description test
Color
Background color
Background image
Border Color
Font Type
Font Size
  1. Question:


    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer:

    MATLAB script source pozar_05_example_01.m and all necessary support functions included in .zip here attached file pozar_05_example_01.zip
    including detailed explanation. Following, the key points:

    For the given load, the component values are

    C1 = 9.227738300997709e-13
    ctype =C [Farad]
    L1 = 3.898484006168380e-08
    ltype =L [Henry]

    L2 = 2.167378326912196e+07
    ctype =L [Henry]
    C2 = 3.847649490485592e+11
    ltype =C [Farad]


    with frequency response

    [​IMG]

    With ADS, using the component DA_SmithCharftMatch that opens the Smith Chart Utility

    [​IMG]

    that readily obtains the component values

    [​IMG]


    [​IMG]


    [​IMG]



    the term 'series' is here used as the jX component connected in both circuits as above.

    But in some literature sources like [MEDLY] a distinction is made between 'cascade' that would the jX component connection above, and 'series' would be this:

    [​IMG]

    [MEDLY] Microwave and RF Circuits: Analysis, Synthesis and Design. Author Max W Medley Jr.

    John BG
  2. Question:

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual


    Answer:

    MATLAB script source pozar_05_exercise_25.m and all necessary support functions included in .zip here attached file pozar_05_exercise_25.zip
    including detailed explanation. Following, the key points:

    [​IMG]

    for a load located here

    [​IMG]

    the following 2-element L-shape match circuits are possible:

    [​IMG]

    the values of the components are

    C1 = 1.258213410121157e-12
    L1 = 5.012370792994983e-09

    L2 = 2.169965544798663e-08
    C2 = 1.263388970843133e-12

    the resulting fractional bandwidths are

    df_ov_BW1 = 0.188090595470227
    df_ov_BW2 = 0.194140292985351

    there are 2 related errors in the solutions manual:

    1.
    [​IMG]
    this dw is f2-f1 so the calculation goes right to left, dw is a known parameter that along with the other values is used to verify

    true(dw1*log(1/gamma_m)=<pi*R/L)
    =
    logical
    1

    true(dw2*log(1/gamma_m)=<pi*R/L)

    =
    logical
    1

    f2 and f1 are also obtained, dw1 dw2 being

    dw1=2*pi*(f2_sol1-f1_sol1)

    dw1 = 2.363105994030242e+09

    dw2=2*pi*(f2_sol2-f1_sol2)

    dw2 = 2.439132536247116e+09



    2.

    [​IMG]
    again, this 174% is not the fractional bandwidth of the only circuit suggested in the solutions manual, the fractional bandwidths for solutions are shown above.

    John BG
    jgb2012@sky.com
  3. Question:

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer:

    MATLAB script source pozar_05_exercise_13.m and all necessary support functions included in .zip here attached file pozar_05_exercise_13.zip

    [​IMG]


    MATLAB, an ADS circuit, the ADS LinCalc Utility and the online free microstrip calculator, these tools are used to dimension microstrip tracks as required in the question. The higher ZL/Z0 the sharper, more selective, becomes the frequency response.

    John BG
    jgb2012@sky.com
  4. Question:

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer:

    As explained in the attached answer the error peaks at multiples of λ/2.

    [​IMG]

    John BG
    jgb2012@sky.com
  5. Question:

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer:

    Basic MATLAB script source pozar_05_exercise_15.m

    I call this one 'basic' because for this exercise the MATLAB script doesn't go much further than getting the cut-off details.

    As the reader can appreciate for this exercise I have used ADS instead to supply the result of the matching waveguide section because
    it's in chapter 3 of [POZAR] where it makes more sense to review 3D electromagnetic models but I chose to start in chapter 5, so this exercise
    can be reviewed once for instance a working Yee model in MATLAB is available, that allows enough flexibility and accuracy
    needed to change waveguide dimensions and fill-up dielectric characteristics in order to reach a valid affordable solution like it's the case here to be a dielectric fin instead of a complete fill-up.

    [​IMG]

    John BG
    jgb2012@sky.com
  6. Question:
    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer:

    MATLAB script source pozar_05_exercise_16.m and all necessary support functions included in .zip here attached file pozar_05_exercise_16.zip

    [​IMG]

    The more sections added the flatter is the pass-band but the size of the circuit increases. Despite Binomial has as flat frequency response around f0 it doesn't have the best insertion loss, not .6 at 2*f0.

