Double the active elements, and ideal EIRP can increase by 6.02 dB.

That means four-times EIRP from only twice the element count.

But that result carries several hidden assumptions.

Per-element RF power must remain constant. The radiating aperture must also increase coherently. Phase, amplitude, matching, thermal performance, and scan loss must remain controlled.

Break those assumptions, and 20log₁₀(N) quickly becomes marketing mathematics.

The Core Physics: Where Does 20log₁₀(N) Come From?

Consider N identical active antenna elements.

Each element delivers:

PE = RF power per element

and provides:

GE = realized element gain

Total RF power becomes:

PTOTAL = N · PE

Therefore, in decibels:

PTOTAL[dBm] = PE[dBm] + 10log₁₀(N)

Now add coherent beamforming.

An ideal N-element aperture gains approximately another:

GARRAY ≈ GE + 10log₁₀(N)

Analog Devices describes antenna gain and EIRP increasing with array size. [Ref. 1]

Combine both terms:

EIRPARRAY ≈ PE + GE + 20log₁₀(N)

before practical losses.

That is the origin of the famous 20log(N) scaling.

The Array Gain Itself Is Not 20log(N)

This distinction matters.

The antenna gain improvement is approximately: +10log₁₀(N)

The total transmitted-power increase contributes another: +10log₁₀(N)

Together:

EIRP increase = +20log₁₀(N)

This assumes each added element receives the same RF power. Confusing these quantities creates misleading phased-array comparisons.

What Doubling N Really Gives You

Every doubling ideally gives:

10log₁₀(2) = +3.01 dB total RF power

and:

10log₁₀(2) = +3.01 dB array gain

Therefore:

ΔEIRP ≈ +6.02 dB

For ideal scaling:

• 1 → 2 elements: +6.02 dB

• 2 → 4 elements: +6.02 dB

• 4 → 8 elements: +6.02 dB

• 64 → 128 elements: +6.02 dB

• 128 → 256 elements: +6.02 dB

That is why active arrays scale EIRP so aggressively.

Consider a Practical Numerical Example

Assume each active element provides: PE = +10 dBm

Assume each radiator has: GE = 5 dBi

Use: N = 256

Assume combined implementation losses total: L = 3 dB

Then: EIRP ≈ 10 + 5 + 48.16 − 3

Therefore: EIRP ≈ 60.2 dBm

That corresponds to approximately:

1 kW isotropic-equivalent radiated power

Yet actual conducted RF power is only:

10 dBm + 24.08 dB ≈ 34.1 dBm

or approximately: 2.56 W total RF power

That is the fundamental power of coherent apertures.

But 20log(N) Has an Important Hidden Condition

The physical aperture must increase with element count.

Keep approximately λ/2 element spacing. Adding elements then increases the effective aperture.

Antenna gain fundamentally depends on effective aperture:

G = 4πAe / λ²

NASA/JPL uses this same gain-to-effective-aperture relationship. [Ref. 2]

So infinite element density does not create infinite antenna gain.

Aperture, not transistor count, ultimately controls directivity.

Pain Point 1: “N” Must Be Defined Before Using 20log(N)

What exactly does N represent?

Is it:

• RF PA channels?

• beamformer channels?

• radiating antenna elements?

• subarrays?

• polarization channels?

These quantities are often different. That difference matters enormously.

Modern Massive MIMO Is a Perfect Example

Ericsson's current AIR 6492 uses 64 transmitters and 64 receivers, but 256 physical antenna elements. [Ref. 3]

Its total RF output power is 480 W.

Ericsson reports approximately 3 dB higher EIRP for this platform.

So: 64T64R does not mean 64 radiating elements.

The RF channels feed a larger electromagnetic aperture.

That distinction is critical when benchmarking Open RAN hardware.

Do Not Apply 20log(N) Blindly to Subarrays

Suppose one PA drives four physical radiators. Those radiators form one analog subarray.

