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RF library

Concepts, tutorials and component guides, written from handset RF experience.

52 articles

Concepts 33

What the numbers mean: short, exact explanations with the formulas.

  • Bessel Filter Response and Why It Keeps Pulse Shape2026-11-03Group delay is τg = −dφ/dω, and a pulse keeps its shape only when that delay is constant across its spectrum. A Bessel low-pass keeps the delay maximally flat, so its step response barely overshoots, but its magnitude roll-off is weaker than a Butterworth of the same order.
  • Chebyshev Ripple and Passband Return Loss Relationship2026-11-03A lossless equal-ripple filter has a minimum passband return loss of RL = 10·log10(1 + 1/k²), where k² = 10^(LAr/10) − 1. A 0.1 dB ripple gives 16.4 dB return loss and a VSWR of about 1.36. A 0.5 dB ripple drops the return loss to 9.6 dB.
  • Transducer, Available and Operating Power Gain Compared2026-11-03G_T = P_L/P_avs, G_P = P_L/P_in and G_A = P_avn/P_avs. With passive terminations on a stable two-port, G_T never exceeds G_P or G_A, and all three become equal under simultaneous conjugate match.
  • Butterworth vs Chebyshev: Flat Passband or Steeper Skirts2026-11-02At N = 3 and twice the cutoff, a Butterworth low-pass gives 18.1 dB of attenuation and a 0.5 dB Chebyshev gives 19.2 dB, about 1.1 dB more. The price is equal ripple in the passband and a cutoff defined at the ripple edge, not the 3 dB point.
  • DC Offset and LO Leakage in Zero-IF Receivers2026-11-02Leaked LO that returns to the mixer RF port self-mixes into a DC term equal to (αA²/2)·cos φ. Because α and φ move with the antenna environment, fixed calibration fails and receivers rely on high-pass filtering or offset cancellation.
  • IQ Imbalance: Gain and Phase Errors vs Image Rejection2026-11-02For small gain error ε and phase error θ in radians, image rejection is approximately 4/(ε²+θ²). A 1% gain error with 1 degree of phase error limits image rejection to about 40 dB.
  • Low-Pass Prototype Element Values: What g1 to gN Mean2026-11-02Low-pass prototype g-values are element values normalized to a 1 Ω source and ωc = 1 rad/s, with g0 and g(N+1) as the source and load terms. For Butterworth, g_k = 2·sin((2k − 1)π/(2N)), so N = 3 gives 1, 2, 1.
  • Why IIP2 Matters in a Zero-IF Phone Receiver2026-11-02The second-order product rises 2 dB per dB of input, so P_IM2 = 2 P_in − IIP2. Two −30 dBm tones into an IIP2 of +40 dBm give a −100 dBm product at f2 − f1, right where a zero-IF receiver's wanted signal sits.
  • Handset PA Output Match: Reading Load-Pull Contours2026-11-02Maximum output power and maximum efficiency occur at different load impedances, so the contours on a Smith chart have two peaks. The designer picks a load in the overlap region and accepts a small loss in each.
  • The Image Frequency Problem in Heterodyne Receivers2026-11-01The image sits 2 f_IF away from the wanted channel, on the far side of the LO, and folds onto the same IF. It must be removed before the mixer, so a higher IF eases the pre-mixer filter.
  • Diplexer vs Duplexer vs Multiplexer: Telling the Three Apart2026-10-31A diplexer splits two well-separated bands, a duplexer splits the TX and RX bands of one FDD system, and a multiplexer handles three or more bands. Count the bands on the common port, then ask whether they are the TX and RX of one system.
  • Phone Antenna S11: What Return Loss Means for Radiated Power2026-11-02A 10 dB return loss means |Γ| = 0.316, VSWR 1.92, with 10% of the power reflected and 90% accepted. S11 only shows what the port accepts, so heat loss in the antenna, hand or case can still waste much of that 90%.
  • Stopband Rejection in a Front-End Filter: How Much Is Enough?2026-10-31A +23 dBm transmit signal falls to −27 dBm after 50 dB of isolation, and 40 dB of filter rejection takes it to −67 dBm. Required rejection is the leakage level minus the level the receiver can tolerate.
  • Carrier Aggregation: Why Extra Bands Mean Extra Filters2026-11-02Aggregated bandwidth is the sum of the component carriers, so two 20 MHz carriers give 40 MHz. When the carriers sit in two bands on one antenna, both band filters must be connected to that antenna at the same time.
  • FDD vs TDD in a Phone: Duplexer or Switch at the Antenna?2026-10-30FDD transmits and receives at the same time on different frequencies, so it needs a three-port duplexer with high transmit-to-receive isolation. TDD uses one frequency and takes turns, so a switch can steer the antenna between the two paths.
