Reference / Paper · 2020
ON7DQ — The NanoVNA: From Theory to Practice
- nanovna
- vna
- smith chart
- swr
- antennas
- measurement
Reference / Paper · 2020
The nanoVNA ... from theory to practice! UBA Section OST – Luc ON7DQ V2.03 March 2020 Preface Time is short ... some things will be explained in a “simple" way, so not always scientifically correct … still too difficult ? Close your eyes, sit back and relax ... Minimal use of math or formulas, but we can’t do without some essential ones Only basic nanoVNA with standard firmware is discussed Halfway ... BREAK ! … You will need a drink ! Powerpoint presentation will be available for download At the end : lots of links to websites, videos and software nanoVNA – ON7DQ 2 Content Some basics (actually … a lot !) Complex impedance and admittance, Transmission Lines, Reflection Coefficient, Return Loss, SWR, S-parameters, the Smith Chart Measuring is knowing - What is a Vector Network Analyzer ? - Functioning, calibration and capabilities of the nanoVNA - Connecting to a PC: using the nanoVNA Saver program - extra features of the nanoVNA Just do it ! - Practical examples: measurements on cables, antennas, filters, components ... nanoVNA – ON7DQ 3 Basic stuff - Complex Impedance We know : R, L & C : in series : add R’s, add L’s in parallel : add C’s Combination of R, L & C COMPLEX IMPEDANCE Z = R + j.X in Ohm (Ω) Reactances also in Ω Real (Re) and Imaginary (Im) part with ω = 2. π. f (angular velocity) XL = ω. L XC = − 1 ω.C e.g. R = 100 Ω, in series with L = 10 nH, at 145 MHz Z = 100 + j.9,11 Let’s put this in a x/y GRAPH Question : Where would one draw Z = 1000 + j.500 ??? (solution is in the Smith Chart … wait a while …) nanoVNA – ON7DQ 4 Complex Impedance • Where do we encounter complex impedances ? • Transmission Lines (cables) • Components • Antennas • Filters • Amplifiers … they all can present a complex impedance ! • ADMITTANCE 1 1 𝑌= = = G + j.B 𝑍 𝑅+𝑗.𝑋 unit S (Siemens)* (*in USA : mho) [ G = the “conductance” , B = the “susceptance” ] Useful in parallel circuits : just add the admittances ! e.g. R = 150 Ω in parallel with C = 100 pF , at 28 MHz Y = 1/R + j.2.𝝅.f.C = 0,0066 + j.0,0176 S but Z = 1/Y = ?? Wait a while … ( ↑ NOTE : capacitive susceptance = positive ! ) nanoVNA – ON7DQ 5 Transmission Lines (TL) Consider an ideal TL : it has NO LOSS, and can be drawn as a cascade of small L/C cells (dx is a small unit of distance) : e.g. for RG-58 : l = 250 nH/m and c = 100 pF/m Zg ldx Eg ldx cdx ldx cdx cdx (Zg ,is the SOURCE , ZL is the LOAD impedance) dx Every cable has a characteristic impedance Z0 𝑍0 = nanoVNA – ON7DQ ZL 𝑙 𝑐 (e.g. 50 Ω, 75 Ω) 6 TL – Velocity Factor Radio waves travel in free space at what speed ? … the speed of light v0 = 300.000 km/s Waves in a TL go much slower … (due to phase shift in the L/C cells), typically 66% of v0, or 200.000 km/s the velocity factor is k = 0,66 (*USA : VF) It depends on the dielectric constant εr of the insulating material and 𝑘 = 1 𝜀𝑟 e.g. if k = 0,66 , εr = 2,30 the “guided wavelength” is λg = k.