Now:

NPA ≠ NRADIATORS

The correct high-level equation becomes:

EIRP = PTOTAL + GREALIZED

This formulation remains valid regardless of architecture. Then calculate both quantities from the real hardware.

Fixed Total Power Changes the Scaling Completely

Suppose total RF power remains constant. Doubling N now halves per-element RF power.

The +3 dB power-growth term disappears. Only ideal aperture gain remains. Therefore, doubling N gives approximately: +3 dB EIRP, not +6 dB.

That is an entirely different architecture trade.

Fixed Physical Aperture Changes It Again

Now keep total aperture size fixed. Increase N by making elements physically smaller.

The aperture cannot provide unlimited additional directivity. Its maximum gain remains constrained by effective area.

Therefore: More elements can improve control without adding equivalent gain.

Possible benefits still include:

• better calibration granularity

• improved beam shaping

• reduced grating-lobe risk

• improved multi-beam flexibility

But the EIRP scaling is no longer simply 20log(N).

This Reveals a Powerful Architecture Trade

For a fixed EIRP target:

PE ≈ EIRPTARGET − GE − 20log₁₀(N)

Double N. Required per-element RF power ideally falls by 6.02 dB.

That means four-times lower power per element. Yet there are twice as many elements.

Total array RF power therefore drops approximately 3.01 dB, when aperture grows proportionally.

That Is Why Large Arrays Can Use Smaller PAs

More aperture can substitute for transmitter power. This is extremely valuable at mm-Wave.

Individual PAs may deliver modest RF power. Coherent aperture gain then creates substantial EIRP.

But there is no free lunch.

More elements require:

• more beamformer channels

• more bias power

• more thermal management

• more calibration

• more digital control

Architecture moves the problem, it does not eliminate it.

Pain Point 2: Coherent Scaling Requires Actual Coherence

The ideal EIRP derivation assumes equal amplitude and perfect phase alignment across every channel.

Real hardware never achieves either perfectly.

The Electric Fields Must Add Coherently

For ideal boresight operation:

EARRAY ∝ N

Therefore:

Power density ∝ |EARRAY|² ∝ N²

That is why relative EIRP follows N².

But phase errors reduce coherent summation. The problem becomes statistical.

Phase Error Can Be Converted Into Coherence Loss

For independent Gaussian phase errors:

ηφ ≈ e^(−σφ²), for sufficiently large arrays.

Here, σφ is RMS phase error in radians.

The corresponding gain loss becomes:

Lφ ≈ −10log₁₀(ηφ)

This produces useful engineering numbers.

RMS Phase Error Versus Coherent Gain Loss

For σφ = 5°, approximate loss: ≈ 0.03 dB

For σφ = 10°, approximate loss: ≈ 0.13 dB

For σφ = 20°, approximate loss: ≈ 0.53 dB

For σφ = 30°, approximate loss: ≈ 1.19 dB

The main beam loses power, sidelobes also change. Those two effects must not be confused.

A 2026 Hardware Result Gives a Useful Benchmark

Analog Devices recently calibrated a 16-channel X-band phased-array subsystem.

Ideal coherent signal gain is: 20log₁₀(16) ≈ 24.08 dB

The measured calibrated transmit combining gain reached approximately: 23 dB on real hardware. [Ref. 4]

That is remarkably close to ideal scaling, but it required deliberate phase alignment.

The Same Platform Demonstrates Why Calibration Matters

The ADI architecture uses 16 transmit and 16 receive channels. It employs synchronized clocking and deterministic multichip timing. [Ref. 5]

Those features exist because coherent scaling is not automatic. Digital channels must behave as one electromagnetic aperture.

That is a systems problem.

Amplitude Error Also Costs Array Efficiency

For element amplitudes an, aperture efficiency can be estimated by:

ηA = |Σan|² / [NΣ|an|²]

Uniform amplitudes maximize boresight gain. Amplitude taper deliberately reduces that maximum.

Why would engineers deliberately sacrifice EIRP?

Because sidelobes matter.

Tapering Trades Main-Beam Gain for Cleaner Spatial Spectrum

A uniform aperture creates approximately −13 dBc first sidelobes.