  • Handset RF Front End Explained: Antenna to Transceiver2026-10-30Receive runs antenna, switch, filters, LNA, transceiver. Transmit runs transceiver, PA, filters, switch, antenna. Loss ahead of the first LNA adds dB for dB to noise figure: 1.5 dB of loss plus a 1 dB receiver gives 2.5 dB.
  • Why Front-End Loss Before the LNA Costs Sensitivity2026-10-30A passive loss of L dB ahead of the first gain stage adds L dB to the system noise figure. With a 1.5 dB switch and filter loss, a 1.31 dB cascade becomes 2.81 dB, while putting the LNA first gives 1.48 dB.
  • Port Extension and De-Embedding for Fixtures and PCB Traces2026-11-02Port extension removes only the phase of an ideal lossless line, using θ = 360 × l / λ. De-embedding removes the full S-parameters of the fixture, including loss, and TRL on the board avoids the fixture model altogether.
  • RF Power Measurement: Power Meter vs Spectrum Analyzer vs VNA2026-11-02A power meter gives total power over its bandwidth, a spectrum analyzer gives power per resolution bandwidth, and a VNA mainly gives ratios. Every +10 dB is ten times the power, and 1 V rms into 50 ohm is 20 mW, about 13 dBm.
  • TRL Calibration Explained: Thru, Reflect and Line2026-11-02TRL needs only the line impedance and line length to be known. The reflect can be any high-reflection device, equal at both ports. The line must be longer than the thru by 20° to 160° of phase, so one line covers about an 8:1 frequency band.
  • VNA Dynamic Range and Noise Floor in Stop-Band Measurements2026-11-02Transmission dynamic range is the source power minus the receiver noise floor, in dB. Raising the source power by 10 dB or narrowing the IF bandwidth by a factor of 10 each gains 10 dB, until the receiver compresses.
  • How a Vector Network Analyzer Measures S-Parameters2026-11-02A VNA measures complex wave ratios: S11 = b1/a1 and S21 = b2/a1 when a2 = 0. Because it reports ratios, S-parameters do not depend on source power while the receivers stay linear, and a magnitude of 0.1 reads -20 dB.
  • The 12-Term Error Model: What VNA Calibration Corrects2026-10-31A full two-port VNA calibration solves 12 error terms, 6 forward and 6 reverse. A one-port calibration needs 3. Measuring known standards lets the VNA solve these repeatable errors and remove them, but not noise or connector repeatability.
  • Amplifier Stability: How to Read the Rollett K Factor2026-10-31An amplifier is unconditionally stable at a frequency when K is greater than 1 and |delta| is less than 1. With S12 = 0.1 and S21 = 2, K is 1.256 and the amplifier passes; with S12 = 0.15 and S21 = 4, K falls to 0.519 and it does not.
  • dB and dBm in a Signal Chain: Adding Gains and Losses2026-10-31A gain or loss in dB is added to a level in dBm to give the new level in dBm. A -10 dBm signal through a 20 dB amplifier and a cable with 3 dB loss ends at +7 dBm, about 5 mW.
  • SMA Connectors: Frequency Limits, Torque and Reflections2026-10-31SMA connectors are 50 ohm and commonly specified up to 18 GHz, and 5 in-lb (about 0.56 N*m) is a common torque for repeatable results. Two connectors with 30 dB return loss each can combine into a reflection of up to 0.063 (about -24 dB), seen as ripple in S11.
  • VSWR Explained: Reflection Coefficient and Mismatch Loss2026-10-31VSWR = (1 + |G|) / (1 - |G|), so a VSWR of 2 means |G| = 0.333, a return loss of 9.54 dB, 11.1 % of the power reflected and 0.512 dB of mismatch loss. SWR and VSWR are the same number.
  • How to Measure RF Power: Power Meters, Analyzers and Losses2026-10-31A reading of -12.3 dBm after 10 dB of attenuator and 1.5 dB of cable means the source is -0.8 dBm, because losses in dB are added back. Mismatch with a VSWR of 1.2 at both ends adds up to about ±0.07 dB of uncertainty.
  • RF Matching Networks: L, Pi and T Compared2026-10-15An L-network has its loaded Q fixed by the resistance ratio: Q = sqrt(R_high / R_low - 1), which is 1.73 for 50 ohm to 200 ohm. Pi and T networks add a third part so you can choose a higher Q and a narrower, more selective match.
  • Smith Chart Basics: How to Read Impedance and Reflection2026-10-15The Smith chart plots the complex reflection coefficient inside a unit circle, with the center as a perfect match. A load of 100 + j50 ohm in 50 ohm gives z = 2 + j1, a reflection coefficient of 0.447 at 26.6 degrees and a VSWR of 2.62.

