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Mixer Spur Calculator

Calculate mixer spurious products (m*fLO +/- n*fRF) for receiver design. Identify spurs near the IF passband and optimize LO/IF planning. Free, instant results.

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Formula

fspur=m⋅fLO±n⋅fRF,m+n≤Nf_{spur} = m \cdot f_{LO} \pm n \cdot f_{RF}, \quad m+n \leq N
fRF— RF input frequency (MHz)
fLO— Local oscillator frequency (MHz)
m— LO harmonic order
n— RF harmonic order
N— Maximum spur order (m+n)
fIF— Intermediate frequency (MHz)

How It Works

Mixer spur calculator identifies and maps all m*fLO ± n*fRF unwanted frequency products in superheterodyne receivers — RF system architects, frequency planners, and radar designers use this to avoid interference and optimize IF selection. Real mixers generate products at m*fLO +/- n*fRF for all integer combinations of m and n due to nonlinear transfer characteristics, per Maas's 'Microwave Mixers' (2nd ed.) and Pozar's 'Microwave Engineering'.

The image frequency is the most critical spur: for high-side LO injection (fLO > fRF), the image at fLO + fIF downconverts to the same IF as the desired signal. A 915 MHz receiver with 1060 MHz LO and 145 MHz IF has its image at 1205 MHz — any signal there appears as co-channel interference. Image rejection requires either a preselector filter (typically 40-60 dB) or image-reject mixer architecture (Hartley/Weaver provides 25-40 dB rejection).

Spur levels decrease with increasing order (m+n) — typically 6 dB per order increase for a square-law mixer. Third-order spurs (2x1, 1x2) are 20-30 dB below fundamentals; fifth-order 40-50 dB below. Double-balanced mixers suppress even-order products (even m or even n) by 20-40 dB through symmetry cancellation. A spur chart plotting all m*fLO +/- n*fRF lines reveals which products fall in the IF passband across the tuning range.

Worked Example

Problem: Plan frequency allocation for an 868 MHz ISM band receiver with 10.7 MHz IF to avoid in-band spurs across 863-870 MHz RF range.

Analysis per frequency planning methodology:

  1. Choose LO injection: High-side (fLO = fRF + fIF)
LO range: 873.7 - 880.7 MHz

  1. Calculate image frequency: f_image = fLO + fIF = fRF + 2*fIF
Image range: 884.4 - 891.4 MHz (outside ISM band, 14.4 MHz separation) Preselector filter requirement: reject 884+ MHz by 50 dB — achievable with 4-pole SAW filter
  1. Identify critical third-order spurs (2xLO-RF, 2xRF-LO):
2xLO - RF: 2*877 - 868 = 886 MHz (outside IF, OK) 2xRF - LO: 2*868 - 877 = 859 MHz (outside IF, OK)
  1. Check LO harmonics: 2xLO = 1754 MHz, 3xLO = 2631 MHz
These can mix with RF harmonics: 2xLO - 2xRF = 2*877 - 2*868 = 18 MHz This 2x2 spur falls 7.3 MHz from IF center — within IF filter bandwidth!
  1. Solution options:
a) Use low-side LO (fLO = 857.3 MHz): 2x2 spur at 2*857 - 2*868 = -22 MHz (negative, appears at +22 MHz, outside IF) b) Use higher IF (21.4 MHz): 2x2 spur offset increases to 14.6 MHz, filterable c) Use double-balanced mixer: suppresses 2x2 by 30+ dB
  1. Final recommendation: Low-side LO with double-balanced mixer provides cleanest spur environment. Image at 846.6 - 853.6 MHz (below ISM band) requires preselector to reject.