    John BG
    jgb2012@sky.com
  7. Question:

    [​IMG]

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer :

    [​IMG]

    MATLAB script source pozar_05_exercise_17.m and all necessary support functions included in .zip here attached file pozar_05_exercise_17.zip

    This question is again the kind that one thinks the Symbolic Toolbox is going to be the perfect tool but again
    the Symbolic Toolbox returns 9 DIN4 pages full of a Symbolic expression that cannot be called a solution. let alone
    handled without a crane.

    Luckily it can be solved numerically, as shown in the attached script and notes.

    Firstly it's convenient to find out Z1 and Z2 to validate the sought expressions
    • Z1(ZL,Z0)
    • Z2(ZL,Z0)
    z1=Z1/Z0;z2=Z2/Z0

    z1 z2 turn out to be 1.1067 and 1.3554

    the frequency response of |Γ| is

    [​IMG]

    As shown in the attached script, the ABCD expressions can be manipulated to obtain the following

    [​IMG]

    that in turn reveals (Z2/Z1) Z2_ov_Z1 = 1.224563802132642

    From here all that's left is to calculate the characteristic impedance of the λ/4 section next to load Z2, from [POZAR] 253pg.

    gamma_n(2)==(ZL_ov_Z0-z2)/(ZL_ov_Z0+z2)

    John BG
    jgb2012@sky.com
  8. Question

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer

    This one is easy

    ZL_ov_Z0=[1.5:.01:6];
    for n=N
    A=2^(-n)*(ZL_ov_Z0-1)./(ZL_ov_Z0+1);
    df_over_f0=2-4./pi*acos(.5*(gamma_m./abs(A)).^(1/n));
    plot(ZL_ov_Z0,df_over_f0);hold all
    end
    title('\Deltaf/f0');xlabel('ZL/Z0');grid on




    [​IMG]

    John BG
    jgb2012@sky.com
  9. Question:

    [​IMG]
    Answer:


    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    [​IMG]

    The question only asks for the short circuit cases, but all open circuit results have been added.

    John BG
    jgb2012@sky.com
  10. Question:
    [​IMG]

    Answer:

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    the solutions manual erroneously solves for single stub, ignoring X2, the reactance of the 2nd stub.

    The sought solutions have to be of the following shape

    · D_OCstub1(d,RL,XL)

    · D_OCstub2(d,RL,XL)

    · D_SCstub1(d,RL,XL)

    · D_SCstub2(d,RL,XL)

    the RL constraint would imply that there would be need for a really long transmission line for really small RL values, or that there would be need for really short transmission line when attempting to match large RL values.

    Numerical and symbolic equations are supplied. For the numerical case 2D slice


    [​IMG]

    is not as meaningful as visualizing the volume with both a static and a shifting plane

    [​IMG]

    John BG
    jgb2012@sky.com
  11. Question

    [​IMG]


    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual



    Answer

    5.9 is already solved here:
    https://forum.allaboutcircuits.com/...ozar-chapter-05-exercise-09-with-matlab.1477/

    MATLAB script source pozar_05_exercise_09.m and all necessary support functions included in .zip here attached file pozar_05_exercise_09.zip

    [​IMG]


    Reducing |s11| the resolution can be improved from 0.001 to 0.0002 without significant increase in processing delay.

    [​IMG]



    For this exercise, the peaks do not show as clearly as in 5.9 so the funciton kmeans comes handy to decide where the |s11| nulls are exactly located.

    [​IMG]

    Verifying the frequency responside directly connecting impedance equations for each component

    [​IMG]

    Like in 5.9 some additional ADS simluations and optimiser results are included, but ADS has more accurate models of all circuit components, even for such basic ones, so the results obtained with an accurate but basic MATLAB script, and using ADS, are not going to always agree.

    John Bofarull Guix
    jgb2012@sky.com
  12. Question

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer

    MATLAB script source pozar_05_exercise_09.m and all necessary support functions included in .zip here attached file pozar_05_exercise_09.zip
    In the attached zip there is a detailed explanation in Adobe format detailing all lines of the solution.

    [​IMG]

    An analytic solution with |s11| surface is show and the frequency response to valide the calculated lengths is obtained with different cross-sections of such surface.