Analog Devices demonstrates this standard array behaviour. Applying Hamming-type taper can suppress sidelobes dramatically. ADI demonstrates roughly 40 dBc sidelobes in one example. [Ref. 6]

But tapering widens the main beam. It also reduces peak antenna gain.

Therefore, maximum EIRP and minimum sidelobes are competing objectives.

A Published EIRP Number Without Taper Information Is Incomplete

Ask whether the array used:

• uniform weighting

• Taylor taper

• Hamming taper

• adaptive nulling

Two arrays can share identical hardware. Their measured EIRP can still differ significantly. That difference may be intentional.

One Failed Element Usually Does Not Cost 3 dB

This misconception appears often.

Consider an ideal 64-element array. One element fails completely.

Relative field becomes 63/64.

Relative boresight power becomes (63/64)².

Therefore, EIRP loss is only: ≈ 0.14 dB

But the radiation pattern may deteriorate more noticeably.

Local amplitude errors create asymmetric sidelobes. Failure impact is therefore not captured by EIRP alone.

Pain Point 3: Boresight EIRP Is Not Wide-Scan EIRP

Most impressive array numbers are measured near boresight. Real phased arrays must scan.

That changes the electromagnetic problem.

The Element Pattern Immediately Creates Scan Loss

Total array response equals: element factor × array factor.

Analog Devices explicitly separates these two contributions. [Ref. 7]

A common simplified element model uses GE(θ) ∝ cos(θ).

ADI uses this cosine behaviour for illustrative array modelling.

At: θ = 60°, the cosine factor is: 0.5.

Therefore, this simplified model already gives: −3.01 dB, before other scan penalties.

Mutual Coupling Makes Scan Loss Harder

Adjacent elements interact electromagnetically. Edge elements also see different environments. Mutual coupling changes as beam angle changes. [Ref. 6]

That changes:

• active impedance

• element gain

• matching

• amplitude

• phase

Therefore, scan-state EIRP needs full-wave validation.

HFSS and CST Should Model Active Element Behaviour

Do not model only one isolated patch.

Extract:

• embedded element patterns

• mutual S-parameters

• active impedance

• array scan states

• realized gain

Then combine those models with BFIC states. The active array is one electromagnetic network.

Phase Quantization Creates Another Scaling Penalty

Digital phase shifters cannot provide continuous phase. Finite resolution creates quantization error. That error generates additional sidelobes.

ADI shows approximately 6 dB quantization-sidelobe improvement per bit. [Ref. 6]

So phase resolution influences radiated-power distribution. It does not merely influence pointing resolution.

PA Compression Can Quietly Remove EIRP

Ideal scaling assumes each PA maintains PE.

Suppose every channel loses: 1 dB output power through compression or derating.

Array EIRP also loses approximately: 1 dB, assuming coherence otherwise remains unchanged.

Now add AM-PM distortion.

The pattern can degrade further. That is why Psat is not enough.

Thermal Scaling Becomes Severe in Large Arrays

Consider 256 active elements. Each delivers 100 mW RF.

Total RF output becomes: 25.6 W

At 40% PAE, approximate DC power becomes 64 W.

Heat generation becomes roughly: 38.4 W

At 20% PAE, DC power becomes 128 W.

Heat becomes approximately: 102.4 W

The EIRP equation did not show any of this. Yet hardware must remove that heat.

Thermal Derating Breaks Ideal N² Scaling

Centre elements may operate hotter. Edge elements often have better heat spreading. Now PE becomes spatially nonuniform.

Phase can also become temperature dependent. The aperture develops correlated amplitude and phase errors.

This links EIRP directly to thermal architecture.

A Useful Current 5G Benchmark

Qorvo's public 5G array calculator models a 64-element mmWave array. Its default 24/26/28 GHz case lists 59.6 dBmi boresight EIRP. That value is specified at P1dB and per polarization. [Ref. 8]

The same model supports approximately ±60° scan volume. Qorvo explicitly notes these are estimated array calculations.

