RF circuit design basics

In short

RF circuit design is the art of making amplifiers, mixers, oscillators, filters and switches work at frequencies where component leads, PCB traces and package parasitics are no longer "wires" but reactances and transmission lines. The design currency changes from volts and amps to power, dBm, reflection coefficients and S-parameters, and the key specifications become gain, noise figure, linearity (P1dB, IP3), stability and phase noise. It is examined in GATE EC (Networks/Electromagnetics/Analog), university papers on RF & Microwave Engineering, and is the core technical round for RF/analog roles at Qualcomm, Samsung R&D, Texas Instruments, Analog Devices, Tejas Networks, Astra Microwave, Data Patterns, DRDO (LRDE, DEAL), ISRO (SAC) and BEL. In India every radio you design must also clear WPC/NFAP spectrum rules and TEC's MTCTE testing, so design limits and regulatory limits are learned together.

Explained

Why RF is different from low-frequency electronics

• Lumped vs distributed: treat an interconnect as lumped only if its length ℓ ≪ λ/10 (commonly λ/20 for careful work). At 2.4 GHz on FR-4 (εr ≈ 4.4, εeff ≈ 3.2 for microstrip), λ ≈ 70 mm, so a 7 mm trace already matters.
• Everything is a reflection problem: signals travel on a 50 Ω environment (75 Ω in cable TV/video); any mismatch reflects power instead of dissipating it, so designers think in Γ, VSWR and return loss rather than node voltages.
• Why 50 Ω: a practical compromise in coaxial lines between minimum attenuation (~77 Ω) and maximum power handling (~30 Ω); it is a convention, not a law of physics.
• Power, not amplitude: levels in dBm (dB relative to 1 mW), ratios in dB, carrier-relative spurs in dBc. Gains and losses in a chain simply add in dB.
• Parasitics dominate: every resistor has series inductance, every capacitor has ESL and ESR, every inductor has winding capacitance, every package has bondwire inductance (~0.5–1 nH/mm).
• Measurement changes too: VNA for S-parameters, spectrum analyser for spurs/harmonics, noise-figure meter or Y-factor method for NF, signal generator pairs for two-tone IP3 — all 50 Ω instruments needing calibration (SOLT) and de-embedding of fixtures.

Resonance, Q and real passive components

• Series resonance: impedance is minimum (= R) at f0; parallel resonance: impedance is maximum (= Rp). Both at f0 = 1/(2π√(LC)).
• Quality factor Q = (energy stored)/(energy lost per radian) = f0/BW₃dB. Unloaded Q (component), loaded Q (circuit with source/load), external Q.
• Q transforms resistance: a series Rs at resonance appears as Rp = (1 + Q²)Rs ≈ Q²Rs — the basis of tapped-L/C impedance transformation and of why high-Q parts are needed for low-loss filters.
• Inductors: Q typically 30–60 for wire-wound chip inductors, only 5–20 for on-chip spiral inductors (substrate and metal loss) — the main limit on CMOS RF performance. Above the self-resonant frequency (SRF) an inductor behaves capacitively; always use it well below SRF.
• Capacitors: above their series resonance (set by ESL) they become inductive. Hence multiple decoupling capacitors of different values, each effective in its own band.
• Skin effect: current crowds into a surface layer of depth δ = 1/√(πfμσ), raising conductor resistance as √f; also proximity effect in coils.
• Choices at RF: LC filters (wideband, low Q), ceramic/SAW/BAW filters (high Q, fixed frequency — SAW/BAW in every mobile front end), crystal and TCXO/OCXO references, distributed (microstrip) elements above ~2–3 GHz.

