Almost every radio system — AM, FM, TV, WiFi, LTE, satellite, software-defined radio — relies on three closely-related operations: modulating a baseband signal onto a high-frequency carrier (creating sidebands), mixing it down to an intermediate frequency (IF) for easier filtering and amplification, and dealing with the unwanted by-products that real mixers always create (image frequency, intermodulation distortion). This calculator covers all four.
Carrier & sidebands (DSB-AM and SC variants)
When a carrier fc is amplitude-modulated by a single tone fm, the result has three frequency components: the carrier itself at fc, the upper sideband (USB) at fc + fm, and the lower sideband (LSB) at fc − fm. The total occupied bandwidth is 2fm. If you only know USB and LSB (e.g., from spectrum-analyzer measurements), you can reconstruct the carrier as their midpoint and the modulating tone as their half-spacing. This works for double-sideband AM (DSB-AM) and suppressed-carrier (DSB-SC) variants alike, since the sidebands sit symmetrically around the carrier in both cases.
Heterodyne IF conversion — the core of every superhet receiver
A superheterodyne ("superhet") receiver mixes the incoming RF signal with a local oscillator (LO) to produce a fixed intermediate frequency (IF). The mixer multiplies the two signals, generating sum and difference components: IF = |RF − LO|. The IF is chosen to be a frequency where high-Q filters and high-gain amplifiers are easier to build (e.g., 455 kHz for AM, 10.7 MHz for FM, 70 MHz for satellite). The advantage: tuning to a new station just means changing the LO — all the filtering and amplification stays at one fixed frequency.
Image frequency — the superhet's Achilles heel
The catch: for any given LO frequency, two RF inputs produce the same IF. If we want IF = LO − RF (low-side LO injection), then any signal at 2 LO − RF, or equivalently LO + IF, also lands in the IF passband. That second signal is the image frequency. It's spaced 2×IF away from the desired signal. To suppress it, receivers use an RF preselector filter (image-reject filter) before the mixer; pick a high-enough IF to make this filter buildable. (1 GHz signals with a 70 MHz IF means the image is 140 MHz away — easy. 100 MHz signals with a 455 kHz IF means the image is only 910 kHz away — very hard.)
Mixer intermodulation distortion (IMD)
Ideal mixers produce only the sum and difference. Real mixers are non-linear and create additional products at m·f1 ± n·f2 for integer m, n. The most troublesome are the third-order intermodulation (IM3) products at 2f1 − f2 and 2f2 − f1, because when f1 and f2 are close in frequency, the IM3 products fall right inside the wanted passband — you can't filter them out. This is why "two-tone IMD" is a standard test for amplifiers, mixers, and receivers, and why specifications like IIP3 (input third-order intercept) exist. Lower IM3 means a more linear device.
If I know USB and LSB from a spectrum analyzer, how do I find the carrier?
The carrier is exactly halfway between them: fc = (USB + LSB) / 2. The modulating tone is half the spacing: fm = (USB − LSB) / 2. This works for DSB-AM with a visible carrier and for DSB-SC where the carrier itself is suppressed but the sidebands stay symmetric. Example: USB = 1005 kHz, LSB = 995 kHz → carrier = 1000 kHz, modulating tone = 5 kHz. Switch to "Sideband → Carrier" mode above to compute any case.
Why does a superhet receiver have an image frequency, and how do I calculate it?
A mixer multiplies RF and LO and outputs sum and difference. The IF is |RF − LO|. But the same |RF − LO| can come from RF = LO ± IF — two different RF frequencies. The unwanted one is the image, located at 2×IF away from the desired signal, on the opposite side of the LO. With high-side LO injection (LO > RF), image = RF + 2×IF. With low-side injection (LO < RF), image = RF − 2×IF. To suppress the image you place an RF bandpass filter before the mixer; a higher IF makes the image farther away and easier to filter.
What are mixer intermodulation products and which matter most?
Any non-linear device fed two tones f1 and f2 creates products at m·f1 ± n·f2 for all integer m, n. The "order" of a product is m + n. Second-order products (f1+f2, f1−f2) are far from the input tones and easy to filter. The dangerous ones are third-order: 2f1−f2 and 2f2−f1 — when f1 and f2 are close, these IM3 products land right next to the originals and can't be filtered out. They define a device's IIP3 (input third-order intercept) specification.
What's the difference between SSB, DSB, AM, and DSB-SC?
All four use the same sideband math (USB = fc + fm, LSB = fc − fm) but differ in what they transmit. AM (DSB-AM) sends carrier + USB + LSB (most spectrum-hungry, simplest demodulation — envelope detector). DSB-SC suppresses the carrier to save power but keeps both sidebands; needs coherent demodulation. SSB transmits only one sideband (LSB or USB) and suppresses both the carrier and the other sideband — uses half the bandwidth of AM, far more power-efficient, used in amateur radio HF. The math here applies to all sideband variants.
Why is the IF chosen at 455 kHz, 10.7 MHz, or 70 MHz so often?
These are historical "industry-standard" IFs picked for the right tradeoff between filter selectivity and image-frequency separation. 455 kHz — low enough that mechanical or ceramic filters work, used in AM broadcast. 10.7 MHz — FM broadcast standard, IF wide enough to pass 200 kHz FM channel without ringing. 70 MHz — satellite and microwave receivers, high enough that image rejection is easy at GHz inputs. Modern direct-conversion (zero-IF) receivers eliminate the image-frequency problem altogether by mixing directly to baseband, but introduce DC offsets and 1/f-noise issues instead.
What is "high-side" vs "low-side" LO injection and which is better?
High-side means LO is set above RF (LO = RF + IF). Low-side means LO is below (LO = RF − IF). Both produce the same IF magnitude. Trade-offs: high-side injection inverts the spectrum (USB becomes LSB after mixing), low-side preserves it. High-side is more common because (a) it's easier to filter the image when the image is below RF (cleaner low-end), and (b) most synthesizers cover a smaller fractional bandwidth at higher absolute frequencies. The "Auto" setting in this tool picks the side from your LO > RF or LO < RF input.
Can the same calculator handle satellite up/down-conversion and SDR LO offsets?
Yes — satellite L-band downlinks use a Low-Noise Block (LNB) that's a mixer with a fixed LO (commonly 9.75 GHz or 10.6 GHz for Ku-band). Plug in the downlink RF and the LNB LO; the IF result is the L-band signal your tuner sees. For SDR LO offset, use the Mixer Products mode with f1 = received signal, f2 = SDR LO offset, and inspect the f1±f2 products. For full RF-chain analysis with multiple mixing stages, run the tool once per stage and chain the results.