ABCD-, s-, h-, T,- Y- Z- Parameter Conversions^©

By Kirt Blattenberger, RF Engineer, RFCafe.com webmaster

Summary

This treatise explains the six most common two-port network matrix descriptions used in circuit theory, RF/microwave engineering, filter design, amplifier design, and transmission-line analysis: Z-parameters, Y-parameters, h-parameters, ABCD-parameters, S-parameters, and scattering-transfer T-parameters. Each representation describes the same linear two-port network, but each chooses a different set of independent and dependent variables. Because of that choice, some matrix types are natural for low-frequency circuit analysis, some for cascade calculations, and some for high-frequency measurement where direct open- and short-circuit tests become impractical.

The most important practical point is that there is no universally harmless conversion. Many formulas contain denominators such as z₂₁, y₂₁, S₂₁, C, B, h₂₁, h₂₂, or matrix determinants. If one of these quantities is zero or very small, the corresponding conversion may be singular or numerically ill-conditioned, even though the physical network itself is perfectly valid. In those cases, use another parameter set, take a limiting form, or use a robust numerical matrix inversion method.

This report uses the standard two-port current convention in which I₁ and I₂ are currents entering their respective ports. For ABCD parameters, the cascade-friendly convention is used:

V₁ = A V₂ - B I₂
I₁ = C V₂ - D I₂

or equivalently:

[ V₁ ; I₁ ] = [ [ A, B ], [ C, D ] ] [ V₂ ; -I₂ ]

This sign convention is common in transmission-line and RF texts because it allows cascaded two-port chains to be represented by ordinary matrix multiplication. However, some books and software packages use a different ABCD sign convention. Always check the convention before using a published formula.

For S-parameters and scattering-transfer T-parameters, this report assumes equal, real reference impedances Z₀ at both ports unless stated otherwise. Generalized S-parameters with unequal or complex reference impedances require modified formulas based on power-wave or pseudo-wave definitions. The power-wave formalism was introduced by Kurokawa and remains important in precision RF metrology; see Kurokawa, “Power Waves and the Scattering Matrix,” IEEE Transactions on Microwave Theory and Techniques, 1965.

Key findings

• Z-parameters are impedance parameters. They express port voltages as functions of port currents. They are intuitive for series impedances and low-frequency circuit models, but their direct measurement requires open-circuit conditions.
• Y-parameters are admittance parameters. They express port currents as functions of port voltages. They are convenient for nodal analysis, shunt elements, and parallel connections, but their direct measurement requires short-circuit conditions.
• h-parameters are hybrid parameters. They mix voltage, current, impedance, admittance, and dimensionless gain quantities. They were historically popular for transistor small-signal models, especially at audio and radio frequencies.
• ABCD-parameters, also called transmission or chain parameters, are especially useful for cascaded networks. The total ABCD matrix of a cascade is the ordered product of the individual ABCD matrices.
• S-parameters are the standard high-frequency measurement parameters. They relate incident and reflected traveling waves rather than port voltages and currents. They are directly measured by vector network analyzers and are emphasized in microwave engineering references such as Pozar’s Microwave Engineering, Keysight’s S-parameter application literature, and Rohde & Schwarz’s S-parameter tutorials.
• Scattering-transfer T-parameters are wave-cascade parameters. They are related to S-parameters but arranged so that cascaded RF/microwave networks can be multiplied in chain order, much like ABCD matrices.
• Conversions are exact for linear two-port networks under the stated assumptions, but the formulas can fail at singular cases. For example, conversion from S to T requires S₂₁ ≠ 0, and conversion from ABCD to Z using the common formulas requires C ≠ 0.
• Reference impedance matters for S-parameters. A set of S-parameters is not complete unless Z₀ or the port reference impedances are specified.

Detailed analysis

1. Two-port network conventions used in this report

A two-port network has four terminal variables:

• V₁: voltage at port 1
• I₁: current entering port 1
• V₂: voltage at port 2
• I₂: current entering port 2

The current convention is important. In this report, both currents enter the two-port. This is the usual network-theory convention for Z, Y, and h parameters. For cascade work, however, the output current used in the ABCD equations is often written as -I₂, because the current leaving the first network enters the next network. This gives the cascade-friendly form:

[ V₁ ; I₁ ] = [ [ A, B ], [ C, D ] ] [ V₂ ; -I₂ ]

That is:

