Inverse-Designed RFICs: When AI Starts Solving Maxwell

1. The research question

RF engineers traditionally begin a design with a recognizable circuit structure: a transformer, Wilkinson divider, transmission-line matching network, balun, hybrid, filter or power-combining network. Analysis and experience provide the initial topology; optimization then adjusts dimensions and component values until circuit and electromagnetic simulations approach the required response.

Recent work from Kaushik Sengupta’s group at Princeton asks a more disruptive question:

What if the designer specifies the required electrical behavior and physical constraints, but does not specify the RF geometry—or even the complete circuit topology?

This is inverse design. The forward problem asks what response a given structure produces. The inverse problem begins with the desired response and searches for a physical structure that produces it.

Conventional RF design

Specifications
     ↓
Known topology selected by an engineer
     ↓
Initial dimensions and device parameters
     ↓
Circuit and EM simulation
     ↓
Repeated tuning
     ↓
Layout, extraction and verification


Inverse-designed RFIC

Specifications + process constraints
     ↓
Architecture, topology and geometry search
     ↓
Learned EM surrogate + optimization
     ↓
Candidate physical layout
     ↓
Conventional circuit/EM verification
     ↓
Fabrication and measurement

The important advance is not merely using machine learning to tune transistor widths. It is expanding the search to include structures that an engineer may never have chosen as the starting point.

2. Where this design sits in a wireless system

The phrase “wireless chip design” can refer to two substantially different engineering domains:

1. Digital and baseband design: source and channel coding, LDPC or polar decoding, modulation, FFT/IFFT processing, channel estimation, MIMO detection, precoding and scheduling.
2. Analog, RF and electromagnetic design: making transistors, passives, interconnects, transmission lines, filters and antennas produce the required behavior at radio frequencies.

The Princeton inverse-design work primarily addresses the second domain. Its newer end-to-end work also begins to search RF circuit architecture and active-device parameters, but it is not synthesizing the NR Layer-1 software stack.

2.1 The transmit chain

A simplified transmitter looks like this:

Bits
  ↓
Coding, modulation, precoding and OFDM
  ↓
Digital I/Q samples
  ↓
DACs
  ↓
Analog I(t) and Q(t)
  ↓
Mixer / upconverter ← Local oscillator
  ↓
RF signal at the carrier frequency
  ↓
Driver amplifier
  ↓
Power amplifier
  ↓
Matching network, balun and filters
  ↓
Antenna
  ↓
Radiated electromagnetic wave

Digital Layer-1 processing produces numerical samples. A DAC converts those samples into analog baseband signals, and an upconversion mixer translates them to the RF carrier. The signal then needs amplification, impedance transformation, filtering, differential-to-single-ended conversion in some architectures, routing and radiation.

An LNA belongs primarily to the receive chain:

Antenna → Filter → LNA → Mixer / downconverter → ADCs → Baseband

There is therefore a large physical design problem between “the baseband generated the waveform” and “energy left the antenna.”

2.2 What blocks are being designed?

An RF or millimeter-wave transceiver can contain active blocks such as:

• low-noise amplifiers (LNAs);
• mixers and frequency converters;
• oscillators and quadrature generators;
• drivers and power amplifiers (PAs).

It also contains passive or electromagnetically distributed structures such as:

• input and output matching networks;
• inductors and transformers;
• baluns and couplers;
• filters;
• power splitters, combiners and distribution networks;
• transmission lines and interconnects;
• antennas and beamforming networks.

The active and passive parts cannot always be designed independently. The impedance presented by a matching network changes transistor gain and output power, while transistor parasitics change the electromagnetic network that is required around it.

3. What an RFIC engineer designs manually

Consider a 28-GHz power amplifier. A mixer or driver supplies a small RF signal, but the transmitter may require roughly 23 dBm at the PA output while also meeting gain, bandwidth, power-added efficiency (PAE), linearity and error-vector-magnitude targets without exceeding device voltage or thermal limits.

A transistor by itself does not satisfy those requirements. The engineer designs the active circuit and the physical network around it.

3.1 Device selection, sizing and bias

The designer chooses parameters including:

• transistor width, number of fingers and device multiplicity;
• bias voltage and current;
• common-source, cascode or stacked-device topology;
• Class A, AB, B or another operating mode;
• number of gain stages and driver sizing;
• single-ended or differential operation;
• two-way, four-way or another power-combining architecture.