Two-port description: S-parameters, gain and stability

• At RF, open/short tests needed for Z- and Y-parameters are impossible (devices oscillate or burn), so S-parameters defined with incident/reflected travelling waves on a reference impedance Z0 are used.
• S11 input reflection, S22 output reflection, S21 forward transmission (gain), S12 reverse transmission (isolation/feedback). Insertion loss = −20log|S21| dB; return loss = −20log|S11| dB.
• Gain definitions: transducer gain GT (power delivered to load / power available from source — what you measure), available gain GA, operating gain GP, and |S21|² = transducer gain when both ports are matched to Z0.
• Unilateral assumption: if |S12| ≈ 0, input and output can be matched independently; otherwise matching one port changes the other and simultaneous-match design is needed.
• Stability: an amplifier oscillates if an input or output reflection coefficient of magnitude > 1 can be presented. Rollett's condition: unconditionally stable if K > 1 and |Δ| < 1; equivalently μ-test with μ > 1.
• If K < 1 (conditionally stable): plot input/output stability circles on the Smith chart and keep source/load impedances in the stable region, or stabilise with a series/shunt resistor, resistive feedback, or a lossy match (all at a cost in NF and gain). Maximum stable gain MSG = |S21/S12| applies in this case.
• Practical cures for instability: good grounding and via stitching, supply decoupling at several frequencies, ferrite beads on bias lines, short feedback paths, avoiding gain at frequencies you do not need (low-frequency oscillation is very common).
• Bias and class: Class A for linearity (small-signal LNA, driver), Class AB/B for efficiency in PAs, Class C/E/F for high-efficiency transmitters; devices are GaAs pHEMT, SiGe HBT, CMOS (integration) and GaN HEMT (high power, radar and base stations).

Noise and sensitivity

• Thermal (Johnson) noise: available noise power = kTB; at T0 = 290 K, kT0 = −174 dBm/Hz. Other sources: shot noise, flicker (1/f) noise, phase noise converted to amplitude.
• Noise figure F = SNRin/SNRout = Nout/(G·Nin) at T0; NF(dB) = 10 log F. Equivalent noise temperature Te = (F − 1)·290 K (preferred in satellite/radio astronomy work).
• Friis cascade: the first stage dominates. A low-loss, low-NF LNA placed first (sometimes at the antenna, as a mast-head amplifier) sets system NF; any loss ahead of it (cable, filter, switch, duplexer) adds almost dB-for-dB to NF.
• Minimum NF needs its own match: the source impedance for minimum noise (Γopt) is not the one for maximum gain. Noise-match the input, gain-match the output, or trade using constant-NF and constant-gain circles.
• Sensitivity: Pmin = −174 dBm/Hz + 10log B + NF + SNRmin — narrower bandwidth and lower NF mean weaker signals can be received.
• Figures of merit: LNA NF 0.5–2 dB; receiver NF 3–8 dB; G/T for earth stations; noise measure when cascading.

Linearity, distortion and dynamic range

• Any real amplifier has odd- and even-order nonlinearity: output = a1v + a2v² + a3v³ + …
• Harmonics at 2f, 3f… are easy to filter; intermodulation of two in-band tones f1, f2 produces 2f1−f2 and 2f2−f1 (third order), which land *inside* the band and cannot be filtered.
• 1 dB compression point (P1dB): input/output level where gain falls 1 dB below small-signal gain — defines the top of the usable range. Rule of thumb for many devices: IIP3 ≈ P1dB + 9.6 dB (verify per device).
• IP3: fictitious level where the extrapolated IM3 product equals the fundamental; IM3 grows 3 dB for every 1 dB of input. Cascade: later stages dominate IP3 because the signal has already been amplified — the opposite of noise figure.
• Other linearity measures: ACPR/ACLR and EVM for modulated signals, AM–AM/AM–PM, second-order IIP2 (critical in direct-conversion receivers), blocking/desensitisation, cross-modulation, gain compression by a strong interferer.
• Dynamic range: SFDR = (2/3)(IIP3 − noise floor) − SNRmin. Low NF *and* high IP3 cannot be had free — both cost current, hence the NF–linearity–power trade-off at the heart of RF design.
• PA-specific: efficiency η = Pout/PDC, PAE = (Pout − Pin)/PDC; back-off needed for high peak-to-average signals (OFDM in LTE/5G ~8–10 dB), recovered partly by Doherty PAs and digital pre-distortion (DPD).