V₁ = A V₂ - B I₂
I₁ = C V₂ - D I₂

For S-parameters, define incident and reflected wave variables a₁, a₂, b₁, and b₂. For equal real reference impedance Z₀:

a_n = (V_n + Z₀I_n) / (2 sqrt(Z₀))
b_n = (V_n - Z₀I_n) / (2 sqrt(Z₀))

The S-parameter definition is:

[ b₁ ; b₂ ] = [ [ S₁₁, S₁₂ ], [ S₂₁, S₂₂ ] ] [ a₁ ; a₂ ]

The scattering-transfer T-parameter definition used here is:

[ a₁ ; b₁ ] = [ [ T₁₁, T₁₂ ], [ T₂₁, T₂₂ ] ] [ b₂ ; a₂ ]

This is one common RF chain-scattering convention, but not the only one. Some references define a transfer matrix using [ b₁ ; a₁ ] or reverse the port order. Therefore, when comparing formulas with software packages or textbooks, verify the ordering of the wave variables. Tools such as scikit-rf and technical references such as Qucs technical documentation explicitly document their conventions.

2. Z-parameters: impedance parameters

Definition

Z-parameters express port voltages as linear functions of port currents:

[ V₁ ; V₂ ] = [ [ z₁₁, z₁₂ ], [ z₂₁, z₂₂ ] ] [ I₁ ; I₂ ]

Expanded:

V₁ = z₁₁I₁ + z₁₂I₂
V₂ = z₂₁I₁ + z₂₂I₂

Parameter meanings

• z₁₁ = V₁ / I₁ with I₂ = 0. This is the input impedance with port 2 open-circuited.
• z₂₂ = V₂ / I₂ with I₁ = 0. This is the output impedance with port 1 open-circuited.
• z₂₁ = V₂ / I₁ with I₂ = 0. This is the forward transfer impedance.
• z₁₂ = V₁ / I₂ with I₁ = 0. This is the reverse transfer impedance.

Why use Z-parameters?

• They are intuitive when the network contains series impedances.
• They are convenient for low-frequency equivalent circuits.
• They connect directly with loop or mesh analysis.
• They are useful when open-circuit conditions are physically reasonable.

Limitations

Direct measurement of Z-parameters requires open-circuiting one port. At high frequency, a physical open circuit is not ideal because it has stray capacitance and radiates. Therefore, RF and microwave engineers usually measure S-parameters instead and convert to Z-parameters if needed.

Example: series impedance

A simple series impedance Z_s between port 1 and port 2 has an ABCD matrix:

[ [ 1, Z_s ], [ 0, 1 ] ]

It does not have a finite ordinary Z-parameter matrix in the same way as a general two-port when the required open-circuit transfer conditions become singular. This illustrates why not every parameter set is numerically well-behaved for every topology.

3. Y-parameters: admittance parameters

Definition

Y-parameters express port currents as linear functions of port voltages:

[ I₁ ; I₂ ] = [ [ y₁₁, y₁₂ ], [ y₂₁, y₂₂ ] ] [ V₁ ; V₂ ]

Expanded:

I₁ = y₁₁V₁ + y₁₂V₂
I₂ = y₂₁V₁ + y₂₂V₂

Parameter meanings

• y₁₁ = I₁ / V₁ with V₂ = 0. This is the input admittance with port 2 short-circuited.
• y₂₂ = I₂ / V₂ with V₁ = 0. This is the output admittance with port 1 short-circuited.
• y₂₁ = I₂ / V₁ with V₂ = 0. This is the forward transfer admittance.
• y₁₂ = I₁ / V₂ with V₁ = 0. This is the reverse transfer admittance.

Why use Y-parameters?

• They are natural for nodal analysis.
• They are convenient for shunt elements and parallel network combinations.
• They are useful in small-signal transistor and active-device modeling.
• Admittance matrices combine directly for parallel-connected two-ports under compatible port connections.

Limitations

Direct Y-parameter measurement requires short-circuit conditions. At RF and microwave frequencies, a short circuit is also nonideal because it has inductance, finite resistance, and fixture parasitics. Therefore, Y-parameters are often computed from measured S-parameters.

4. h-parameters: hybrid parameters

Definition

h-parameters mix voltage and current variables:

[ V₁ ; I₂ ] = [ [ h₁₁, h₁₂ ], [ h₂₁, h₂₂ ] ] [ I₁ ; V₂ ]

Expanded:

V₁ = h₁₁I₁ + h₁₂V₂
I₂ = h₂₁I₁ + h₂₂V₂

Parameter meanings

• h₁₁ = V₁ / I₁ with V₂ = 0. This is an input impedance with output short-circuited.
• h₁₂ = V₁ / V₂ with I₁ = 0. This is a reverse voltage ratio with input open-circuited.
• h₂₁ = I₂ / I₁ with V₂ = 0. This is a forward current ratio with output short-circuited.
• h₂₂ = I₂ / V₂ with I₁ = 0. This is an output admittance with input open-circuited.

