Mixers &
Frequency Conversion

Failure: the wanted IF has an unwanted twin

The wanted channel lands at 100 MHz. Why does the receiver still hear the wrong signal?

Our fictional gateway observation receiver must translate 2.400000–2.500000 GHz to a low IF centered at 100.000 MHz. A −80.000 dBm wanted signal occupies that entire declared 100.000 MHz RF span. A narrow −30.000 dBm interferer sits at 2.250000 GHz. Both powers are available at R1-RF from nominally matched 50 Ω sources.

The 50 dB comparison is a declared total-versus-tone screening rule, not a channel SNR or demodulation result. The wanted spectral density and receiver processing are unspecified. This lesson builds a driven multiport frequency map; it does not simulate the gateway waveform.

Bring the time/frequency representations, I/Q convention, two-port reference planes, and conditional model card. By the end, you will derive both images, track inversion, trace a bounded spur family and reject one injection plan.

Multiplication translates frequency

Adding sinusoids leaves their frequencies in place. Multiplying makes one oscillation change the instantaneous scale of the other. Expand each cosine as two complex exponentials; the four pairings collect into a difference pair and a sum pair.

At 2.450000 and 2.350000 GHz, the products are 100.000 MHz and 4.800000 GHz. Each normalized cosine coefficient is ½. That is not a universal 6 dB mixer loss: port impedances, multiplier scaling and LO drive have not been specified in this identity. Oppenheim’s modulation notes connect time-domain multiplication with shifted spectra.

ADI MT-080 distinguishes a linear multiplier from an LO-driven sign switch. A practical mixer aims for useful RF linearity while the LO drives periodic switching. Next attach those signals to real ports.

RF, LO, and IF are physical ports

RF, LO and IF name physical interfaces and their roles in this conversion direction. The LO is an applied signal with power, impedance, bandwidth and noise. The IF port does not magically reject every frequency outside its name.

1. RF → mixerR1-RF: wanted 2.400000–2.500000 GHz; −80.000 dBm total available; all interferers share this plane. Nominal 50 Ω source.
2. LO → mixerR1-LO: 2.350000 or 2.550000 GHz; narrowband +7.000 dBm available and, when matched, delivered. Nominal 50 Ω source.
3. Mixer → IFA1-IF: 50.000–150.000 MHz selected output; −87.000 dBm wanted total delivered to 50 Ω. Out-of-band leakage requires filtering.

The local passive fixture has no DC bias and stays at 25 °C. Its conversion RF/LO/IF validity ranges are respectively 2.200000–2.800000 GHz, 2.200000–2.700000 GHz and 10.000–500.000 MHz. Those are teaching-proxy limits, not component specifications. Directional isolation is a separate mapping with separately declared observation bandwidth.

An ordinary same-frequency S21 does not describe all frequency-conversion paths of a driven device. A conversion measurement relates distinct input and output frequencies under a fixed LO state. This extends the network discipline of Pozar’s microwave-network framework; it does not discard the planes.

The RF signal-chain role of the mixer is summarized in CIR-2. We will first solve its signed mapping, then return to real-device evidence.

High-side, low-side, and spectral orientation

Use the portfolio convention without changing Q polarity midway:

Let u(t)=exp(j2πfbt). The RF tone is fc+fb. For low-side LO=fc−fIF, its signed difference is fIF+fb. For high-side LO=fc+fIF, the signed difference is −fIF+fb; converting the negative band to a positive physical-frequency display gives fIF−fb. Its order reverses.

The image must be rejected before it overlaps

Solve the inverse mapping instead of memorizing an image formula. For a positive IF, |fin−fLO|=fIF has two signed candidates: fin=fLO−fIF and fin=fLO+fIF. Retain only physically positive RF candidates. One is wanted; the other is its first-order image.

Reflecting the full wanted band about the LO gives 2.200000–2.300000 GHz for low side and 2.600000–2.700000 GHz for high side. Both are 100.000 MHz away from the nearest wanted edge. Those are preselector rejection regions to specify, not guaranteed attenuation. The pinned image interferers are narrower lines inside them.

MT-080’s image discussion supports this filtering boundary. The filter lesson turns the frequency regions into magnitude, delay, loss and tolerance requirements. No physical filter slope is assumed here.

