1 / 56

590 likes | 981 Views

Capacitance method of moments. Q. a. Capacitance of hollow sphere. Capacitance of parallel plates. Capacitance of a circular disk. r. R. . . Voltage at origin = 0. a. 2 - . Capacitance of a circular disk. r. . a. R. . 2 - . Charge density is uniform s0.

Download Presentation
## Capacitance method of moments

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Capacitance**method of moments**Q**a Capacitance of hollow sphere**Capacitance of a circular disk**r R Voltage at origin = 0 a 2 - **Capacitance of a circular disk**r a R 2 - Charge density is uniform s0**Capacitance of a circular disk**r a R 2 - Charge density decreases s0(1-r/a)**This technique was developed**in a Ph.D. thesis by Ken Mei in 1962. His adviser was Jean van Bladel.**Method of moments**• a known charge causes a potential • what is the potential? • a measured or known potential is caused by an unknown charge • what was that charge? • used in em to find current distributions on antennas, scattering objects such as cubes, sleds, planes, and missles • PhD theses, faculty publications**V(a)**V(b) Q2 Q1 2 equations 2 unknowns**V(a)**V(b) Q2 Q1**>> A = [1/4 1/5 ; 1/5 1/4] ;**>> V = [1 ; 1] ; >> Q = V’ / A % ‘transpose Q = 2.2222 2.2222 >> QQ = A \ V; QQ = 2.2222 2.2222**complications???**r1 r2 • The potential @ each charge sphere is specified as V1 or V2 • Locations are with respect to an origin.**solution to singularity**Assume that the potential is uniform within the sphere and it is equal to the value at its edge r = a.**1**1 1 1 1 1**Q =**• 4.69 2.56 4.69 -4.69 -2.56 -4.69 • >>**a**b -a -a a -b -b b Capacitor C = Q / V rj ri**b**-b -b b Capacitor C = Q / V Harrington – p. 27 Dwight 200.01 & 731.2**b**-b -b b Capacitor C = Q / V**MATLAB**• clear; clf; • N=9; • az=37.5; • el=5;**%identify subareas**• for m = 1:2 • for h = 1:N • for k = 1:N • a(m - 1)*N*N + (h - 1)*N + k, :)=[m, h, k]; • end • end • end**%calculate matrix elements**• for h=1:2*N*N • for k=1:2*N*N • aa=norm(a(h, :) - a(k, :)); • if aa==0 • b(h, k) = 2 * sqrt(pi); • else • b(h, k) =1 / aa; • end • end • end**%set voltages on plates**• for h=1:N*N • V(h) = +1/2; • V(h+N*N) = -1/2; • end**%calculate charges**• Q = V*inv(b); • %top plate • QA(1:N*N) = Q(1:N*N); • %bottom plate • QB(1:N*N)=Q(N*N+1:2*N*N);**%plot**• [x,y]=meshgrid(1:N); • for i=1:N • za(1:N,i)=QA((i-1)*N+1:(i-1)*N+N)'; • zb(1:N,i)=QB((i-1)*N+1:(i-1)*N+N)'; • end • mesh(x,y,za) • hold on • mesh(x,y,zb)**QT=0;**for j=1:N*N QT=QT+Q(j); end QT**What have you done?**You have learned a technique, to accurately calculate the capacitance of a parallel plate capacitor! Big deal!**Capacitance of a circular disk**r a R 2 - Charge density is uniform s0**Capacitance of a circular disk**r a R 2 - Charge density is noniform**C = 3.9420**C = 3.2367 C = 2.7026 C = 3.6332**capacitance of a unit cube**Hwang & Mascogni – “Electrical capacitance of a unit cube” – Journal of Applied Physics 3798-3802 (2004).**2a**C a**note the charge**density at the corner**a**h Sava V. Savov February 1, 2004**1 2 3**x. • E = s /2 • V = x s /2 • V1 = 2 [0/2 s1 + 1 s2 + 2/2 s3 ] • V2 = 2 [1/2 s1 + 0 s2 + 1/2 s3] • V3 = 2 [2/2 s1 + 1 s2 + 0/2 s3]**1 2 3**• V1 0 1 2/2 s1 • V2 = 2 1/2 0 1/2 s2 • V3 2/2 1 0 s3 • pn junction • double layer • VLSI**pn junction**• linear quadratic • V[-2d] - 0.36 - 2 • V[-d] - 0.18 - 3/2 • V[0] = 0 or 0 • V[d] + 0.18 + 3/2 • V[2d] + 0.36 + 2**matrix**• 0 1 2 3 4/2 • 1/2 0 1 2 3/2 • 2/2 1 0 1 2/2 • 3/2 2 1 0 1/2 • 42 3 2 1 0**MATLAB**• [V] = [matrix] [Q] V V r r x x**Calculate vector “V”**• clear • clf • m=input('What is the size of the matrix? ...'); • for i=1:m • v(i)=NaN; • end • v**Calculate matrix “a”**• for i=1:m • for j=1:m • a(i,j)=NaN; • end • end**for i=1:m**• for j=i:m • if i==j • a(i,j)=0; • b(i)=i; • elseif i<j & j<m a(i,j)=(j-b(i)); elseif i<j & j==m • a(i,j)=(j-b(i))/2; • end • end • end

More Related