | | | | | | |_| / Time | | | | | | | |_| | | | | | |_| | | | |_| | | | | |_| ======================COMPONENTS_MAGNETIC====================== B = uH V = N*A*delta_B/delta_time energy = C*V^2/2 = i^2*L/2 ^ B /_\ | ________ B = u*H H*L =N*I | _-- _-- |/ / V = N*delta_Phi/delta_time / / /| / L = N*delta_Phi/delta_I ________/_|__/_________\ H / | / / Phi =B*Area u =u_0*u_r Phi = Flux B = Flux density H = Magnetic field u = permeablity m_r = 2000-> 6000 machine materials ---------------------------------------------------------------------- Motors V N*delta_Phi/delta_time w*N*Phi*sin(wt) Torque K*I *sin(wt) ---------------------------------------------------------------------- 8 ohm speaker _ _ _ /*\/ \/ \ __ | () () | | |__| 100uH |__ |__| | | | /| |_/\ _____| _|_/ | \/ 300 | | | | 8 ohm speaker __ | |___| | | |_____________| | \ | |__| | \| ---------------------------------------------------------------------- Ferrite Bead _ _ _ /*\/ \/ \ __ | () () | __ | |__| .65uH |__| | |__| | | |__| |_/\ __| \/ 3ohms Ferrite Bead ________ / \ \ ______/_ \ \_______ ()_______) | |_______) \ / / \_/______/ ---------------------------------------------------------------------- capacitors Remember, Current always flows in loops.. _______\_____ I <--- | / | ____________|____ | | \ | _____ /|\ \ \|/ H Field \ | __\__ | \ | _____ | \ | \ | \ ---> I \ | AREA in SPACE DEFINES \____________\ | INDUCTANCE | | |______/______| \ Self_Inductance _ _ _ /*\/ \/ \ Capacitance ___ | () () | ___ | |__| |____||____/\ ____| | |___| || \/ |___| CAPACITOR_IMPEDANCE_Ohms 100 .................................... | C . . . | . . L . | . . . | C . L . | . . . 10 |..........C.........L............... | . . . | . C L . . | . . . | . R . . | . R . . 1|___________________________________. 1MHz 10MHz 100MHz FREQUENCY ---------------------------------------------------------------------- Inductance_Q_factor Together with a perfect capacitor, How does the serie resistance in the inductor appear ? L _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ perfect C __ | __ | |_________________|____| | |__| |__| ring freq where Impedance_L = Impedance_C 2*PI()*Freq*L 1/(2*PI()*Freq*C) Q_factor ( Impedance_L )/R cycles to settle _ | | _ | | | | _ | | | | | | _ PULSE RESPONSE | | | | | | | | _ | | | | | | | | | | _ |_|_|_|_|_|_|_|_|_|_|_|_____\ | | | | | | | | | |_| / Time | | | | | | | |_| | | | | | |_| | | | |_| | | | | |_| ---------------------------------------------------------------------- Self_Inductance_wire __\_ H | / | _______________|_____________ ()_____________\|/____________) R_cm --> I | V L_cm |_/_ \ L_uH =.002*L_cm*( ln(2*L_cm/R_cm) -.75 ) __\_ H | / | L_cm _______________|_____________ |\ --> I | \ W_cm \ \_____________|______________\ \|____________\|/______________| T_cm | V |_/_ \ L_uH = 0.002*L_cm*( ln(2*L_cm/( W_cm +T_cm ) +.5 ) <--L_inch----> __ __ __ _/\ \/\ \/\ \___ ^ |__/\ \/\ \/\ \__| | R_inch \_\ \_\ \_\ L_uH = (N_turns*R_inch)^2/(9*R_inch + 10*L_inch) <-Dia_cm--> __________ ______ | | __ | | -|-|-_| | | | |____| | |________| L_nH = 8.5*Dia_cm*N_turns^(5/3) <--L_inch----> __ __ __ _/\ \/\ \/\ \___ ^ |__/\ \/\ \/\ \__| | R_inch \_\ \_\ \_\ L_uH = (N_turns*R_inch)^2/(9*R_inch + 10*L_inch) _ _ Dia_inch | | | | _| | | |_ / __| |__ \ / / ^ \ \ R_inch/Dia_inch > 2.5 / / /|\ \ \ | | | | | | | R_inch | | \ \ / / \ \__ __/ / \_ --- _/ ------- L_uH =(R_inch/100)*(7.353*log(16*R_inch/Dia_inch)-6.386) 0 0 0 0 0 0 ^ _________ | R_in | | | Single Layer air-core Coil |<-L_in-->| V within 1% or 2% | | |_________| 0 0 0 0 0 0 L_uH = R_in^2*N_turns^2/( 9*R_in + 10*L_in) 0 0 0 0 0 0 0 0 0 0 0 0 ^ _________ | R_in | | | |<-L_in-->| V Multiple Layer Coil | | |_________| 0 0 0 0 0 0 ^ B_in 0 0 0 0 0 0 | L_uH = 0.8*R_in^2*N_turns^2/(6*R_in +19*L_in +10*B_in) 0 0 ^ _ | R_in | | | | | V Single layer single row Layer Coil | | |_| 0 ^ B_in 0 | L_uH = 0.8*R_in^2*N_turns^2/( 8*R_in + 11*B_in) about 9nH for small wire.. __\_ | / | _______________|_____________ ()_____________\|/____________) | V |_/_ \ _______ / a \ Inductance inside coax / ___ \ | / ^ \ b | In inches | | |_|__\| \ \___/ // \ / \_______/ L = (a/100)*( 7.353*log(16*a/6) -6.386 ) uHenries C = 8.5*er*( ((b/a)+1)/((b/a)-1) ) pF per foot <--L----> _/\\/\\/\\___ ^ |__/\\/\\/\\__| | R in inches \\ \\ \\ L = n^2*( r^2/ (9*r+10*l) ) microhenies L = FormF*D*n^2 in micro henries D in inches FormF = 0.025*(D/L) <---D--> __________ ______ | | __ | | -|-|-_| | | D in cm | |____| | |________| L = 85e-10*D*N^(5/3) n = number turns D in cm on chip modeled a 2.8nH with a Q of 12.5 ---------------------------------------------------------------------- Mutual Inductance _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) L_cm __ L_cm > D_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) __ 1X + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ L1 = L1a+L1b L2 = L2a+L2b Turn Ratio =1:1 L2a _ _ _ L2b _ _ _ K = L1b/L1 = L2b/L2 /*\/ \/ \ /*\/ \/ \ VL1b M=K*sqrt(L1*L2) __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| 1X 0 0 \___/ |__| + VL2b - VL1 = (dI1/dt)*L1 + (dI2/dt)*M K = coupling coeffecient VL2 = (dI2/dt)*L2 + (dI1/dt)*M ---------------------------------------------------------------------- Typical Transformer __ P =10 + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | (P/S)*VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ L1 = L1a+L1b L2 = L2a+L2b Turn Ratio =P:S L2a _ _ _ L2b _ _ _ K=L1b/L1=L2b/L2=99% /*\/ \/ \ /*\/ \/ \ (S/P)*VL1b __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| S=100 0 0 \___/ |__| + VL2b - M= K*sqrt(L1*L2) VL1 = (dI1/dt)*L1 + (dI2/dt)*M*(P/S) K = coupling coeffecient VL2 = (dI2/dt)*L2 + (dI1/dt)*M*(S/P) VL1/VL2 = P/S __ 1X + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ Mutual Inductance L2a _ _ _ L2b _ _ _ /*\/ \/ \ /*\/ \/ \ VL1b __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| 1X 0 0 \___/ |__| + VL2b - L1 L1a+L1b L2 L2a+L2b Turn Ratio 1:1 K coupling coeffecient L1b/L1 = L2b/L2 M Mutual Inductance K*sqrt(L1*L2) VL1 (dI1/dt)*L1 + (dI2/dt)*M VL2 (dI2/dt)*L2 + (dI1/dt)*M __ P =10 + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | (P/S)*VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ Typical Transformer Turn Ratio =P:S L2a _ _ _ L2b _ _ _ K = L1b/L1 = L2b/L2 = 99% /*\/ \/ \ /*\/ \/ \ (S/P)*VL1b M = K*sqrt(L1*L2) __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| S=100 