Real mixers create a family of products

Write each possible line as q=mfin±nfLO, then display |q| while retaining source, coefficients and sign. A periodic switching function introduces LO harmonics; real nonlinear behavior can add RF harmonics. Balance can suppress products, but a location table alone does not establish that suppression.

The clock line’s fundamental lands at 40.000 MHz low side, outside the default guard. Its 2RF−2LO lineage lands at 80.000 MHz, inside the IF; its amplitude is unknown. Under high side, those same lineages move to 160.000 and 320.000 MHz. A higher coefficient can change a decision’s evidence burden without predicting a larger spur.

ADI’s mixer seminar separates spur trajectories from device rejection evidence. A measured spur table additionally needs its RF/LO drive, signs, reference carrier, output plane, frequency coverage and censoring rules.

Conversion loss or gain depends on conditions

Transducer conversion gain compares IF power delivered to the load with RF power available from the source. Loss is its negative in dB. The conversion branch and integrated bandwidth belong to that statement.

At +7.000 dBm drive, −80.000−7.000=−87.000 dBm. At +3.500 dBm drive, piecewise-linear interpolation gives 8.500 dB loss and −88.500 dBm output. Increasing drive beyond the optimum can increase loss in this explicitly synthetic fixture. It also changes direct LO leakage; it never supplies amplitudes for sum or higher-order rows.

The proxy is frequency-flat only within its declared envelope: the entire source support must be in 2.200000–2.800000 GHz, LO in 2.200000–2.700000 GHz, and the entire displayed output in 10.000–500.000 MHz. RF available input must be ≤−10.000 dBm, with all ports matched to 50 Ω, 25 °C and no DC bias. Outside any condition, even a fundamental difference row says unknown—conversion proxy outside validity.

These two source cards illustrate why the local +7 dBm/7 dB fixture is not a real part. No product values below drive the planner.

A port leakage in dBm, isolation in dB and a spur ratio in dBc are three different quantities. Keep the stated reference with each. The two example devices also have different test drive, sideband and plane conditions; their typical headlines cannot be compared as a gateway qualification.

Isolation, feedthrough, DC offsets, and self-mixing

Isolation describes a specified leakage direction. It is not conversion loss. LO feedthrough stays at fLO; RF feedthrough stays at fin. A reflected LO leak can return to the RF port and mix with its own source. The equal-frequency difference includes DC; changing reflection phase can change that offset.

The synthetic leakage observation paths intentionally cover RF-origin 2.200000–2.800000 GHz at receiving LO/IF ports, and LO-origin 2.200000–2.700000 GHz at receiving RF/IF ports. They are separate from the narrow 50.000–150.000 MHz selected IF and the 10.000–500.000 MHz conversion-proxy envelope. Every enabled RF source must stay inside the isolation fixture’s frequency/power conditions before its leakage tuple is assigned.

LO leakage toward the antenna can become radiated energy after the external network; leakage at IF can overload later circuitry even when it lies outside the intended IF band. Self-mixing and asymmetry can create DC offsets. Their actual levels require path phase, gain and nonlinear evidence; this fixture calculates only direct leakage. Detailed I/Q calibration, phase-noise convolution and instrument procedures remain with their owning paths.

Noise, compression, and intermodulation

“Passive” states that the conversion core does not take DC power; it does not promise a noiseless or perfectly linear signal path. “Switching” describes operation and can apply to passive or active implementations. It is not a third mutually exclusive power class.

A mixer’s SSB or DSB noise figure needs a signal-sideband convention and the noise admitted from the image side. Do not apply a matched thermal attenuator’s NF=loss shortcut indiscriminately to a driven frequency converter. The ADI seminar’s sideband-noise discussion makes that distinction explicit.

Compression is a gain-deviation condition for a named stimulus. Intercept is a small-signal extrapolation at stated per-tone powers and spacing; it is not attainable output power. Multiple strong RF inputs can generate intermodulation even if none of their individual fundamental differences collides. A coherent sum, a modulated waveform, or a phase-noise skirt needs additional evidence.

You now have the prerequisites for the planner: multiplication, physical ports, signed orientation, images, closed intervals, conditional conversion and directional leakage. Apply them before reading the final recommendation.