Changing the device geometry changes transconductance, output resistance and parasitic capacitances such as Cgs, Cgd and Cds. Those changes affect gain, bandwidth, stability, efficiency and the impedance that the surrounding network must present.

3.2 Finding the required load impedance

RF systems commonly expose a nominal 50-ohm interface, but a power transistor rarely produces maximum power or efficiency when it directly sees 50 ohms.

Suppose load-pull simulation indicates that a transistor should see approximately

Zopt = 8 + j5 Ω

at 28 GHz. The engineer must design an output network that transforms the system load:

50 Ω ↔ 8 + j5 Ω

while also satisfying bandwidth, insertion-loss, harmonic, stability and physical-area constraints. The implementation might use lumped capacitors and inductors, transmission-line stubs, transformers or a combination of them.

3.3 Designing an integrated transformer

Choosing “use a transformer” does not complete the design. An on-chip transformer introduces geometric choices:

• metal layer and metal thickness;
• trace width and spacing;
• inner and outer diameter;
• number of turns;
• primary and secondary placement;
• coupling coefficient and quality factor;
• ground shielding and substrate spacing;
• differential routing and connection geometry.

Those choices determine the primary and secondary inductances, mutual inductance, coupling factor, series loss, parasitic capacitance and self-resonance. The transformer is simultaneously a circuit component and a three-dimensional electromagnetic object.

3.4 At mmWave, a wire is no longer just a connection

At sufficiently low frequency, a short wire can often be approximated as an ideal connection. At millimeter-wave frequencies, a metal trace may behave simultaneously as:

resistance + inductance + capacitance
+ transmission line + coupling structure + radiator

Two nearby traces exchange energy through electric and magnetic fields. Current also interacts with the lossy silicon substrate, ground structures, neighboring blocks and package. Consequently, layout is part of the circuit rather than a drawing produced after the circuit has been completed.

This is why RFIC designers use full-wave electromagnetic solvers such as Ansys HFSS in addition to transistor-level circuit simulators. The EM solver derives scattering parameters or field behavior from the actual conductor and dielectric geometry.

3.5 Splitting and combining RF power

A multi-way PA may divide an input among several active paths and recombine their outputs:

                 ┌→ PA₁ ─┐
                 ├→ PA₂ ─┤
Input → splitter ├→ PA₃ ─┼→ combiner → antenna
                 └→ PA₄ ─┘

The splitter and combiner must provide specified amplitude and phase relationships with low loss, acceptable isolation, suitable impedances and tolerable area. Traditionally, the engineer first selects a known family—perhaps a Wilkinson divider, transformer combiner, branch-line structure or hybrid—and then calculates and tunes its geometry.

Inverse design removes that initial restriction. The request can instead be expressed through multi-port behavior such as

|S₂₁| ≈ |S₃₁| ≈ |S₄₁| ≈ |S₅₁|

plus return-loss, isolation and relative-phase constraints. The optimizer can then search for a metal pattern that produces those relationships without requiring the result to resemble a named divider or combiner.

4. The traditional manual RFIC workflow

The pre-inverse-design process is an expert-driven loop rather than one calculation.

Step 1 — Translate system requirements

A system team might specify:

Frequency: 26–30 GHz
Gain:      > 20 dB
Pout:      > 22 dBm
PAE:       > 20%
EVM:       below a specified limit
Area:      below a specified limit

The RFIC designer must also account for supply voltage, linearity under the intended waveform, thermal limits, process variation, reliability and interfaces to adjacent blocks.

Step 2 — Select the architecture

The designer chooses the number of stages, device configuration, single-ended or differential signaling, and whether power should be combined from multiple paths. Experience and previously proven topologies strongly influence these decisions.

Step 3 — Design and simulate the active circuit

Device sizes and bias points are selected. Small-signal S-parameters, gain, input/output match and stability are evaluated, followed by nonlinear behavior such as compression, output power, efficiency and distortion.

Step 4 — Perform source-pull and load-pull analysis

The engineer searches the source and load impedances that produce the preferred trade-off among output power, PAE, gain and linearity. There may be no single optimum because the objectives conflict.