Mixers, oscillators and synthesizers

• Mixer: multiplies RF with LO, producing fIF = |fRF ± fLO|. Specs: conversion gain/loss (passive diode mixers lose 6–8 dB), NF, IIP3, LO–RF and LO–IF isolation, port-to-port balance.
• Types: single-ended, single-balanced, double-balanced (Gilbert cell, diode ring) — rejects LO and even-order spurs; image-reject (Hartley/Weaver) and I/Q mixers for quadrature up/down conversion.
• Image problem: with fIF fixed, two RF frequencies (fLO ± fIF) map to the same IF. Example: fRF = 900 MHz, fLO = 830 MHz, fIF = 70 MHz → image at 760 MHz, removed by an RF pre-select filter; high IF eases image rejection but strains the IF filter — the classic superhet trade-off. Also check half-IF and spurious (m·fRF ± n·fLO) spurs during frequency planning.
• Oscillators: positive feedback meeting Barkhausen criteria (loop gain |Aβ| = 1, phase = 0/360°) or a negative-resistance device cancelling tank loss. Topologies: Hartley (tapped inductor), Colpitts (tapped capacitor), Clapp (Colpitts with series C for better stability), cross-coupled LC in CMOS, crystal oscillators (Pierce) for references, dielectric-resonator oscillators at microwave.
• Phase noise L(Δf) in dBc/Hz is the key oscillator spec (it limits EVM, radar Doppler resolution and reciprocal mixing). Leeson's model shows it falls as 1/QL², so loaded Q is everything; VCO tuning by varactor always trades tuning range against Q and phase noise.
• PLL frequency synthesizer: reference → phase/frequency detector → charge pump + loop filter → VCO → ÷N back to the detector, giving fout = N·fref. Integer-N (channel spacing = fref), fractional-N (fine steps, needs ΔΣ modulator to push quantisation noise away), plus lock time vs loop-bandwidth trade-off: inside the loop bandwidth the reference's noise (×20logN) dominates, outside it the VCO's.

From blocks to a radio: architectures, layout and Indian practice

• Receiver architectures: superheterodyne (best selectivity, needs image filter and IF chain), direct conversion / zero-IF (integrated, but suffers DC offset, LO leakage, I/Q imbalance, 1/f noise and IIP2 issues), low-IF (compromise, used in Bluetooth/GNSS), and digital/software-defined radio where a wideband ADC follows a single down-conversion.
• Transmitter chain: baseband DAC → reconstruction filter → I/Q modulator → driver → PA → harmonic filter → duplexer/switch → antenna, with a coupler and detector for power control.
• Layout is part of the design: controlled-impedance microstrip, uninterrupted ground plane under RF traces, via stitching and fences, short grounds for bypass capacitors, RF/analog/digital partitioning, shielding cans, and keeping high-power PA output away from the LNA input and the VCO.
• EMI/EMC and compliance in India: spectrum use is governed by the National Frequency Allocation Plan (NFAP) administered by the WPC Wing of DoT; licence-exempt bands include 2.400–2.4835 GHz, parts of 5 GHz (low-power indoor Wi-Fi) and 865–867 MHz for low-power RFID/IoT (later DoT exemptions widened the low-power band — check the current notification, as these limits on power/EIRP and duty cycle are revised periodically).
• Approvals: ETA (Equipment Type Approval) from WPC for radios in delicensed bands (self-declaration route for many products), MTCTE certification through TEC for notified telecom equipment, BIS registration for safety, SACFA siting clearance for transmitting installations, with TRAI as the sector regulator. The Telecommunications Act, 2023 replaces much of the Indian Telegraph Act, 1885 and the Wireless Telegraphy Act, 1933; its provisions and rules have been notified in phases, so verify the clause in force before quoting it.
• Indian 5G work centres on n78 (3.3–3.67 GHz) and n258 (26 GHz); indigenous RF design happens at C-DOT, Signalchip/Saankhya, Tejas, DRDO labs and ISRO's Space Applications Centre.