0 0 \___/ |__| + VL2b - L1 L1a+L1b L2 L2a+L2b Turn Ratio P:S K coupling coeffecient L1b/L1 = L2b/L2 = 99% M Mutual InductanceK*sqrt(L1*L2) VL1 (dI1/dt)*L1 + (dI2/dt)*M*(P/S) VL2 (dI2/dt)*L2 + (dI1/dt)*M*(S/P) VL1/VL2 P/S Lp_Leak Lsec_Leak _ _ _ _ _ _ RL*(Np/Ns)^2 __ Rp / \/ \/ \ / \/ \/ \ Rs __ | |_ /\_| () () |____| () () |_ /\___| |_ |__| \/ | | | _ _ _ \/ | |__| | _|_ Rc / | / \/ \/ \ _|_ / Cp ___ core \ |_| () () | Cs ___ \ __ | loss / K*Lprime | | __ / | |______|_______|____________|______|_| |_| |__| |__| L Ip*Np Is*Ns Vp/Np Vs/Ns Rp winding resistance primary Lp winding reactance primary Rs winding resistance secondary Ls winding reactance secondary Rc core heating LK*Lp magnetic current __ __ | |__ <-L-> __| | K = coef of coupling |__| | | |__| K = M/sqrt(L1*L2) | () () | \_/\_/\_/ L1 K = sqrt(1-Lclose/Lopen) M _ _ _ Lopen = L1*K / \/ \/ \ L2 Lclose =L1*(K^2 -1)*K __ | () () | __ | |__| |__| | if K=1 then M=sqrt(L1*L2) |__| |__| Lopen = L1 and Lclose =0 ---------------------------------------------------------------------- Transmission_Line ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | Lb = 0 if (L1 = L2 = M) __ | () () | | | |__| |_____| |__| __ | |__ _____ |__| | | | La = L1 + L2 +2*M |*() () | | if L1 = L2 = M \_/\_/\_/ L1 | then Lb=4*L La M _ _ _ | / \/ \/*\ L2 |K =((La-Lb)/4)/sqrt(L1*L2) __ | () () | | K = M/sqrt(L1*L2 | |__| |_____| |__| Voltage dropping current \ -----> \ \____\ \______\ \ \ \ \ \ \ _ \ _ ->E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V Voltage \ |_/ \ __/_ \ Pulse \ __/_ |_/ \ \ \ |_/ \ | _V | voltage \ \ - + \ \____\ \______\ \ \ \ \ \ ---> \ _ \ _ | E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V \ |_/ \ __/_ \ __/_ ->E |_/ \ \ |_/ \ \|/ | | v H \ \ \ \____\ \______\ \ \ \ \ current <------ Voltage increasing Dielectric Constant E TFE 2.1 ethylene propylene 2.24 polyethylene 2.3 cellular polyethylene 1.4-2.1 silicone rubber 2.08-3.5 polyvinylchoride 3-8 _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) __-----__ / d_inch \ Impedances inside coax / ___ \ | / ^ \ | | | |_ |__\| \ \___/ // \ D_inch/ \__ __/ ----- L_R_C Coaxial(D_inch,d_inch) Z_ohms = sqrt(L/C) = 138*log(D_inch/d_inch)/sqrt(E) C_pf/ft = 7.36*E/log(D_inch/d_inch) L_uH/ft = 0.14*log(D_inch/d_inch)) Delay_ns/ft = 1.016*sqrt(E) Propagation_%_c = 100/sqrt(E) CutOffFreq_Ghz = 7.5/( sqrt(E)*(D_inch+d_inch) ) ------------------------------------------------------------- _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) L_cm __ L_cm > D_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) L _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ C __ | __ | |_________________|____| | |__| |__| Will ring where Impedance_L = Impedance_C 2*PI()*Freq*L = 1/(2*PI()*Freq*C) Q_factor =( Impedance_L )/R Q_factor = cycles to settle _ | | _ | | | | _ | | | | | | _ PULSE RESPONSE | | | | | | | | _ | | | | | | | | | | _ |_|_|_|_|_|_|_|_|_|_|_|_____\ | | | | | | | | | |_| / Time | | | | | | | |_| | | | | | |_| | | | |_| | | | | |_| ------------Self_Inductance---------------- ------------------------------------------------------------- -----------------SimTransmissionLines-------------------- ___\__ --> I _______ ______|___/__|______________| | ->()___________\|/_____________| | |_/____| _/___ |50 Ohms| ________\_______|_\___|_____| | <-()_____________________|_____| | <-- I |___\_| |_______| / ------------------------------------------------------------------ 40 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOOOOO O IIIOIIIIOIOIOIOI_ 5V O I OOOOO O I IIIOIII I O I O IOIOIOOO 10ns =1/100MHz ------------------------------------------------------------------ 50 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOIOIOIOIOI 5V O I O I IIIOIII I O I O IOIOIOOO 10ns ------------------------------------------------------------------ 80 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOIOIOIOIOIO 5V IIIOIII OOOOOOO O I O I IIIOIII I O I O IOIOIOOO 10ns ------------------------------------------------------------------ 50 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 50 \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 IIIOIOIOIOIOIO 2.5 I O I O IOIOIOOO 10ns ------------------------------------------------------------------ 25 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 50 \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:2 IIIIIIOIOIOIOIOIO 3.33V = 5V*50/75 I O I O IOIOIOOOOOO 20ns = 2*1/100MHz ------------------------------------------------------------------ 25 ___ _/\ __________ _________ ______________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ _ /_ 5V\+Vin _________ 25 \/ |__ Need cap /| | \ 25 _| |_ | _|_ \ |_| / __/\ __| |_________| |______/\ ___| ___1fF \____/ _|__ \/ | 25 \/ _|_ _|_ /5V_ \-Vin Z0:50 | /// /// /| | | \ Freq:100M | ___ \|_| | / L_norm:2 |____________| | \____/ |___| _|_ /// IIIIIIOIOIOIOIOIO 2.5V I O I O IOIOIOOOOOO 20ns = 2*1/100MHz IOIOIOIOOOOOO 2.5V I O I O IIIIIIOIOIOIOIOIO 20ns = 2*1/100MHz ------------------------------------------------------------------ K = N-channel fet ======================COMPONENTS_MAGNETIC========================== ------------------------------------------------------------- B = uH V = N*A*delta_B/delta_time energy = C*V^2/2 =i^2*L/2 ------------------------------------------------------------- ------------------------------------------------------------- Lp_Leak Lsec_Leak _ _ _ _ _ _ RL*(Np/Ns)^2 __ Rp / \/ \/ \ / \/ \/ \ Rs __ | |_ /\_| () () |____| () () |_ /\___| |_ |__| \/ | | | _ _ _ \/ | |__| | _|_ Rc / | / \/ \/ \ _|_ / Cp ___ core \ |_| () () | Cs ___ \ __ | loss / K*Lprime | | __ / | |______|_______|____________|______|_| |_| |__| |__| L Ip*Np Is*Ns Vp/Np Vs/Ns Rp winding resistance primary Lp winding reactance primary Rs winding resistance secondary Ls winding reactance secondary Rc core heating LK*Lp magnetic current ------------------------------------------------------------- ^ B /_\ | ________ B = u*H H*L =N*I | _-- _-- |/ / V = N*delta_Phi/delta_time / / /| / L = N*delta_Phi/delta_I ________/_|__/_________\ H / | / / Phi =B*Area u =u_0*u_r Phi = Flux B = Flux density H = Magnetic field u = permeablity m_r = 2000-> 6000 machine materials ------------------------------------------------------------- Motors V N*delta_Phi/delta_time w*N*Phi*sin(wt) Torque K*I *sin(wt) Mutual