Step 5 — Synthesize matching and combining networks

The required impedances are transformed using selected passive topologies. Initial values may come from circuit theory, closed-form transmission-line relationships, Smith-chart reasoning and prior designs.

Step 6 — Convert the schematic into physical layout

Ideal inductors, transformers and lines become metal polygons, vias and structures in a real process stack. Routing and coupling to nearby blocks enter the problem.

Step 7 — Run electromagnetic extraction

The physical passives and interconnects are solved electromagnetically. Their extracted S-parameters or equivalent models are returned to the circuit simulation.

Step 8 — Discover the post-layout degradation and iterate

Loss, coupling, substrate effects and self-resonance may reduce gain, bandwidth or efficiency. The engineer changes the transformer, line, capacitor, routing or transistor and repeats circuit and EM simulations.

Choose topology
      ↓
Calculate and lay out geometry
      ↓
Circuit + EM simulation
      ↓
Find loss, mismatch or coupling problem
      ↓
Modify devices or geometry
      └───────────────↺

Each full-wave solve and expert redesign consumes time. More importantly, this workflow explores variations of the topology the engineer selected; it does not efficiently search every possible electromagnetic structure.

5. Why the geometry can look unintuitive

Human-designed microwave structures are usually regular and symmetric because those properties make them easier to analyze, parameterize and debug. Maxwell’s equations impose no equivalent requirement that the optimum conductor pattern resemble a familiar textbook component.

An inverse-designed region may therefore look pixelated or irregular:

██   ███      █
 ████   ██ ███
██  █ █████
   ██ █   ████
███    ███

The geometry is not random. Each conducting or non-conducting region contributes to distributed inductance, capacitance, coupling, phase and radiation. The optimizer is exploiting the complete electromagnetic structure rather than assembling a circuit only from recognizable lumped or transmission-line elements.

This matters increasingly at millimeter-wave and sub-terahertz frequencies. Interconnects, discontinuities and passive structures occupy electrically significant dimensions, so the boundary between a circuit and its electromagnetic layout becomes difficult to maintain.

6. From RF specifications to an electromagnetic structure

Consider a simplified target such as:

|S₁₁(f)| < −15 dB

over a specified band, together with targets for insertion loss, impedance transformation, isolation, area or radiation pattern. A conventional workflow selects a topology before optimizing it. An inverse-design workflow treats the spatial distribution of conductor and dielectric as part of the optimization variable.

In the Princeton work, an electromagnetic design region can be represented as a binary pixel grid. A 25 × 25 grid contains 625 binary decisions and therefore

2⁶²⁵ ≈ 10¹⁸⁸

possible geometries.

Exhaustively simulating that space is impossible. Even a tiny fraction would require far too many full-wave finite-element or method-of-moments solutions.

7. The learned EM surrogate

The enabling mechanism is a deep-learning surrogate model. It learns the forward relationship

geometry → S-parameters and/or radiation response

After training on electromagnetic simulation data, the surrogate can evaluate candidate structures far faster than invoking a full-wave solver for every search step. An optimizer can then explore a much larger and less intuitive design space.

Candidate geometry
        ↓
Learned EM surrogate
        ↓
Predicted S-parameters / radiation
        ↓
Objective and constraint evaluation
        ↓
Updated candidate geometry

The surrogate does not replace Maxwell’s equations in final sign-off. It makes the search computationally tractable. Promising candidates must still be checked with conventional electromagnetic and circuit simulation, design-rule verification and, ultimately, measured silicon.

8. What the 2024 work demonstrated

The group’s 2024 Nature Communications paper generalized inverse design to arbitrary-shaped, multi-port RF and sub-terahertz passive structures co-designed with active circuits. The reported examples included filters, antennas, multi-port networks and integrated millimeter-wave circuits.

This was not only a simulated layout-generation exercise. Structures and circuits were fabricated in a 90-nm SiGe BiCMOS process, while candidate designs were checked with established electromagnetic verification flows, including full-wave and full-die simulations.

Multi-port synthesis is especially important. A useful RF front end requires more than a single input impedance match: power division and combination, differential conversion, isolation, phase control and interaction with active devices all create coupled constraints.