Key points

• dBm - absolute power relative to 1 mW; 0 dBm = 1 mW = 223.6 mV rms across 50 Ω.
• Γ, VSWR, return loss - the same mismatch expressed three ways; |Γ| = 0.2 → VSWR 1.5, RL 14 dB.
• λ/10 rule - below it, treat as lumped; above it, as a transmission line.
• S-parameters - travelling-wave two-port description, measurable with a VNA without open/short tests.
• Q = f0/BW - sets selectivity; Rp ≈ Q²Rs makes Q an impedance transformer too.
• SRF - frequency above which an inductor turns capacitive (and a capacitor inductive).
• Skin depth δ ∝ 1/√f - why conductor loss rises with frequency (2.1 µm in copper at 1 GHz).
• Friis - total NF is dominated by the first stage; pre-LNA loss adds directly to NF.
• −174 dBm/Hz - thermal noise floor at 290 K; sensitivity = −174 + 10logB + NF + SNRmin.
• P1dB - top of linear range; IP3 - extrapolated intermod intercept, IM3 rises 3 dB per 1 dB of input.
• Cascade rule reversal - the first stage sets noise, the last stage sets linearity.
• SFDR = (2/3)(IIP3 − noise floor) − SNRmin - the usable window between noise and distortion.
• K > 1 and |Δ| < 1 - unconditional stability; otherwise use stability circles or resistive loading.
• Noise match ≠ gain match - minimum NF and maximum gain need different source impedances.
• Image frequency = fLO ± fIF - the fundamental weakness of a single-conversion superhet.
• Phase noise ∝ 1/QL² (Leeson) - high loaded Q and high signal power in the tank reduce it.
• Integer-N PLL - fout = N·fref; in-band noise scales as 20 log N.
• Indian compliance - NFAP/WPC for spectrum, ETA for delicensed radios, MTCTE/TEC for notified equipment, SACFA for sites.

Formulas and examples

Example 1 — Levels and mismatch. A transmitter delivers +23 dBm into a 50 Ω load through a cable of 2.5 dB loss and an antenna with ZL = 75 Ω.

• Power: 23 dBm = 10^23/10 mW = 200 mW. After the cable: 23 − 2.5 = 20.5 dBm (112 mW).
• Γ = (75 − 50)/(75 + 50) = 0.2 → VSWR = 1.2/0.8 = 1.5; RL = −20 log 0.2 = 14 dB.
• Mismatch loss = −10 log(1 − 0.04) = 0.18 dB, so radiated power ≈ 20.3 dBm (107 mW). Reflected power = 4% of 112 mW = 4.5 mW.
• Voltage at 20.5 dBm across 50 Ω: V_rms = √(0.112 × 50) = 2.37 V rms.

Example 2 — Tank design and component limits. L = 10 nH with series Rs = 1.5 Ω and parasitic Cp = 0.3 pF; tuned with C = 2.5 pF.

• f₀ = 1/(2π√(10 nH × 2.5 pF)) = 1/(2π√(2.5 × 10⁻²⁰)) = 1.007 GHz.
• ω₀L = 2π(1.007 × 10⁹)(10 × 10⁻⁹) = 63.2 Ω → Q = 63.2/1.5 = 42.2.
• BW₃dB = f₀/Q = 1007/42.2 = 23.9 MHz; equivalent parallel resistance Rp ≈ Q²Rs = 1781 × 1.5 ≈ 2.67 kΩ.
• Inductor SRF = 1/(2π√(10 nH × 0.3 pF)) = 2.9 GHz — only 2.9× the operating frequency, so Q is already degraded; a smaller, lower-Cp part is preferable.
• Copper skin depth at 1 GHz: δ = 1/√(π × 10⁹ × 1.2566 × 10⁻⁶ × 5.8 × 10⁷) = 1/(4.79 × 10⁵) = 2.09 µm.

Example 3 — Cascaded noise figure and sensitivity. Chain: LNA (G = 15 dB, NF = 1.5 dB) → mixer (G = −7 dB, NF = 8 dB) → IF amplifier (G = 30 dB, NF = 5 dB); channel bandwidth 1 MHz, required SNR 10 dB.