    The sought Open Ciruit shunt stub lengths are the shortest D1 D2 that null |s11|

    [​IMG]

    The obtention of the |s11| surface nulls, the exact location where D1 D2 cancel reflections is found reversing the surface and catching peaks.
    This is because when attemting too small D1 D2 steps, with conventional computer platforms MATLAB may reach default limits or borrow excessive
    time.

    The Laplacian obtained with del2 is here conveniently used to reduce the amount of peaks returned by command findpeaks.

    [​IMG]

    1st solution, stubs with lengths below 0.5:

    D11=0.086

    D12=0.375


    2nd solution
    D21=0.199

    D22=0.375



    Some of the support functions used in previous questions have been ugraded to solve this exercise with the Smith chart.

    1st stub, next to load, 1st length. The red is ZL and the green marker is YL=1/ZL.
    the 1st stub has to bring YL to the magenta circle, to the intersection blue marker to the left hand side of YL.

    [​IMG]

    1st stub, 2nd length, reaching the 2nd intersection now with opposite sign reactance.

    [​IMG]

    2nd stub, 1st length, 3rd and 4th intersections again are the blue markers.

    [​IMG]


    2nd stub, 2nd length

    [​IMG]

    The resulting stub lengths match those obtained analytically.

    Verifying results with frequency response:

    It turns out that for a given pair D1 D2 the frequency resonse is already a particular cross section of surface |s11|.
    Choosing 2 cross sections including those pairs D1 D2 reaching |s11| nulls,

    [​IMG]

    And the extracted contours are

    [​IMG]
    and

    [​IMG]

    Any comments welcome

    John Bofarull Guix
    jgb2012@sky.com
  13. Question:

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer:

    [​IMG]

    Certain loads can be matched at a single frequency with just a transmission line with the correct characteristic impedance and length.

    Attached MATLAB script to to calculate Z1 and L of such transmission load to match to Z0, not all loads can be matched with such simple circuit.

    John BG
    jgb2012@sky.com
  14. Question

    [​IMG]

    Literature source [POZAR] available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual

    Answer

    [​IMG]

    For Open Circuit and Short circuit lossy transmission line stubs there are peaks of valleys of reactance close to multiples of λ/4 and 3λ/4 (equivalent electric lengths π/2 and 3π/2).

    Since there's always some real part of the input impedance, it's about choosing a length that supplies high enough |reactance| while keeping the resistive part low enough for the OC/SC stub to be considered an equivalent 'good' capacitor or inductor.

    Attached MATLAB script that shows how to find such reactance peaks and valleys for a section of lossy transmission line.
  15. Question

    [​IMG]

    Answer

    the literature source [POZAR] is available here:
    https://www.amazon.co.uk/Microwave-Engineering-David-M-Pozar/dp/0470631554

    There's also a solutions manual available here:
    https://www.scribd.com/doc/176505749/Microwave-engineering-pozar-4th-Ed-solutions-manual


    [​IMG]


    this is the OC series stub impedance match circuit on single frequency.

    [​IMG]

    The arcs of the transmission line lengths on the Smith chart are:

    [​IMG]


    [​IMG]

    And the OC series stub arcs:

    [​IMG]


    [​IMG]

    There's also an alternative graph to find the required transmission line and stub lengths; |s11| surface.

    clc;clear all;close all
    ZL=90+1j*60;Z0=75;
    Dstep=.001;drange=[0: Dstep:1];
    D1=drange;D2=D1;
    [D1,D2]=meshgrid(drange);


    Z1=Z0*(ZL+1j*Z0*tan(2*pi*D1))./(Z0+1j*ZL*tan(2*pi*D1));
    Zin_stub=Z0./(1j*tan(2*pi*D2));
    % series oc stub
    Zin=Z1+Zin_stub;
    s11=(Zin-Z0)./(Zin+Z0);


    surf(abs(s11),'LineStyle','none')
    ax=gca
    xlabel('D1');ylabel('D2');
    ax.XTickLabelMode='manual'; ax.YTickLabelMode='manual';
    ax.XTickLabel=[0:0.1:1];ax.YTickLabel=[0:0.1:1];
    ax.XTick=[0:100:1000];ax.YTick=[0:100:1000];
    ax.PlotBoxAspectRatio=[1 1 1]