9. From passive inverse design to end-to-end RFIC synthesis

At ISSCC 2025, the work expanded from electromagnetic passive synthesis toward an end-to-end design flow combining reinforcement learning and inverse EM methods.

The search covered multiple levels:

1. Circuit architecture
2. Circuit topology
3. Active-device and circuit parameters
4. Passive electromagnetic structures
5. Physical layout consistent with fabrication constraints

The reported silicon included a power amplifier operating approximately from 34 to 70 GHz, with a peak saturated output power of 21.2 dBm and maximum power-added efficiency of 26%. A second design operated from 100 to 120 GHz and reached 12.6 dBm peak saturated output power.

Those results make the work more consequential than parameter optimization around a human-selected RF topology. The design question can begin to shift from

Use this architecture and matching network; find the best dimensions.

to

Here are the RF specifications, process rules and physical limits; search for the architecture and its electromagnetic realization.

10. Why this is not an autonomous AI radio designer

The phrase “AI designed a chip” hides substantial human and engineering input. Designers still define:

• the semiconductor process and available metal stack;
• ports, frequency bands and source/load conditions;
• power, gain, bandwidth, efficiency and linearity objectives;
• chip area and routing constraints;
• permitted design region and geometric resolution;
• training data, loss functions and optimization strategy;
• verification, fabrication and measurement methodology.

Surrogate models can also be inaccurate outside their training distribution. An optimizer may exploit prediction errors and produce a candidate that looks excellent to the model but fails full-wave verification. Manufacturing variation, thermal behavior, breakdown, stability, reliability, packaging and interaction with the rest of the transceiver remain physical engineering problems.

The correct interpretation is therefore not that RF expertise has become unnecessary. The advance changes where expertise is applied: engineers define the problem, constraints and verification envelope while algorithms search a design space too large and irregular for manual exploration.

11. Why this matters for 6G hardware

Candidate 6G systems are expected to investigate upper-mmWave and sub-THz operation, very wide bandwidths, dense antenna integration, joint communication and sensing, and more tightly integrated radio and packaging technologies. These directions increase the importance of distributed electromagnetic effects while multiplying design objectives.

Inverse design could help explore:

• broadband matching and power combining at mmWave and sub-THz frequencies;
• compact multi-port structures for phased arrays and MIMO radios;
• antennas and front ends co-designed with active circuits;
• frequency-selective and spatially selective structures;
• joint communication-and-sensing RF hardware;
• unconventional structures adapted to process and packaging constraints.

The connection to 6G should still be stated carefully. The demonstrated chips are research prototypes and inverse-designed RFICs are not a defined 6G requirement. Their importance is methodological: as frequency rises and the design space becomes more electromagnetic, specification-driven synthesis may uncover hardware architectures that conventional template-based design would not reach.

12. The deeper transition

Traditional electronic design automation usually optimizes parameters inside a structure selected by a human. Inverse RF design begins to make the structure itself a search variable.

Earlier automation

Human chooses architecture and topology
                 ↓
Tool optimizes parameters


Emerging inverse-design automation

Human defines objectives and constraints
                 ↓
Tool searches architecture, topology,
parameters and electromagnetic geometry

That is the real research frontier. AI is not “solving Maxwell” by replacing electromagnetic physics. It is learning fast approximations to electromagnetic behavior so that optimization can explore designs humans cannot enumerate—and then returning to Maxwell-based tools and measured hardware to determine whether the result is real.

References

1. E. A. Karahan et al., “Deep-learning enabled generalized inverse design of multi-port radio-frequency and sub-terahertz passives and integrated circuits,” Nature Communications, vol. 15, article 10734, 2024.
2. J. Zhou et al., “AI-Enabled Design Space Discovery and End-to-End Synthesis for RFICs with Reinforcement Learning and Inverse Methods Demonstrating mm-Wave/sub-THz PAs between 30 and 120 GHz,” IEEE International Solid-State Circuits Conference (ISSCC), 2025.
3. K. Sengupta et al., “AI Enabling Discovery and Design of Radio and High-Frequency Wireless Chips Beyond Human Intuition,” Computer, vol. 58, no. 8, 2025.
4. K. Sengupta, “AI-enabled RF-to-terahertz chip design beyond human intuition,” Applied Optics, vol. 64, no. 30, 2025.