λ0 (with λ0 : the wavelength in free space = v0/f) so k is also a “shortening” factor e.g. How long is a piece of RG-58 to obtain a λ/4 in the 2m band ? Answer : +/- 34 cm , not 50 cm ! nanoVNA – ON7DQ 7 „Waves“ in a TL … and „Reflections“ e.g. : the load is a SHORT … we all know there can’t be any voltage on a short, right ? Ei = incident wave, Er = reflected wave Ex is the sum, at ZL it’s always ZERO, but not so in other places, it depends on amplitude & phase of Ei and Er in those places And so … also the impedance Zx can be any value ! . . . Involves complex math, but … We’ll leave that to a PC program ! nanoVNA – ON7DQ 8 Three ways to express how bad the “mismatch” is Reflection Coefficient Return Loss (V)SWR nanoVNA – ON7DQ 9 Reflection Coefficient : how much reflected voltage ? • the load (e.g. a 150 Ω antenna) is not “matched” to the cable (e.g. a coax with Z0 = 50 Ω ). There will be reflections ! • We want to express in one number how much voltage is reflected, and not only the magnitude, but also the phase : the reflection coefficient : Γ𝑥 (gamma) • 𝐸𝑟 Γ𝑥 = 𝐸𝑖 nanoVNA – ON7DQ It is a complex number : |ΓL| = 0 to 1 (0,05 is GOOD) and ∠ ΓL = 0° to 360° 10 Reflection Coefficient • At the load ZL we have : 𝑍𝐿 − 𝑍0 Γ𝐿 = 𝑍𝐿 +𝑍0 150 −50 100 • For the same example as before : ΓL = = = 0,5 ∠ 0° 150+50 200 or 50% of the voltage is reflected, and in phase • Some special cases : Short circuit : ZL = 0 ΓL = -1 , all voltage is reflected , 180° out of phase Open circuit : ZL = ∞ ΓL = +1 , all voltage is reflected , in phase (and the LOAD will have DOUBLE voltage !) Matched condition : ZL = Z0 ΓL = 0 , no reflected voltage at all • The reflection coefficient will be the basis for the Smith Chart nanoVNA – ON7DQ 11 Measuring in dB ? … the Return Loss (RL) • We send a wave along a TL … some of it will return, we hope it is LESS than what we sent, hi … How many dB will that reflection be LOWER than the incident wave ? This is the RETURN LOSS RL = 20.log ( |Γ𝑥 | ) • NOT a complex number, and always negative ! ( Some (e.g. HP ;-) may say it’s positive … well, tomato - tomato) • At full reflection : RL = 0 dB • No reflection : RL = - ∞ dB • Who can measure = - ∞ dB ? Not possible limit = internal equipment noise • RL = -26 dB is GOOD • For our example : RL = 20.log (0,5) = - 6 dB nanoVNA – ON7DQ 12 Amateurs are most familiar with „SWR“ , but what is it ? • “Standing Waves” are a misnomer , our waves are always on the move ! (Ei and Er are both travelling waves) BUT … the combination of two travelling waves makes a stationary “voltage pattern” with nodes and anti-nodes in fixed locations • Total voltage is always ‘maximum’, ‘minimum’ or something in between e.g. ZL = 3.Z0 then ΓL = 0,5 (50% reflects,in phase) here : vector • the sum Ex varies between 0,5.Ei and 1,5.Ei e.g. if Ei = 1V, then Ex = 0,5 to 1,5 V here : modulus • Note : Ei rotates CCW, Er rotates CW, when moving from load to source nanoVNA – ON7DQ 13 The Standing Wave Ratio or VSWR or for short : SWR (Voltage) Standing Wave Ratio or 𝑺𝑾𝑹 = 𝝈 𝑬𝑴𝑨𝑿 = 𝑬𝑴𝑰𝑵 ( σ = sigma) In our example EMAX = 1,5 V , EMIN = 0,5 V, SWR = 3 (NOT 3:1 … who invented that ?) SWR is always a REAL number, varies from 1 (no reflection) to … +∞ (full reflection) (and 1,11 is GOOD ) Now have you ever … our “SWR meter” does NOT measure SWR at all !! It would require measuring voltage at two seperate locations along the line (it can be done with a “slotted line”) We actually measure the modulus of the reflection coefficient (|ΓL| ) with a “directional coupler” or a resistive “bridge” … and have a scale calibrated for SWR 1+|Γ | ( with this formula : 𝑆𝑊𝑅 = 1 −|Γ𝐿 | ) 𝐿 nanoVNA – ON7DQ 14 Typical SWR meter … and some directional couplers e.g. Google “Bruene bridge” … nanoVNA – ON7DQ 15 SWR at matched condition … ZL = Z0 No reflection , and no maximum or minimum voltage or EMAX = EMIN = Ei and so SWR = 1 Another handy trick … IF ZL is purely resistive (and only then !) 