• Ratios: F₁ = 1.413, G₁ = 31.62; F₂ = 6.310, G₂ = 0.1995; F₃ = 3.162.
• F = 1.413 + (6.310 − 1)/31.62 + (3.162 − 1)/(31.62 × 0.1995) = 1.413 + 0.168 + 0.343 = 1.923 → NF = 2.84 dB; total gain = 15 − 7 + 30 = 38 dB.
• Noise floor = −174 + 10 log(10⁶) + 2.84 = −174 + 60 + 2.84 = −111.2 dBm; sensitivity = −111.2 + 10 = −101.2 dBm.
• Noise temperature: Te = (1.923 − 1) × 290 = 268 K. If a 2 dB cable loss were added ahead of the LNA, NF would rise to ≈ 4.84 dB and sensitivity worsen to ≈ −99.2 dBm.

Example 4 — Cascaded IIP3, IM3 and dynamic range. Same LNA (G₁ = 15 dB, IIP3₁ = −5 dBm) followed by the mixer (IIP3₂ = +5 dBm).

• Linear: IIP3₁ = 0.3162 mW, IIP3₂ = 3.162 mW, G₁ = 31.62.
• 1/IIP3 = 1/0.3162 + 31.62/3.162 = 3.162 + 10.0 = 13.16 → IIP3 = 0.076 mW = −11.2 dBm (the mixer dominates, contributing 76% of the distortion).
• Two interferers at −30 dBm each: IM3 suppression = 2(−11.2 + 30) = 37.6 dBc, i.e. IM3 products at −67.6 dBm input-referred — well above the −111.2 dBm noise floor, so they will be seen.
• SFDR = (2/3)(−11.2 + 111.2) − 10 = 56.7 dB. Expected P1dB ≈ −11.2 − 9.6 ≈ −20.8 dBm input.

Example 5 — Amplifier stability and maximum gain. S₁₁ = 0.7∠−60°, S₂₂ = 0.5∠−40°, S₁₂ = 0.1∠20°, S₂₁ = 3∠80° at 2 GHz.

• Δ = S₁₁S₂₂ − S₁₂S₂₁ = 0.35∠−100° − 0.3∠100° = (−0.0608 − j0.3447) − (−0.0521 + j0.2954) = −0.0087 − j0.6401 → |Δ| = 0.640 (< 1).
• K = (1 − 0.49 − 0.25 + 0.410)/(2 × 0.3) = 0.670/0.600 = 1.12 (> 1) → unconditionally stable; any passive source/load may be used.
• MAG = |S₂₁/S₁₂|(K − √(K² − 1)) = 30 × (1.116 − 0.496) = 18.6 → 12.7 dB, against |S₂₁|² = 9 → 9.5 dB with 50 Ω terminations: simultaneous matching buys about 3.2 dB.

Where it is used

• Mobile handset and chipset design: front-end modules, LNAs, PAs, duplexers and transceiver ICs — Qualcomm India, Samsung R&D Bengaluru/Noida, MediaTek, Skyworks/Qorvo design and test teams.
• Telecom infrastructure: 5G radio units and massive-MIMO front ends at Tejas Networks, Nokia and Ericsson India R&D, C-DOT; GaN PAs for base stations.
• Defence and space: radar transmit-receive modules and microwave subsystems at DRDO (LRDE, DEAL), BEL, Astra Microwave, Data Patterns; satellite transponders and TTC chains at ISRO (SAC Ahmedabad, URSC).
• IoT, RFID and automotive: 865–867 MHz LoRa/RFID readers, 2.4 GHz BLE/Wi-Fi modules, 77 GHz automotive radar design and validation.
• Test, certification and EMI/EMC labs: VNA/spectrum-analyser based characterisation, TEC-recognised MTCTE labs, ERTL and NABL-accredited EMC labs; application engineering at Keysight, Rohde & Schwarz and Anritsu India.
• Job roles: RF design engineer, RFIC/analog layout engineer, RF systems and link-budget engineer, antenna/RF integration engineer, RF test and compliance engineer.