That caveat is important.

A 2026 D-Band Benchmark Shows Another Extreme

IEEE published a 160 GHz active phased-array transmitter module. It integrates four beamforming chains with 1×4 antenna subarrays.

The measured realized gain reached: 14.3 dBi, and measured EIRP reached: 7.1 dBm at 160 GHz. The demonstrated scan range was approximately ±40°. [Ref. 9]

This demonstrates how packaging dominates at sub-THz frequencies.

Why Those Two EIRP Numbers Should Never Be Compared Directly

The frequencies differ dramatically, the technologies differ, the apertures differ, the PA powers differ, the integration and packaging losses differ.

So “higher EIRP” alone tells little about engineering quality.

Context is everything.

The Better Benchmark Is a Normalized Set of Metrics

When comparing active arrays, report:

• number of active RF channels

• number of radiating elements

• per-channel output power

• total conducted RF power

• realized array gain

• measured EIRP

• DC consumption

• aperture area

• scan angle

• operating frequency

• modulation condition

Only then does comparison become meaningful.

EIRP per Watt Is Often More Revealing

Define:

ηEIRP = EIRPlinear / PDC

This is not conventional PA efficiency. It is a system-level directional efficiency metric.

It rewards:

• high aperture efficiency

• good PA efficiency

• low feed loss

• good calibration

• low thermal derating

For procurement, this can be more useful than EIRP alone.

Aperture-Normalized EIRP Can Reveal Another Truth

Also consider:

EIRP / Aperture Area

This measures directional radiated-power density per aperture. It helps compare arrays with different physical sizes. But it still requires frequency context.

An aperture measured in square wavelengths is often more meaningful.

5G Infrastructure Needs More Than Maximum Boresight EIRP

Massive MIMO radios rarely operate as one static beam. They serve multiple users and beams.

Real metrics include:

• EIRP versus scan

• EIRP versus bandwidth

• EVM versus beam

• power consumption

• thermal derating

• multi-user efficiency

Open RAN procurement should request these conditions explicitly.

Modern Massive MIMO Also Separates Channels From Elements

Ericsson's AIR 6492 combines 64T64R architecture with 256 antenna elements. [Ref. 3]

That is exactly why raw element count can mislead. System architecture determines how aperture and power combine.

Radar Places Different Demands on EIRP

Radar may prioritize peak EIRP, but waveform duty cycle changes thermal loading. Sidelobe control can matter more than another decibel boresight. Wide scan also reduces available gain.

So radar arrays should report:

• peak EIRP

• average EIRP

• scan EIRP

• sidelobe level

• pulse duty cycle

One maximum number is inadequate.

Satellite Communications Adds Link-Budget Discipline

SatCom transmit performance depends strongly on EIRP.

Receive performance depends on G/T instead.

A transmit-optimized aperture may not maximize receive performance. Ground stations also need wide scan toward low elevations. There, scan loss can dominate.

LEO Terminals Make Thermal Efficiency Especially Important

Electronically steered terminals operate continuously across moving beams. They must maintain EIRP while scanning.

Mechanical size and thermal budgets remain constrained. Therefore, theoretical array gain is only the beginning.

System efficiency decides commercial viability.

Aerospace & Defense Adds Reliability and Calibration Drift

Radar and EW apertures operate across extreme temperatures.

PA gain can drift. Phase shifters can drift. Mechanical deformation can also alter phase.

Recent calibration research emphasizes correcting hardware amplitude and phase errors. [Ref. 11]

Calibration is therefore an operational requirement, not merely factory characterization.

The Strategic Engineering Solution

Top-tier engineering teams should build an EIRP budget.

Do not rely on one 20log(N) equation.

1. Start With the Simplest Ideal Model

Use: EIRPIDEAL = PE + GE + 20log₁₀(N)

This creates the theoretical ceiling.

Do not call it expected measured performance.

2. Separate Power Scaling From Aperture Gain

Calculate: PTOTAL = PE + 10log₁₀(N)

Then calculate, GARRAY independently.