Practical Tips

  • ✓Generate spur chart across entire tuning range, not just single frequency — spurs that miss IF at one frequency may fall in-band at another; plot m*fLO +/- n*fRF for m,n = 0 to 5
  • ✓Compare high-side vs low-side LO injection — one typically has fewer problematic spurs; image frequency position relative to interferer sources often determines best choice
  • ✓Double-balanced mixers are strongly preferred for receivers — 20-40 dB suppression of even-order spurs significantly simplifies frequency planning; single-ended mixers require careful spur analysis
  • ✓For wide-tuning receivers, consider double- or triple-conversion architecture — first conversion to high IF (> 100 MHz) for image rejection, then to low IF for selectivity

Common Mistakes

  • ✗Ignoring the image frequency — the most common receiver design error; image signal converts to IF with unity gain, indistinguishable from desired signal without filtering or image-reject architecture
  • ✗Assuming higher-order spurs are negligible — at high LO drive or near compression, 5th-order products can be within 30 dB of fundamentals; always verify spur levels empirically
  • ✗Confusing balanced mixer spur suppression — double-balanced mixers suppress products where m OR n is even, not where m+n is even; 2x1 and 1x2 are suppressed, 3x3 is not
  • ✗Not accounting for LO harmonic content — a -20 dBc second harmonic on the LO creates additional spur families at 2*fLO +/- n*fRF that may not be shown on ideal spur charts

Frequently Asked Questions

A mixer spur is an unwanted output at frequency m*fLO +/- n*fRF produced by the nonlinear mixing process. Ideal mixer output contains only fLO-fRF (desired IF) and fLO+fRF (filtered). Real mixers have nonlinear transfer functions that generate harmonics of both inputs; these harmonics inter-mix to create products at every m*fLO +/- n*fRF combination. Products falling within the IF filter passband appear as interference. The spur 'order' is m+n; lower orders are stronger, typically decreasing 6 dB per order increase.
A spur chart plots m*fLO +/- n*fRF products as lines on a frequency axis. The horizontal band around IF center represents the IF filter passband. Any spur line crossing this band indicates a potential interference frequency. To use: (1) Identify all line crossings within IF band across your RF tuning range. (2) Determine if the spur is from desired RF (acceptable) or could be from an interferer (problematic). (3) Calculate interferer frequency that would cause the spur: f_interferer = (m*fLO +/- fIF)/n. (4) Assess likelihood of that interferer being present.
The image frequency is an input that produces the same IF as the desired signal through a different mixing product. For high-side LO (fLO > fRF): f_image = fLO + fIF = fRF + 2*fIF. For low-side LO (fLO < fRF): f_image = fLO - fIF = fRF - 2*fIF. The image is the 1x1 spur (m=1, n=1) with opposite sign from the desired conversion. Image rejection is critical because image signals convert with the same gain as desired signals — a -60 dBm interferer at the image frequency appears as -60 dBm at IF without filtering.
In double-balanced mixers, circuit symmetry cancels products where m or n is even — these appear 20-40 dB below odd-order products. Odd-order spurs (1x1, 3x1, 1x3, 3x3, etc.) pass through without cancellation. In single-ended or single-balanced mixers, all orders are present at levels determined by the nonlinearity. The 'even-order suppression' advantage of double-balanced mixers is one of their primary benefits, reducing the number of problematic spurs from dozens to a handful.
IF selection balances competing requirements: (1) Image rejection: Higher IF places image further from desired signal, easier to filter. Rule: IF > RF_bandwidth/2 for adequate image filtering. (2) Spur density: Higher IF has more spur products near the IF band (more m,n combinations). (3) Filter availability: Standard IF frequencies (10.7, 21.4, 45, 70, 140 MHz) have readily available filters. (4) IF bandwidth: Lower IF allows sharper selectivity (higher filter Q). For narrowband receivers, 10.7 MHz IF is common; for wideband, 70-140 MHz or dual-conversion architectures.
High-side: fLO > fRF, so IF = fLO - fRF. Image is above the desired RF. Spectral inversion occurs (upper sideband becomes lower). Low-side: fLO < fRF, so IF = fRF - fLO. Image is below the desired RF. No spectral inversion. Choice affects: (1) Image position relative to interferers; (2) LO frequency requirements (high-side needs higher-frequency synthesizer); (3) Spur locations. Analyze both options with a spur chart — one typically has fewer in-band spurs for a given application.

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