𝑍𝐿 𝑆𝑊𝑅 = 𝑍0 𝑍0 or 𝑆𝑊𝑅 = (largest one is on top) 𝑍𝐿 In our example : SWR = 150/50 = 3 nanoVNA – ON7DQ 16 Reflection Coefficient – Return Loss – SWR relations ? Print this handy table – see link at the end (here RL is positive) nanoVNA – ON7DQ 17 S-Parameters (scattered parameters) a = wave incident to the network b = wave reflecting from the network ONE-PORT : only one S-parameter : S11 e.g. Antenna, Dummy Load, Component b1 = S11. a1 nanoVNA – ON7DQ or S11 = b1/a1 = Er/Ei = the complex reflection coefficient ! 18 S-Parameters (scattered parameters) TWO-PORT : now we have 4 S-parameters ! Wat do they mean ? s11 = reflection coefficient at PORT 1 (while PORT 2 has a matched load) s22 = reflection coefficient at PORT 2 (while PORT 1 has a matched load) s21 = the forward GAIN (but can be < 1, and always is for passive circuits) s12 = the reverse GAIN (most often < 1, and we hope so for amplifiers ;-) nanoVNA – ON7DQ 19 Properties of S-parameters • S-parameters are complex numbers, they contain phase information • Modulus (the magnitude of the reflection or gain) • Argument (the phase in degrees) • Frequency dependant : you need to measure them for all frequencies, or look them up in a databook Always referenced to a 50 “system impedance” There are three- four- …n- port S-parameters too (think of diplexers etc …) • • • Easy to use if in a computer file in .s1p en een .s2p format • e.g. a BFY90 transistor nanoVNA – ON7DQ 20 Smith Chart Is a graphical representation of Γ, impedances and admittances, and is a handy complex calculator In the old days : Paper chart, not easy to learn and use Now : Very easy to use program with an appropriate name : SMITH ! nanoVNA – ON7DQ 21 Smith Chart It will help us in designing a MATCHING NETWORK Why would we want to MATCH anyway ? • Maximum power transfer • Reflections disturb the stability of amplifiers, distort signals, etc. • Standing Wave pattern may cause a breakdown in the dielectric at EMAX • Constant impedance along the line : lets you connect the source at any point Possible techniques • lumped components (L/C), in series or in parallel one example given • λ/4 transformer (not now) • TL in series (not now) • stubs (not now) nanoVNA – ON7DQ 22 Smith Chart is a reflection coefficient plane We want to graph ALL possible values of the reflection-coefficient Γx This results in a CLOSED DISK with radius = 1 |Γx | = 0…1 and ∡Γx = 0…360° e.g. Γ1 ≅ 0,5 ∡ 45° SMITH Γ2 = 1 ∡-90 nanoVNA – ON7DQ 23 Smith Chart is also an impedance plane To be able to plot all possible impedances, we use NORMALIZATION Normalized impedance (z in lower case) ZL zL = = rL + j.xL Z0 R-circles : all points having the same r-value X-circles (arcs) : all points having the same x-value nanoVNA – ON7DQ 24 Smith Chart : impedances Special values on the Smith Chart : The outside border, where |ΓL| = 1, is where all purely inductive (upper half) or all purely capacitive (lower half) impedances are (and r = 0) Horizontal axis is the r-axis = all purely resistive impedances On this line : Left = short circuit Right = open circuit Center = matched, zL = 1 Nodes and antinodes : NODE = lowest z or minimum voltage ANTINODE = highest z or maximum voltage nanoVNA – ON7DQ 25 Smith