Tutorials 16

Step-by-step guides for S-parameters, Smith charts, matching and measurement.

  • Low-Pass to High-Pass Transformation: Swapping L and C2026-11-03The mapping ω → −ωc/ω turns a series-inductor element g into a series capacitor C' = 1/(Z0·ωc·g) and a shunt-capacitor element g into a shunt inductor L' = Z0/(ωc·g). For g = 1, 50 Ω and 1 GHz that gives 3.18 pF and 7.96 nH.
  • Unilateral Figure of Merit: When Can You Ignore S12?2026-11-03The true gain lies between 1/(1+U)² and 1/(1−U)² times the unilateral gain G_TU. For U = 0.1 that is −0.83 dB to +0.92 dB, and for U = 0.05 it is about −0.42 dB to +0.45 dB.
  • Hartley vs Weaver Image-Reject Receivers Compared2026-11-02Both receivers cancel the image by combining quadrature I and Q paths, but the rejection is always finite. For small errors IRR ≈ 4/(ε² + θ²), so a 1% gain error with a 0.01 rad phase error gives about 43 dB.
  • How Much Duplexer Isolation? TX Noise in the RX Band2026-11-02Required isolation equals the TX noise in the RX band minus the receiver noise floor, plus a margin. With -60 dBm of TX noise in 10 MHz, a -99 dBm floor and a 10 dB margin, the duplexer needs 49 dB of TX-to-RX isolation.
  • How to Pick Filter Order From a Rejection Requirement2026-11-02A Butterworth needs N ≥ log10(10^(LAs/10) − 1) / (2·log10(ωs/ωc)), so 40 dB at twice the cut-off needs N = 7. A Chebyshev with 0.5 dB ripple meets the same 40 dB at ratio 2 with N = 5.
  • Scaling a Low-Pass Prototype to 50 Ohm and Real Frequency2026-11-02Scale each prototype element with L = R0·g/ωc and C = g/(R0·ωc). At 1 GHz and 50 Ω, a g = 1, 2, 1 Butterworth becomes a 3.18 pF shunt C, a 15.9 nH series L and a 3.18 pF shunt C.
  • Turning a Low-Pass Prototype Into a Band-Pass Filter2026-11-02The band-pass mapping replaces each series inductor with a series LC and each shunt capacitor with a parallel LC, all resonant at ω0 = sqrt(ω1·ω2). For g = 1, 50 Ω, 1 GHz and Δ = 0.1, the series branch is 79.6 nH with 0.318 pF.
  • Reading a Front-End Module Data Sheet: Key Numbers First2026-11-02Read the band and test conditions first, then insertion loss, isolation and return loss. A 1 dB insertion loss means |S21| ≈ 0.891, so about 79% of the power gets through, and the number only counts under the stated conditions.
  • Test Cable Flexure and Phase Stability After Calibration2026-11-02A 1 cm change of electrical length in a cable with a 0.21 m wavelength shifts phase by about 17 degrees at 1 GHz, and the error grows in proportion to frequency. Keep the cable still after calibration and use phase to estimate how far it moved.
  • VNA IF Bandwidth and Averaging: Noise vs Sweep Time2026-11-02Each 10 dB of noise reduction costs about 10 times the sweep time, whether you cut the IF bandwidth by 10 or average 10 sweeps. Averaging cannot remove drift, systematic errors or crosstalk, so check those first.
  • SOLT Calibration Step by Step: Short, Open, Load and Thru2026-10-31A SOLT calibration measures an ideal short (reflection coefficient -1), an open (+1) and a load (0), then a thru between the ports. The result holds only for the frequency range, IF bandwidth, power level and cable setup used.
  • L-Network Matching: Low-Pass or High-Pass Version?2026-10-31Matching 50 ohm to 200 ohm needs Q = sqrt(3) = 1.732. The low-pass version uses 13.78 nH and 1.378 pF, the high-pass version 1.838 pF and 18.38 nH, and the choice depends on the DC path and the filtering you want.
  • Microstrip Width for 50 Ohm on a 1.6 mm FR-4 Board2026-10-31On FR-4 (er 4.4) a microstrip line reaches 50 ohm at a width-to-height ratio of about 1.9, which is about 3 mm on a 1.6 mm board. Wider strips lower the impedance and narrower strips raise it.
  • When to Put an Attenuator Pad in an RF Chain2026-10-31A fixed pad of A dB passes 10^(A/10) of the power, so a 10 dB pad passes 0.1 and turns the other 0.9 into heat. It can improve return loss by up to twice its attenuation, but it costs signal level and, in front of a receiver, noise figure.
  • How to Read One Line of an S2P File (MA, DB and RI Formats)2026-10-31A two-port S2P data line holds nine numbers: the frequency, then the pairs for S11, S21, S12 and S22 in that order. The option line tells you whether each pair is MA, DB or RI, and a magnitude of 0.99 is about -0.087 dB.
  • How to Open an S2P (Touchstone) File: 6 Ways and a Free Viewer2026-10-31An S2P file is a plain-text Touchstone file holding the two-port S-parameters of a device at many frequencies. You can plot it right here in your browser (the file never leaves your computer), read it in a text editor, or open it in RF View, Python, MATLAB or a spreadsheet.

Components 2

How real parts behave: inductors, capacitors, filters and cables.

Measured examples 1

Real S-parameter files read step by step: duplexers, filters, an antenna, fixture traces and capacitors.

  • Band 71 Duplexer, Measured: Loss and Isolation2026-11-05This Band 71 duplexer, measured as a raw part, loses 1.0 to 2.8 dB in the TX band and 1.3 to 2.3 dB in the RX band, with at least 57.7 dB of TX-to-RX isolation. The worst loss sits on the band edges, not in the middle.