FMCW Radar Calculator | Chirp & Resolution Tool

What an FMCW Radar Calculator Does

An FMCW radar calculator takes your chirp parameters—sweep bandwidth, chirp duration, carrier frequency and ADC sampling rate—and returns the key performance figures: range resolution, maximum unambiguous range, beat frequency for a given target distance, and velocity resolution. Instead of re-deriving these every time you change a parameter, the tool closes the loop in seconds so you can iterate on waveform design before committing to hardware.

The relationships are straightforward once you see them together, but keeping all the units consistent (GHz vs. MHz, µs vs. ms, m vs. km) is where mistakes creep in. The calculator below handles that automatically.

Core FMCW Equations Explained

Range Resolution (ΔR)

Range resolution is the minimum separation at which two targets can be distinguished. It depends only on the sweep bandwidth B:

ΔR = c / (2 × B)

where c ≈ 3 × 10⁸ m/s. A 1 GHz bandwidth gives ΔR = 0.15 m (15 cm); a 4 GHz bandwidth (common in 77 GHz automotive radar using devices like the TI AWR series) pushes resolution down to about 3.75 cm. More bandwidth always means finer resolution, but it also demands wider IF bandwidth and faster ADCs on the PCB.

Maximum Unambiguous Range (R_max)

The farthest target you can detect without aliasing is set by the ADC sample rate f_s and the chirp slope S = B / T_c, where T_c is the chirp duration:

R_max = (f_s × c) / (2 × S) = (f_s × T_c × c) / (2 × B)

For a 77 GHz radar with B = 4 GHz, T_c = 40 µs and f_s = 10 MHz, R_max works out to roughly 150 m—adequate for short-range automotive but tight for long-range cruise-control applications. Increasing chirp duration or sample rate extends R_max, at the cost of slower frame rate or higher data throughput.

Beat Frequency (f_b)

The beat (IF) frequency for a stationary target at range R is:

f_b = (2 × R × B) / (c × T_c) = 2 × R × S / c

This is the frequency you actually measure after mixing the received chirp with the transmitted one. Knowing f_b for your maximum design range tells you the minimum IF bandwidth and ADC sample rate you need on the radar front-end board.

Velocity Resolution (Δv)

Velocity resolution comes from the coherent processing interval across multiple chirps. For a frame of N chirps each of duration T_c:

Δv = λ / (2 × N × T_c)

where λ = c / f_c is the carrier wavelength. At 77 GHz (λ ≈ 3.9 mm), 128 chirps of 40 µs each yield Δv ≈ 0.38 m/s. To resolve slower-moving targets or separate closely spaced velocities, increase the number of chirps per frame—but that raises the frame time and may conflict with maximum-range ambiguity requirements.

Interactive FMCW Radar Parameter Calculator

Enter your chirp bandwidth (GHz), chirp duration (µs), carrier frequency (GHz), ADC sample rate (Msps) and target range (m). The tool returns range resolution, maximum unambiguous range, beat frequency, chirp slope and velocity resolution.

A realistic starting point for a 77 GHz short-range radar: set bandwidth to 4 GHz, chirp duration to 40 µs, carrier frequency to 77 GHz, ADC sample rate to 10 Msps, and target range to 50 m. You should see a range resolution of about 3.75 cm, a maximum range near 150 m, and a beat frequency around 3.33 MHz for the 50 m target. If your beat frequency exceeds half the ADC sample rate, either widen the chirp duration or raise the sample rate—otherwise you will alias that target into a ghost range bin. For Doppler processing with 128 chirps per frame, the velocity resolution will be roughly 0.38 m/s.

Design Trade-Offs Behind the Numbers

Bandwidth vs. Achievable PCB Performance

Wider chirp bandwidth improves range resolution but stresses the RF PCB. A 4 GHz sweep at 77 GHz means the board must maintain controlled impedance and low insertion loss from 75 GHz to 79 GHz. Substrate choice matters: Rogers RO3003 (Dk 3.00, Df 0.0010 at 77 GHz) is a common pick for millimeter-wave radar front-ends, while lower-cost materials like RO4350B (Dk 3.48) work well up to about 40 GHz but show increasing dielectric loss at W-band. You can compare laminate properties in our searchable Dk Df database.