Finally:

EIRP = PTOTAL + GARRAY

This prevents double-counting. It also handles subarray architectures correctly.

3. Define N Explicitly

Report:

NPA

NBFIC

NRF channels

Nradiators

These may all differ. Do not use one ambiguous element count.

4. Build an Array-Efficiency Budget

Define:

ηARRAY = ηrad · ηmatch · ηtaper · ηphase · ηamp · ηscan

Then:

GREAL = GIDEAL + 10log₁₀(ηARRAY)

This exposes where the missing decibels went.

5. Include Feed and Packaging Loss Before the Antenna

For mmWave hardware, include:

• BFIC insertion loss

• PA-to-patch transition

• package loss

• PCB feed loss

• via transitions

Do not hide them inside miscellaneous margin. Measure or EM-extract them.

6. Include PA Compression at the Real Waveform

Measure per-channel output under:

• CW

• P1dB

• modulated waveform

• required EVM

• maximum temperature

The useful EIRP may be far below Psat EIRP.

7. Model Every Required Scan State

Do not validate only: θ = 0°.

Include:

• ±30°

• ±45°

• ±60°

or the actual specification.

Extract realized gain and active impedance.

8. Calibrate Amplitude and Phase Across Frequency

A single-frequency calibration is insufficient for wideband arrays.

Measure corrections against:

• frequency

• temperature

• power

• beam state

ADI's 2026 platform demonstrates approximately 23 dB coherent gain after calibration. [Ref. 4]

That is what real coherence looks like.

9. Do Not Optimize EIRP Alone

Simultaneously evaluate:

• EVM

• ACLR

• sidelobes

• cross-polarization

• thermal load

• DC efficiency

More EIRP can create a worse radio.

10. Measure EIRP Over the Air

Integrated active arrays may have no meaningful conducted reference plane. OTA measurement becomes essential.

Keysight's 2026 phased-array workflow measures EIRP directly. It also measures EVM, ACPR, patterns, and G/T. The platform also supports thermal-conditioned characterization. [Ref. 11]

That is the correct system-level validation.

The Procurement Implication

A supplier statement saying: “This is a 256-element phased array.”, is incomplete.

Ask:

• How many active transmit channels?

• How many physical radiators?

• What is per-channel P1dB?

• What is total conducted RF power?

• What is measured boresight EIRP?

• What is EIRP at maximum scan?

• At what temperature?

• At what modulation?

• What EVM was maintained?

• What taper was applied?

Those questions expose the real architecture.

Do Not Compare Array Gain With EIRP

These metrics answer different questions.

Array gain describes directional antenna amplification.

Total RF power describes transmitter power generation.

EIRP combines power and realized directional gain.

EIRP per watt adds system efficiency.

G/T describes receive sensitivity.

Mixing these quantities produces misleading benchmarks.

Do Not Compare P1dB EIRP With Linear Modulated EIRP

A phased array may achieve enormous CW EIRP. The required waveform may force substantial back-off.

For 64-QAM or higher modulation, linearity can dominate.

Therefore, report both peak EIRP and linear modulated EIRP. Those numbers serve different system decisions.

The Executive Takeaway

For an ideal active array: PTOTAL ∝ N and GARRAY ∝ N.

Therefore:

EIRP ∝ N²

or:

EIRP[dB] ≈ PE + GE + 20log₁₀(N)

So doubling active radiators ideally gives: +6.02 dB EIRP.

A 256-element array theoretically gains: 48.16 dB EIRP relative to one equal-power element, but only under strict assumptions.

Real arrays lose EIRP through:

• phase error

• amplitude error

• tapering

• feed loss

• mutual coupling

• scan loss

• PA compression

• thermal derating

The deeper truth is therefore simple:

20log(N) is the theoretical ceiling, not the product specification.

And the right benchmarking question is not:

“How many elements does the array have?”

It is:

“How efficiently does the hardware convert DC power and aperture into EIRP?”