Interview questions

• Q: Why are S-parameters used instead of h- or y-parameters at RF? A: They are defined with matched 50 Ω terminations and travelling waves, so they can actually be measured with a VNA; open and short terminations needed for h/y parameters are not realisable at RF and can make active devices oscillate.
• Q: 0 dBm into 50 Ω — what is the rms voltage? A: 1 mW, so V = √(0.001 × 50) = 0.224 V rms (about 0.63 V peak-to-peak).
• Q: Why does the first stage dominate the noise figure but the last stage dominate linearity? A: By Friis, later stages' noise contributions are divided by the preceding gain, whereas the signal reaching later stages has already been amplified, so they compress and intermodulate first.
• Q: What happens to system NF if you put a 1 dB filter before the LNA? A: NF rises by almost exactly 1 dB, since the loss attenuates the signal before any gain and adds its own thermal noise — this is why pre-LNA loss is minimised.
• Q: State the condition for unconditional stability. A: Rollett's factor K > 1 together with |Δ| < 1 (equivalently μ > 1); if K < 1 the amplifier is only conditionally stable and source/load must stay outside the stability circles.
• Q: Why is maximum gain match not used in an LNA? A: The source impedance for minimum noise figure differs from that for maximum gain; the input is noise-matched (possibly with a small gain sacrifice) and the output gain-matched.
• Q: What is the image frequency and how is it suppressed? A: The frequency on the other side of the LO (fLO ± fIF) that converts to the same IF; suppressed by an RF pre-select filter, by choosing a higher IF, or by an image-reject/quadrature mixer.
• Q: Why is a double-balanced mixer preferred? A: It suppresses LO and RF leakage to the IF port and rejects even-order products, giving much better port-to-port isolation and spurious performance than a single-ended mixer.
• Q: What does phase noise of −100 dBc/Hz at 100 kHz offset mean, and what sets it? A: The noise power in a 1 Hz bandwidth 100 kHz from the carrier is 100 dB below the carrier; it is set mainly by loaded Q, tank signal power and device noise, as Leeson's model shows.
• Q: An inductor's SRF is 3 GHz — can it be used at 2.5 GHz? A: Not sensibly; its effective inductance is inflated and Q is badly degraded near SRF, so a part with SRF at least 3–5× the operating frequency should be used.
• Q: Why is back-off needed for an OFDM power amplifier? A: OFDM has a high peak-to-average power ratio (roughly 8–10 dB), so the PA must be operated well below P1dB to keep ACLR and EVM within spec; Doherty and digital pre-distortion recover some efficiency.
• Q: Which Indian approvals does a 2.4 GHz Wi-Fi module need? A: The band is licence-exempt under NFAP within the permitted power limits, but the equipment needs ETA from WPC, MTCTE certification through TEC if it is notified equipment, and BIS safety registration — the exact list depends on the current notifications.

Common mistakes

• Adding noise figures or IP3 values in dB as if they cascaded linearly — Friis and the IP3 cascade must be done in linear ratios and powers.
• Mixing up input- and output-referred quantities (IIP3 vs OIP3, input vs output P1dB) and forgetting to subtract the gain.
• Taking |S21|² as "the gain" regardless of terminations; it is the transducer gain only when both ports see Z0.
• Checking stability only in the operating band — most oscillations occur out of band, where device gain is highest.
• Designing both ports for conjugate match while ignoring S12, then being surprised that the input match shifts.
• Treating a chip inductor or capacitor as ideal near its self-resonance, and ignoring bondwire/via inductance and PCB pad capacitance in simulation.
• Using the noise floor without the bandwidth term, or using −174 dBm/Hz as though it already included the channel bandwidth.
• Quoting Indian power limits or band edges from memory — EIRP limits, duty-cycle rules and the delicensed band edges are revised by DoT/WPC notifications and must be checked against the current NFAP.

Related topics

Electromagnetic waves and transmission lines · Smith chart and impedance matching · Microwave engineering basics · Antennas and wave propagation · Analog circuit design and feedback amplifiers · Digital communication and link budgets