Chirp Duration vs. Frame Rate

Longer chirps push R_max out and lower the required ADC sample rate, but each frame takes longer. If you need a 30 ms frame time and 128 chirps, each chirp can be at most about 230 µs—including the idle time between chirps. That ceiling in turn sets a floor on the ADC rate for a given R_max.

Number of Chirps vs. Velocity Resolution

More chirps per frame sharpen velocity resolution but increase processing load and frame time. In MIMO radar with multiple TX antennas, the effective number of chirps per virtual channel drops by the number of TX elements if you use time-division multiplexing, so plan accordingly.

IF Bandwidth and Noise

The beat frequency at maximum range defines your minimum IF bandwidth. Wider IF bandwidth admits more thermal noise, degrading SNR. A cascaded noise figure calculator helps you budget the entire receive chain—LNA, mixer, IF amplifier and ADC—so that weak targets at R_max remain above the detection threshold.

From Waveform to PCB: Practical Considerations

Transmission-Line Design at mmWave

At 77 GHz, a 50 Ω microstrip on 5 mil (0.127 mm) RO3003 is roughly 0.30 mm wide. Tolerances of ±0.5 mil shift impedance by several ohms, so specify IPC Class 3 fabrication and verify with a TDR coupon. Grounded coplanar waveguide (GCPW) is often preferred because the ground slots provide better mode control and reduce radiation loss. Matching networks at these frequencies are usually distributed; our interactive Smith chart tool can help visualize the transformation.

Power Distribution and Antenna Feed

FMCW radar modules with multiple receive channels need clean, equal-phase power splitting. A Wilkinson divider calculator sizes the quarter-wave sections and isolation resistors for a given frequency and impedance. For phased-array radar front-ends, the element spacing and grating-lobe limits can be checked with an array factor calculator before layout.

Thermal Management

Millimeter-wave transceivers like the TI AWR2243 dissipate 2–3 W in a small BGA footprint. Thermal vias under the exposed pad are essential; a thermal via array calculator tells you how many vias at what diameter keep junction temperature within limits on your chosen stackup.

Common Pitfalls

• Ignoring ADC aliasing: If f_b at R_max exceeds f_s / 2, distant targets fold back into closer range bins. Always check this with the calculator before finalizing the chirp slope.
• Confusing range resolution with range accuracy: Resolution (ΔR) is the ability to separate two targets; accuracy depends on SNR and can be much finer than ΔR through interpolation.
• Neglecting chirp non-linearity: The equations assume a perfectly linear frequency sweep. PLL settling time, VCO pulling and power-supply noise all degrade linearity, smearing range bins. Budget 5–10 % of the chirp as a settling guard band.
• Under-specifying the PCB: A radar waveform that looks fine in simulation will under-perform if the board has excessive trace loss, impedance variation or poor via transitions at mmWave. Validate the stackup against the operating band early.

Quick-Reference Formula Table

FAQ

What chirp bandwidth do I need for 5 cm range resolution?

From ΔR = c / (2B), solving for B gives B = c / (2 × 0.05) = 3 GHz. The 76–81 GHz automotive band provides up to 5 GHz of usable bandwidth, so 5 cm resolution is comfortably achievable at W-band.

Can I use this calculator for 24 GHz ISM-band radar?

Yes. Set the carrier frequency to 24.125 GHz and the bandwidth to 250 MHz (the maximum allowed in the 24.0–24.25 GHz ISM band). You will see a range resolution of 0.6 m—much coarser than 77 GHz designs, which is why most new automotive and industrial radars have moved to the wider 77 GHz band.

How does FMCW differ from pulsed radar in resolution?

Pulsed radar range resolution depends on pulse width (ΔR = cτ/2), requiring very short pulses—and therefore high peak power—for fine resolution. FMCW achieves the same resolution through bandwidth alone, using continuous low-power transmission, which simplifies the RF front-end and is easier to implement on a PCB with standard MMIC transceivers. See Wikipedia’s FMCW radar overview for a broader comparison.

What sets the maximum unambiguous velocity?

Maximum unambiguous velocity is v_max = λ / (4 · T_c). At 77 GHz with a 40 µs chirp, v_max ≈ 24.4 m/s (about 88 km/h). Shorter chirps raise v_max but require a faster ADC to maintain the same R_max.