    [​IMG]


    hold all;x0=find(drange==.5) % plotting corner to box D1<.5 D2<.5
    plot3([x0 x0 0],[0 x0 x0],[5 5 5],'Color',[1 0 0],'LineWidth',3)

    % moving camera birdeye view
    ax.CameraPosition=[500 500 10]

    camzoom(ax,1.5) % zoom in a bit, camzoom is cumulative
    % zoom_factor within [0 1) zooms out zoom_factor>1 zooms in

    ax.CameraUpVector = [0 1 0]; % camera attitude
    ax.CameraTarget = [500 500 0]; % centring
    ax.CameraViewAngle =8*pi; % focus

    [​IMG]

    automating peaks capture: findpeaks with MinPeakProminence=2.5 returns the right amount of peaks. MinPeakProminence larger or smaller than 2.5 then either too few or too many peaks.

    With MinPeakHeight=2 command findpeaks doesn't catch the right amount of peaks for any MinPeakDistance, going from 6 peaks only to too many peaks.

    With Threshold=2 doesn't catch a single peak but Threshold=1 gets the right amount of peaks.



    To get zeros exact locations, it's useful to invert |s11| surface just plotted, with the Laplacian of the surface, command del2

    V=1e3*del2(abs(s11));
    figure(2);ax=gca;surf(V,'Lines','none');
    xlabel('D1');ylabel('D2');
    ax.XTickLabelMode='manual';
    ax.YTickLabelMode='manual'; ax.XTickLabel=[0:0.1:1];ax.YTickLabel=[0:0.1:1];
    ax.XTick=[0:100:1000];ax.YTick=[0:100:1000];
    [pks,locs]=findpeaks(V( : ),'Threshold',1);
    [nd1,nd2]=ind2sub(size(V),locs);

    hold all;figure(2);plot3(nd2,nd1,V(nd2,nd1)+2,'ro');
    % plot peaks
    ax.PlotBoxAspectRatio=[1 1 1]

    x0=find(drange==.5) % plot corner to box D1<.5 D2<.5
    figure(2);
    plot3([x0 x0 0],[0 x0 x0],[.5 .5 .5],'Color',[1 0 0],'LineWidth',3)
    ax2=gca

    ax2.CameraPosition=[500 500 10]
    % moving camera bird-eye view
    ax2.CameraUpVector = [0 1 0]; % camera attitude

    camzoom(ax,1.5) % zoom in a bit, camzoom is cumulative

    % zoom_factor within [0 1) zooms out zoom_factor>1 zooms in
    ax2.CameraTarget = [500 500 0]; % centring

    abs(s11(sub2ind(size(V),nd1,nd2)))

    = 0.001390798787950
    0.001390798787950
    0.002883920448033
    0.002883920448033
    0.001390798787950
    0.001390798787950
    0.002883920448033
    0.002883920448033

    unique(sort(drange(nd1)))
    = 0.1470 0.3530 0.6470 0.8530

    numel(nd1)
    = 8

    among these stub lengths

    D1=unique(drange(nd1))
    = 0.1470 0.3530 0.6470 0.8530

    D2=unique(drange(nd2))

    = 0.1740 0.4820 0.6740 0.9820


    the stub lengths inside D<.5 are the smallest ones

    Dstub1= D1([1 2])
    = 0.1470 0.3530

    Dstub2= D2([1 2])

    = 0.1740 0.4820

    The resulting frequency response is the same as the one obtained with the MATLAB solution

    [​IMG]

    So the problem is simple enough to find transmission line and stub length on a surface.


    Quick check how short circuit and open circuit stubs behave over frequency:

    Zin_sc_stub=1j*Z0*tan(beta*L)

    Zin_oc_stub=-1j*Z0*cot(beta*L)

    da=pi/2000;a=[-2*pi:da:2*pi];
    y_OC=-cot(a); y_SC=tan(a);
    figure;plot(a,y_OC,a,y_SC);
    grid on;axis([-2*pi 2*pi -10 10])
    legend('SC','OC')
    ylabel('Stub Z_i_n');xlabel('\betaL')
    xticks([-2*pi -2*pi*3/4 -pi -pi/2 0 pi/2 pi 3*pi/2 2*pi])
    xticklabels({'-2\pi','-3\pi/4','-\pi','-\pi/2','0','\pi/2','\pi','3\pi/2','2\pi'})


    [​IMG]


    John BG
    jgb2012@sky.com