RF Frequency Planning
Frequency planning determines how a receiver's LO, IF chain, and filters interact to pass or reject signals. A poor frequency plan cannot be fixed with better components — it must be solved at the architecture level.
Superheterodyne Architecture
The superhet receiver mixes RF with a local oscillator (LO) to produce an intermediate frequency (IF). The mixing process produces sum and difference frequencies — f_out = |m·f_RF ± n·f_LO| for integers m, n. Frequency planning chooses LO and IF so that no spur falls in-band.
All products: fout = |m·fRF ± n·fLO| for integers m, n
IF Selection Criteria
| Criterion | Requirement | Implication |
|---|---|---|
| Image rejection | Image outside pre-selector BW | Higher IF → image further from RF → easier filter |
| IF filter selectivity | Adjacent channel rejection | Lower IF → easier sharp filter |
| Half-IF spur | No strong signal at f_RF ± f_IF/2 | IF must be large enough that f_IF/2 is outside pre-select BW |
| Component availability | SAW/crystal filters at IF | Standard IFs: 70 MHz, 140 MHz, 455 kHz, 10.7 MHz |
| Spurious-free | No clock harmonic at IF | Avoid IFs that are multiples of ADC clocks |
Image Frequency
High-side LO: f_LO = f_RF + f_IF → f_image = f_RF + 2·f_IF
Image separation from RF = 2 × f_IF
High-side LO: f_LO = 108.7 MHz · Image: 119.4 MHz · Separation: 21.4 MHz → easy to reject ✓
Image at 2.2 GHz — only 200 MHz (8.3%) from desired. Impractical to reject with 2.4 GHz BPF.
Better: f_IF=1 GHz → image at 1.4 GHz (2 GHz separation = 83%) — trivially filtered ✓
The Half-IF Spur Problem
2nd harmonic: 2·f_int = 2·f_RF − f_IF
Mix with 2nd LO harmonic: 2·f_LO = 2·f_RF − 2·f_IF
Product: 2·f_int − 2·f_LO = f_IF ← falls exactly in-band!
| IF Choice @ 900 MHz | Half-IF Location | Pre-select feasibility |
|---|---|---|
| 10.7 MHz | 894.65 MHz (5.35 MHz away) | Very difficult |
| 70 MHz | 865 MHz (35 MHz away) | Manageable with 5th-order BPF |
LO Placement
| LO Type | f_LO | Image location | Common Use |
|---|---|---|---|
| Low-side | f_RF − f_IF | f_RF − 2·f_IF (below RF) | Cellular receivers (image below band) |
| High-side | f_RF + f_IF | f_RF + 2·f_IF (above RF) | Satellite LNBs, some radar |
Mixer Spur Table
Check all |m·f_RF ± n·f_LO| products for m,n = 1..5 to verify none fall in the IF passband. Lower order (m+n) spurs are stronger and most dangerous.
| m | n | |m·f_RF − n·f_LO| | In-band? |
|---|---|---|---|
| 1 | 1 | 0.700 GHz | ✓ DESIRED |
| 2 | 1 | 10.7 GHz | No |
| 1 | 2 | 8.6 GHz | No |
| 2 | 2 | 1.4 GHz | No |
| 2 | 3 | 7.9 GHz | No |
Result: Clean frequency plan — no low-order spur falls in ±100 MHz IF window. Use the Mixer Spur Calculator to automate this.
DC Offset in Zero-IF Receivers
Zero-IF (direct conversion) avoids the image problem by converting directly to baseband (f_IF=0). But LO leakage to the RF input mixes with the LO itself, producing DC that can saturate IF amplifiers.
– Digital DC cancellation in DSP (background tracking)
– High IIP2 mixer (>+60 dBm) via differential matched layout
– Low-IF architecture (f_IF ≈ 1 MHz) then DDC to baseband
Frequency Coexistence
| Interferer → Victim | Mechanism | Mitigation |
|---|---|---|
| LTE Band 40 → WiFi 2.4 GHz | TX harmonics at 2.4 GHz | Inter-band isolation >40 dB, coexistence filter |
| WiFi 2.4 GHz → Bluetooth | Direct channel overlap | Adaptive Frequency Hopping (BT), PTA arbitration |
| 5G n77 → GPS L1 | TX noise in GPS band | GPS pre-select filter, 5G TX BPF |
| LTE TX → co-located RX (FDD) | TX noise floor in RX band | Duplexer isolation 50–60 dB |
Frequency Plan Examples
f_IF = 700 MHz (> 200 MHz BW → half-IF at 9.65 GHz, outside receive window ✓)
f_LO = 9.3 GHz (low-side) · Image at 8.6 GHz → well below band, easy to reject ✓
Spur check: all m,n products clear of ±100 MHz IF window ✓
2nd IF: 700 MHz → 30 MHz via 670 MHz 2nd LO ✓ — matches real production X-band radar design
Architecture: Direct conversion (zero-IF) — standard for 5G base stations
f_LO = 3.5 GHz from PLL (N=350, f_ref=10 MHz TCXO, f_loop=300 kHz)
PLL in-band PN: −155+50.9 = −104 dBc/Hz @ 1 kHz
EVM from PN: ≈0.45% — acceptable for 256-QAM (3.5% max) ✓
IIP2 requirement: >+60 dBm for DC offset management ✓
Frequency Planning Rules
| # | Rule | Why |
|---|---|---|
| 1 | f_IF ≥ signal BW × 5 to avoid half-IF problem | Half-IF is at f_RF ± f_IF/2; must be outside pre-select filter |
| 2 | Higher IF → better image rejection, harder IF filter | Image separation = 2×f_IF |
| 3 | Check spurs at orders 2, 3, 4 minimum | Orders 2–3 often only 15–30 dBc below desired |
| 4 | Avoid IFs that are multiples of system clocks | ADC, FPGA, crystal harmonics create CW interferers at IF |
| 5 | Double-conversion: 1st IF high, 2nd IF low | Classic solution — image rejection + selectivity |
| 6 | Zero-IF: IIP2 > +60 dBm for 4G/5G | DC offset ∝ 1/IIP2; poor IIP2 saturates baseband chain |
| 7 | Standard IFs to consider: 70 MHz, 140 MHz, 700 MHz | Off-the-shelf filters, amplifiers, test equipment available |
| 8 | Co-locate antennas with >30 dB isolation for FDD | TX at 43 dBm, RX sensitivity −100 dBm → 143 dB dynamic range needed |
RF Frequency Planning — IF Selection and Spur Avoidance
Frequency planning is the architectural-level discipline that determines which signals interfere with reception. It must be done before any component selection — a poor frequency plan cannot be rescued by better amplifiers or filters, because spurious products fall exactly at the intended IF frequency.
The Half-IF Spur — Most Common Frequency Planning Mistake
The half-IF spur arises when a signal at f_RF − f_IF/2 enters the mixer. Second-order nonlinearity creates a product at f_IF — indistinguishable from the desired signal. For 100 MHz IF at 2.4 GHz, the half-IF input is at 2.35 GHz — only 50 MHz away. No practical BPF can reject this. The solution is to choose IF large enough that f_IF/2 is outside the pre-select filter passband, or use direct-conversion with IQ image rejection.
Direct Conversion vs Superheterodyne
The shift to direct-conversion (zero-IF) in 4G/5G smartphones eliminated the image problem but introduced DC offset and IQ imbalance challenges. Modern RFICs address these through careful differential layout (IIP2 > +60 dBm), foreground calibration at power-up, and background digital DC cancellation. Understanding both architectures and when to choose each is a core frequency planning skill.