Chart : impedances Why use normalization ? Makes us independant of the “system” impedance e.g. 100 Ω in a 50 Ω system ... z = 100/50 = 2 600 Ω in a 300 Ω system … z = 600/300 = 2 = the same point on chart ! e.g. : given : Z0 = 50 Ω , load ZL = 50 + j.70 Ω where is this on the Smith Chart ? SMITH The SMITH program does all the normalization/de-normalization for us ! (see : SETTINGS Default Z0) And now for that 1000 + j.500 Ω … no longer a problem ! SMITH nanoVNA – ON7DQ 26 Smith Chart : moving along the line Moving along a TL, going from load source , Ei and Er will have different phases with respect to each other (see standing waves slide). In a lossless line, only phase of Γx will change, modulus remains constant We make a clockwise ROTATION around the center point ( z0) e.g. we move a quarter wave from the load ZL Ei and Er will each change over 90°, and Γx will change a 180° , this is half a turn on the chart. A full turn around the chart is ? … half wavelength ! Application : use a n x λg/2 cable to measure an antenna : Zin is again = ZL e.g. an antenna was measured as ZL = 50 + j.70 Ω (INDUCTIVE), what is the impedance at λg/4 away from the antenna ? (note : now the velocity factor and the frequency are important) Solution : ZL2 = 17,2 – j.23,5 Ω SMITH And conclusion : now the impedance is CAPACITIVE ! nanoVNA – ON7DQ 27 Smith Chart : even more CIRCLES ? In SMITH, make the ADMITTANCE plane visible (Tools Settings Y-Plane (on/off) ) Now we see the g-circles (conductance) and b-circles (susceptance) BEWARE : an inductive impedance IS STILL an inductive admittance, but the sign for the reactive part will change ! (+ j - j or – j + j) Constant SWR Circles : concentric circles around z0 (Tools Circles SWR tick the required boxes) see SMITH nanoVNA – ON7DQ 28 Smith Chart : add L or C, in series or in parallel We do a SHIFT along an r (in series) or a g circle (in parallel) Remember : L = “eLevate” = move UP C = “Crash” = move DOWN (tnx W2AEW for this trick) Example from a few slides ago : R = 150 Ω , in parallel with C = 100 pF , at 28 MHz Y was = 0,0066 + j.0,0176 S But how to calculate Z = 1/Y ? It’s really simple now SMITH Solution : Z ≈ 19 - j.50 Ω (see later : my “DUT” measures as 17,7 – j.47,6 Ω ) Let’s make a matching network to 50 Ω, shall we ? It’s “poepsimpel”* with SMITH ! (solution : Lseries = 420 nH**, Cparallel 148 pF) [* that’s Dutch, try translating it with Google Translate, hi] [** without further details : 9 turns on a T50-6 core , see excellent program Mini Ringcore Calculator] nanoVNA – ON7DQ 29 EXTRA : add L or C There are 8 possible L/C combinations What impedances can be matched with what circuit ? The first 4 : source W2AEW video nanoVNA – ON7DQ 30 EXTRA : add L or C And four more networks, now C/C or L/L configurations : source W2AEW video nanoVNA – ON7DQ 31 Smith Chart : add L or C, series or parallel Nice ! But will this be true in practice ? the nanoVNA will tell it … after the BREAK ! nanoVNA – ON7DQ 32 Measuring is Knowing … the nanoVNA ! SIZE of a Credit Card nanoVNA – ON7DQ 33 nanoVNA inside nanoVNA – ON7DQ 34 nanoVNA with N-connectors Source K6JCA nanoVNA – ON7DQ 35 Scalar Network Analyzer Only measures the magnitude of reflection Can not measure complex impedance Wideband detector measures any signal picked up by the antenna >> used in most simple antenna analyzers & Arduino projects (e.g. K6BEZ) >> a bit better : the ANTUINO by HF SIGNALS (from India, see Bitx40 & µBitx) nanoVNA – ON7DQ 36 VNA = a Vector Network Analyzer Classic setup nanoVNA – ON7DQ 37 nanoVNA block diagram - operation nanoVNA – ON7DQ 38 nanoVNA specifications Frequency range : 50kHz to 900MHz (300 - 900MHz with harmonics) RF output: -13dbm (maximum -9dbm) , so approx. 