Inductance __ 1X + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ L1 = L1a+L1b L2 = L2a+L2b Turn Ratio =1:1 L2a _ _ _ L2b _ _ _ K = L1b/L1 = L2b/L2 /*\/ \/ \ /*\/ \/ \ VL1b M=K*sqrt(L1*L2) __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| 1X 0 0 \___/ |__| + VL2b - VL1 = (dI1/dt)*L1 + (dI2/dt)*M K = coupling coeffecient VL2 = (dI2/dt)*L2 + (dI1/dt)*M Typical Transformer __ P =10 + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | (P/S)*VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ L1 = L1a+L1b L2 = L2a+L2b Turn Ratio =P:S L2a _ _ _ L2b _ _ _ K=L1b/L1=L2b/L2=99% /*\/ \/ \ /*\/ \/ \ (S/P)*VL1b __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| S=100 0 0 \___/ |__| + VL2b - M= K*sqrt(L1*L2) VL1 = (dI1/dt)*L1 + (dI2/dt)*M*(P/S) K = coupling coeffecient VL2 = (dI2/dt)*L2 + (dI1/dt)*M*(S/P) VL1/VL2 = P/S CAPACITOR_IMPEDANCE_Ohms 100 .................................... | C . . . | . . L . | . . . | C . L . | . . . 10 |..........C.........L............... | . . . | . C L . . | . . . | . R . . | . R . . 1|___________________________________. 1MHz 10MHz 100MHz FREQUENCY _______\_____ I <--- | / | ____________|____ | | \ | _____ /|\ \ \|/ H Field \ | __\__ | \ | _____ | \ | \ | \ ---> I \ | AREA in SPACE DEFINES \____________\ | INDUCTANCE | | |______/______| \ Remember, Current always flows in loops.. Even for transismision lines like below. ------------------------------------------------------------- _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) L_cm __ L_cm > D_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) ------------------------------------------------------------- ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | if L1 = L2 =M __ | () () | | | |__| |_____| then Lb=0 |__| __ | |__ _____ |__| | | | La = L1 + L2 +2*M |*() () | | if L1 = L2 =M \_/\_/\_/ L1 | then Lb=4*L La M _ _ _ | / \/ \/*\ L2 |K =((La-Lb)/4)/sqrt(L1*L2) __ | () () | | K = M/sqrt(L1*L2 | |__| |_____| |__| __ __ | |__ <-L-> __| | K = coef of coupling |__| | | |__| K = M/sqrt(L1*L2) | () () | \_/\_/\_/ L1 K = sqrt(1-Lclose/Lopen) M _ _ _ Lopen = L1*K / \/ \/ \ L2 Lclose =L1*(K^2 -1)*K __ | () () | __ | |__| |__| | if K=1 then M=sqrt(L1*L2) |__| |__| Lopen = L1 and Lclose =0 ------------------------------------------------------------- _____________________________ ->()____________________________) D_cm _____________________________ ->()____________________________) L_cm __ L_cm > D_cm __ | |__ __| | |__| | | |__| |*() () | \_/\_/\_/ M _ _ _ /*\/ \/ \ __ | () () | __ | |__| |__| | |__| |__| M_uH=.002*L_cm*( ln(2*L_cm/D_cm) -1 +D_cm/L_cm ) L _ _ _ __ R / \/ \/ \ __ | |_ /\_| () () |______| | |__| \/ | |__| _|_ ___ C __ | __ | |_________________|____| | |__| |__| Will ring where Impedance_L = Impedance_C 2*PI()*Freq*L = 1/(2*PI()*Freq*C) Q_factor =( Impedance_L )/R Q_factor = cycles to settle ------------Self_Inductance---------------- ----------------------Inductor--------------------------- __ 1X + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ Mutual Inductance L2a _ _ _ L2b _ _ _ /*\/ \/ \ /*\/ \/ \ VL1b __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| 1X 0 0 \___/ |__| + VL2b - L1 L1a+L1b L2 L2a+L2b Turn Ratio 1:1 K coupling coeffecient L1b/L1 = L2b/L2 M Mutual Inductance K*sqrt(L1*L2) VL1 (dI1/dt)*L1 + (dI2/dt)*M VL2 (dI2/dt)*L2 + (dI1/dt)*M ------------------------------------------------------------- __ P =10 + VL1b - ___ __ | |__ ____0 0___/ \___| | |__| | | | | +\___/- |__| |*() () | |*() () | (P/S)*VL2b L1a\_/\_/\_/ L1b\_/\_/\_/ Typical Transformer Turn Ratio =P:S L2a _ _ _ L2b _ _ _ K = L1b/L1 = L2b/L2 = 99% /*\/ \/ \ /*\/ \/ \ (S/P)*VL1b M = K*sqrt(L1*L2) __ | () () | | () () | + ___ - __ | |__| |____| |___/ \___| | |__| S=100 0 0 \___/ |__| + VL2b - L1 L1a+L1b L2 L2a+L2b Turn Ratio P:S K coupling coeffecient L1b/L1 = L2b/L2 = 99% M Mutual InductanceK*sqrt(L1*L2) VL1 (dI1/dt)*L1 + (dI2/dt)*M*(P/S) VL2 (dI2/dt)*L2 + (dI1/dt)*M*(S/P) VL1/VL2 P/S ------------------------------------------------------------- __\_ H | / | L_cm _______________|_____________ |\ --> I | \ W_cm \ \_____________|______________\ \|____________\|/______________| T_cm | V |_/_ L_uH = 0.002*L_cm*( ln(2*L_cm/( W_cm +T_cm ) +.5 ) ------------------------------------------------------------- <--L_inch----> __ __ __ _/\ \/\ \/\ \___ ^ |__/\ \/\ \/\ \__| | R_inch \_\ \_\ \_\ SELF INDUCTANCE Coil (L_cm,R_cm, N_turns) L_uH (N_turns*R_inch)^2/(9*R_inch + 10*L_inch) ------------------------------------------------------------- <-Dia_cm--> __________ ______ | | __ | | -|-|-_| | | | |____| | |________| L_nH= 8.5*Dia_cm*N_turns^(5/3) N_turns ->set 15 Dia_cm ->set =0.01/2.54 L_nH = 8.5*B15*B14^(5/3) ------------------------------------------------------------- _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) ------------------------------------------------------------- __-----__ / d_inch \ Impedances inside coax / ___ \ | / ^ \ | | | |_ |__\| \ \___/ // \ D_inch/ \__ __/ ----- L_R_C Coaxial(D_inch,d_inch) Z_ohms = sqrt(L/C) = 138*log(D_inch/d_inch)/sqrt(E) C_pf/ft = 7.36*E/log(D_inch/d_inch) L_uH/ft = 0.14*log(D_inch/d_inch)) Delay_ns/ft = 1.016*sqrt(E) Propagation_%_c = 100/sqrt(E) CutOffFreq_Ghz = 7.5/( sqrt(E)*(D_inch+d_inch) ) ------------------------------------------------------------- Dielectric Constant E TFE 2.1 ethylene propylene 2.24 polyethylene 2.3 cellular polyethylene 1.4-2.1 silicone rubber 2.08-3.5 polyvinylchoride 3-8 ------------------------------------------------------------- The inductance (I), in microhenrys. N number of turns and I inductance in microhenrys. L and R distances in inches. 0 0 0 0 0 0 ^ _________ | R | | | Single Layer air-core Coil |<---L--->| V within 1% or 2% | | I_uH = R^2*N^2/( 9*R + 10*L) |_________| 0 0 0 0 0 0 ------------------------------------------------------------- 0 0 0 0 0 0 0 0 0 0 0 0 ^ _________ | R | | | |<---L--->| V Multiple Layer Coil | | I_uH = 0.8*R^2*N^2/(6*R +19*L +10*B) |_________| 0 0 0 0 0 0 ^ B 0 0 0 0 0 0 | ------------------------------------------------------------- 0 0 ^ _ | R | | | | | V CASE 3: Single layer single row Layer Coil | | I_uH = 0.8*R^2*N^2/( 8*R + 11*B) |_| 0 ^ B 0 | ------------------------------------------------------------- _____________________________ ->()____________________________) <- d_cm | D_cm Z_ohms sqrt(L/C) | _____________________________ ->()____________________________) L_cm Z_ohms = 276.0*log(2*D_cm/d_cm) C_pf/meter = 12.06/log(2*D_cm/d_cm) L_uH/meter = 0.920*log(2*D_cm/d_cm) w0 = sqrt(L*C) = sqrt(dL*dC*X^2) = X*sqrt(dL*dC) velocity = (2*pi()/sqrt(dL*dC) ------------------------------------------------------------- ___\__ --> I ______|___/__|________________ ->()___________\|/______________ | |_/____| _/___ | | ________\_______|_\___|_____| | <-()_____________________|_______| <-- I |___\_| __ / | |__ _____ |__| | | | |*() () | | \_/\_/\_/ L1 | Lb M _ _ _ | Lb = L1 + L2 -2*M /*\/ \/ \ L2 | Lb = 0 if (L1 = L2 = M) __ | () () | | | |__| |_____| |__| Voltage dropping current \ -----> \ \____\ \______\ \ \ \ \ \ \ _ \ _ ->E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V Voltage \ |_/ \ __/_ \ Pulse \ __/_ |_/ \ \ \ |_/ \ | _V | voltage \ \ - + \ \____\ \______\ \ \ \ \ \ ---> \ _ \ _ | E \| \ \ _ \| \ \|/ _ /_ \ ^ _ /_ v H |_/ \ _V \ |_/ \ __/_ \ __/_ ->E |_/ \ \ |_/ \ \|/ | | v H \ \ \ \____\ \______\ \ \ \ \ current <------ Voltage increasing ----------------------------SimTransmissionLines-------------------- ___\__ --> I _______ ______|___/__|______________| | ->()___________\|/_____________| | |_/____| _/___ |50 Ohms| ________\_______|_\___|_____| | <-()_____________________|_____| | <-- I |___\_| |_______| / ------------------------------------------------------------------ 40 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOOOOO O IIIOIIIIOIOIOIOI_ 5V O I OOOOO O I IIIOIII I O I O IOIOIOOO 10ns =1/100MHz ------------------------------------------------------------------ 50 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOIOIOIOIOI 5V O I O I IIIOIII I O I O IOIOIOOO 10ns ------------------------------------------------------------------ 80 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 5K \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 OOOIOIOIOIOIO 5V IIIOIII OOOOOOO O I O I IIIOIII I O I O IOIOIOOO 10ns ------------------------------------------------------------------ 50 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 50 \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:1 IIIOIOIOIOIOIO 2.5 I O I O IOIOIOOO 10ns ------------------------------------------------------------------ 25 ___ _/\ __________ _________ _________________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ ___ /_ 5V\ _________ 50 \/ | /| | \ _| |_ | \ |_| / ___| |_________| |_______________| \____/ Vin | | _|_ _|_ Z0:50 _|_ /// /// Freq:100M /// L_norm:2 IIIIIIOIOIOIOIOIO 3.33V = 5V*50/75 I O I O IOIOIOOOOOO 20ns = 2*1/100MHz ------------------------------------------------------------------ 25 ___ _/\ __________ _________ ______________| | | \/ |_| |_| | |___| _|__ |_________| |___/\ _ /_ 5V\+Vin _________ 25 \/ |__ Need cap /| | \ 25 _| |_ | _|_ \ |_| / __/\ __| |_________| |______/\ ___| ___1fF \____/ _|__ \/ | 25 \/ _|_ _|_ /5V_ \-Vin Z0:50 | /// /// /| | | \ Freq:100M | ___ \|_| | / L_norm:2 |____________| | \____/ |___| _|_ /// IIIIIIOIOIOIOIOIO 2.5V I O I O IOIOIOOOOOO 20ns = 2*1/100MHz IOIOIOIOOOOOO 2.5V I O I O IIIIIIOIOIOIOIOIO 20ns = 2*1/100MHz ------------------------------------------------------------------