0.1 mW Dynamic range : 70dB (50kHz - 300MHz), 60dB (300MHz - 600MHz), 50dB (600MHz - 900MHz) Display: 2.8 inch TFT, resolution 320x240 … like the “new” Nokia 3310 ! USB interface: USB type C (power/charging + data connection to PC) Power: USB 5V 120mA , LiPo battery +/- 500 mAh Number of points : 101 (fixed) biggest disadvantage ! Display : 4 traces, 4 markers + 5 memories for calibration & settings (C0-C4) Frequency error : < 0.5 ppm (e.g. 50 Hz error at 100 MHz) nanoVNA – ON7DQ 39 Want to build your own ? … here is the schematic ! nanoVNA – ON7DQ 40 nanoVNA Manual ? Gunthard Kraus, DG8GB, wrote a nice manual in German and in English 54 pages, lots of nice examples … and it’s FREE! nanoVNA – ON7DQ 41 nanoVNA „standalone“ : basic controls • “Rocker switch” is of little use … use a PalmPilot or Nintendo DS stylus ! • Tap the screen to see the menu • Display > Trace > T0 – T4 > the selected TRACE stays active for other operations like FORMAT, SCALE, PORT … • Enter numbers : e.g. STIMULUS > START then tap the “white zone” near the frequency then tap 145.400 and M = 145.4 MHz • CALIBRATION : first do a RESET ! then CALIBRATE with “SOLT “ (see manual) then SAVE in C0 to C4 (C0 loads as the default at startup) nanoVNA – ON7DQ 42 nanoVNA „standalone“ : the MENU Structure MAIN MENU -------------------DISPLAY MARKER STIMULUS CAL RECALL/SAVE CLOSE nanoVNA – ON7DQ 43 More versatile with PC software : nanoVNA Saver Regular updates … always use the latest one ! nanoVNA – ON7DQ 44 Just do it ! … the nanoVNA in practice ! FIRST : Calibrate ! 50 kHz – 900 MHz calibration is the default (in C0), but is only 101 points ! e.g. We want to measure an 80m antenna : first point is at 50 kHz, second point is at 8,9 MHz ! No calibration point in 80m ! BETTER : do a calibration over a limited range or even better : do it on the PC, where you can use “segmented” scanning, and a large number of points, and you can SAVE as many calibration files as you like Measuring cables should be included in the calibration ! And finally : check your calibration by connecting the SOL elements again ! e.g. Lets measure some 50 Ω resistors (commercial load, homebrew loads : carbon, wirewound …) nanoVNA – ON7DQ 45 Just do it ! … the nanoVNA in practice ! An ANTENNA ! e.g. Groundplane for 70 cm, copper wire 1,5 mm², + a ballpoint “spring” to tune it, see the effect Demo “continuous sweep” , best: narrow band + 1 segment nanoVNA – ON7DQ 46 nanoVNA … in practice Measuring at the antenna ? the nanoVNA is very portable … so you can take it up to your antenna ? At HF not a good idea (RF ingress into the nanoVNA or other unwanted coupling) Also see the many demo’s on YouTube, flapping about a VHF whip on a cable (and no ground) near the nanoVNA … useless ! Use a cable with a “Common Mode Choke” , and calibrate at the antenna end Source : DF9CY nanoVNA – ON7DQ W6LG 47 nanoVNA … in practice : a MATCHING network ! Previous example : match a load of 150 Ω // 100pF at 28 MHz Measure the load : ZL = 17,75 – j.47,6 Ω - Match with L = 420 nH in series, then C = 150 pF in parallel (@28 MHz : my values were L = 438 nH, C = 165 pF) After matching : Z = 58,09 –j.5,62 Ω … We’re a little bit “off”, but it’s good for CB ! ;-) TIP : “Set current as Reference” to compare with previous measurement blue line = without the C + add SWR circle (e.g. SWR= 1.5) effect of extra board ˅ ▼ nanoVNA – ON7DQ 48 nanoVNA … in practice : a FILTER ! e.g. a LOW PASS FILTER for 30m Design it with ELSIE* , or use the tables by W3NQN* (* see links) Circuit : Realisation : C1,C7 = 270 pF C3,C5 = 560 pF L2,L6 = 1,09 µH (T50-2, 15t) L4 = 1,26 µH (T50-2, 16t) nanoVNA – ON7DQ 49 nanoVNA … in practice LOW PASS FILTER for 30m + CALIBRATION at 505 points with nanoVNA Saver @10.1 MHz: S21 = -0.55 dB RL = - 12 dB (could be better) @20.2 MHz S21 = -54.5 dB nanoVNA – ON7DQ 50 nanoVNA … in practice LOW PASS FILTER for 30m Another handy function : Automatic Analysis of filters (the “Analysis ...” button is at the bottom of the Marker Data pane) nanoVNA – ON7DQ 51 nanoVNA … TDR measurement TDR = TIME DOMAIN REFLECTOMETRY 2 principles : The old IMPULSE method = in the low frequency spectrum (~100 kHz) Impulsgenerator Zg = 50 Ohm T-stuk testkabel ZL Oscilloscoop (probe 10:1) Calculate the response from S11 at several frequencies From frequency domain to time domain using Inverse Fast Fourier Transform* A peak in the time response relates to the PLACE of the discontinuity ! Maximum length that can be measured is determined by the frequency step and the velocity factor (not essential to know this, but here’s the formula anyway …) 𝑘.𝑣 𝐿𝑀𝐴𝑋 = ∆𝑓0 e.g. k=0,66 , step = 1 Mhz L = 0,66. 3.108 / 1.106 = 198 m nanoVNA – ON7DQ 52 nanoVNA … TDR measurement nanoVNA Saver does all the work … e.g. cable RG223 measured as 1,05 m, k = 0,66 Length measured by nanoVNA Saver = 1,045 m Also handy : Z0 of the cable is also shown (not very accurate, but good enough to distinguish between a 50 or 75 Ω cable ) nanoVNA – ON7DQ 53 nanoVNA … other method to measure Z0 of a cable The λ/8 method A short TL (called a “Lecher line”), length = λ/8, is left open at its LOAD end. Input Impedance will be : - j.Z0 So on the chart, starting from OPEN, find the frequency where Z = a SHORT There the line is a λ/4 Now measure Z at half that frequency The reactance will be –j.Z0 e.g. the same cable of 105 cm, k=0.66 At 23,038 Mhz it is a λ/8, the reactance is –j.50,39 Ω, so Z0 = 50,39 Ω A 75 Ω cable will not show at -90°, but at it’s normalized impedance of 0 – j.1.5 (or -67°), which equals 0 – j.75 Ω nanoVNA – ON7DQ 54 nanoVNA as a Component Tester Menu STIMULUS > CW FREQ > 50 kHz (or your actual “working frequency”) Component adapter + SOL calibration + two prongs bent out for SMD’s L, C, R are calculated from measured impedance Also (loss) resistance , Q factor, etc can be measured … see manual nanoVNA – ON7DQ 55 nanoVNA as a Signal Generator • Antenna or cable on CH0 • Menu STIMULUS > CW FREQ > enter frequency • Output is a SQUARE wave (with harmonics) • Level can not be adjusted, it varies between -7 dBm … - 19 dBm • No modulation possible (e.g. VNWA3E has AM, FM and level adjust) • You can set a small sweep range … hear some “ticking” in the receiver • RF generators from China ? … e.g. more expensive than a nanoVNA ! nanoVNA – ON7DQ 56 nanoVNA as a Spectrum Analyzer ? CH1 is an INPUT, so it should be possible ! Connect an antenna or probe to CH1 Put Trace 1 or 3 on LOGMAG = spectrum display, but it can not be calibrated + “images” at 10 kHz (twice the IF of 5 kHz), so just good enough to “have a look” NOTE : only 101 discrete frequencies with a 1 kHz bandwidth : what you see is NOT what you get ! (signals not on one of those 101 frequencies are not shown !) e.g. view of the 40m band - In nanoVNA: 7.074 MHz (FT-8) shows up twice Display > Scale > Ref. Pos. = 15 - In nanoVNA Saver : Sweep settings >Average sweep 5/2 nanoVNA – ON7DQ 57 Finally … some alternative software : nanoVNA Sharp nanoVNA – ON7DQ 58 Alternative software : TAPR VNA nanoVNA – ON7DQ 59 Software for Android : nanoVNA WebApp Needs a USB OTG cable nanoVNA – ON7DQ 60 Other FIRMWARE ? Have not tested this , so not much to tell … do it at your own risk Use a pincet to short two contacts and Power ON, nanopVNA will enter DFU mode (“Device Firmware Update”) Then using PC software, load the new Firmware … it sounds simple ! Many versions around • Only the function Antenna Analyzer • Only 2 traces , but a larger font • Only the basic frequency range (50 kHz – 300 MHz) • With built-in TDR function • With menu item for voor DFU mode • Etc … Still a lot to explore and learn ! nanoVNA – ON7DQ 61 nanoVNA Forum + Wiki = All you wanted to know but … nanoVNA – ON7DQ 62 Sources / Links THEORY Smith Chart http://k6jca.blogspot.com/2015/03/a-brief-tutorial-on-smith-charts.html Video on L/C matching networks https://www.youtube.com/watch?v=IgeRHDI-ukc Table Reflection Coefficient - RL - SWR https://www.markimicrowave.com/blog/wpcontent/uploads/2016/11/return-loss-to-vswr.pdf Arduino Antenne Analyzer by K6BEZ http://www.hamstack.com/hs_projects/k6bez_antenna_analyzer.pdf A better Antenne Analyzer : the Antuino http://www.hfsignals.com/index.php/antuino/ W3NQN Basic LPF tables (from GQRP club) http://www.gqrp.com/harmonic_filters.pdf W3NQN Improved “CWAZ” LPF article https://www.arrl.org/files/file/Technology/tis/info/pdf/9902044.pdf TDR theory on Inverse Fourier Transform https://nuclearrambo.com/wordpress/accurately-measuring-cable-length-withnanovna/ nanoVNA – ON7DQ 63 Sources / Links nanoVNA nanoVNA best video ! https://www.youtube.com/watch?v=mKi6s3WvBAM nanoVNA Forum https://groups.io/g/nanovna-users Original manual for standalone use http://nanovna.com/ The menu structure https://oristopo.github.io/nVhelp/html/Menu.htm A more comprehensive manual, many good examples & use of nanoVNA Saver http://gunthard-kraus.de/fertig_NanoVNA/English_NanoVNA_V1.4.2._final.pdf Idea for mounting N-connectors https://groups.io/g/nanovnausers/files/Housing%20and%20Case%20Designs/N%20connectors%20for%20t he%20NanoVNA%20-%20k6jca.pdf nanoVNA – ON7DQ 64 Sources / Links SOFTWARE Program SMITH https://www.fritz.dellsperger.net/smith.html , the site has also a good introduction on the Smith Chart (ppt) and many examples ELSIE Filter Design http://tonnesoftware.com/elsie.html Mini Ringcore Calculator : all calculations for coils with iron powder, ferrite and air cores http://www.dl0hst.de/mini-ringkern-rechner.htm nanoVNA Saver download https://github.com/mihtjel/nanovna-saver/releases + good introduction on its use https://zs1sci.com/blog/nanovnasaver/ nanoVNA Sharp https://drive.google.com/drive/folders/1JViWLBOIzaHTdwdONX2RP8S4EgWxoND nanoVNA WebApp (Android) https://play.google.com/store/apps/details?id=net.lowreal.nanovnawebapp&hl=nl nanoVNA – ON7DQ 65 Any questions ? You can wake up and go home now ! Digimodes – ON7DQ