Why use h-parameters?

• They historically fit transistor amplifier analysis well.
• h₁₁ resembles input resistance, h₂₁ resembles current gain, h₁₂ resembles reverse voltage feedback, and h₂₂ resembles output admittance.
• They are useful when one side of the network is naturally voltage-driven and the other is naturally current-observed.

Limitations

h-parameters are less common in modern microwave work because open and short test conditions are difficult at high frequency and because S-parameters are directly measurable with a vector network analyzer. Also, h-parameter sign conventions can be confusing because two-port network current directions may differ from transistor data-sheet conventions.

5. ABCD-parameters: transmission or chain parameters

Definition

ABCD-parameters relate the input-port voltage and current to the output-port voltage and the negative of output-port current:

[ V₁ ; I₁ ] = [ [ A, B ], [ C, D ] ] [ V₂ ; -I₂ ]

Expanded:

V₁ = A V₂ - B I₂
I₁ = C V₂ - D I₂

Parameter meanings

• A = V₁ / V₂ with I₂ = 0. This is a voltage ratio with port 2 open-circuited.
• B = -V₁ / I₂ with V₂ = 0. This has units of ohms.
• C = I₁ / V₂ with I₂ = 0. This has units of siemens.
• D = -I₁ / I₂ with V₂ = 0. This is a current ratio.

Why use ABCD-parameters?

The main reason is cascading. Suppose network 1 feeds network 2. If each has an ABCD matrix, the total cascade is:

[ABCD]_total = [ABCD]₁ [ABCD]₂

For a chain of N networks:

[ABCD]_total = [ABCD]₁ [ABCD]₂ ... [ABCD]_N

The order matters. Matrix multiplication is generally not commutative.

Common ABCD building blocks

Transmission-line ABCD formulas are standard in microwave network theory; see Pozar’s Microwave Engineering and the open microwave network text by Steer at LibreTexts.

Step-by-step cascade example

Suppose a network consists of a series impedance Z₁, then a shunt admittance Y₂, then a series impedance Z₃. The individual ABCD matrices are:

M₁ = [ [ 1, Z₁ ], [ 0, 1 ] ]
M₂ = [ [ 1, 0 ], [ Y₂, 1 ] ]
M₃ = [ [ 1, Z₃ ], [ 0, 1 ] ]

The total matrix is:

M_total = M₁M₂M₃

First multiply M₁M₂:

M₁₂ = [ [ 1 + Z₁Y₂, Z₁ ], [ Y₂, 1 ] ]

Then multiply by M₃:

M_total = [ [ 1 + Z₁Y₂, Z₁ + Z₃ + Z₁Y₂Z₃ ], [ Y₂, 1 + Y₂Z₃ ] ]

Thus:

A = 1 + Z₁Y₂
B = Z₁ + Z₃ + Z₁Y₂Z₃
C = Y₂
D = 1 + Y₂Z₃

6. S-parameters: scattering parameters

Definition

S-parameters relate reflected waves to incident waves:

[ b₁ ; b₂ ] = [ [ S₁₁, S₁₂ ], [ S₂₁, S₂₂ ] ] [ a₁ ; a₂ ]

Expanded:

b₁ = S₁₁a₁ + S₁₂a₂
b₂ = S₂₁a₁ + S₂₂a₂

Parameter meanings

• S₁₁: input reflection coefficient with port 2 terminated in Z₀.
• S₂₂: output reflection coefficient with port 1 terminated in Z₀.
• S₂₁: forward transmission coefficient or gain from port 1 to port 2.
• S₁₂: reverse transmission coefficient or isolation from port 2 to port 1.

Why use S-parameters?

• They are directly measurable at RF and microwave frequencies with a vector network analyzer.
• They avoid requiring ideal open and short circuits at the device ports.
• They naturally describe reflection, insertion loss, gain, return loss, and isolation.
• They are widely used in data files such as Touchstone files.

Industry measurement practice is strongly centered on S-parameters; see Keysight’s S-parameter application note and Rohde & Schwarz’s S-parameter overview.

Important S-parameter quantities

• Return loss at port 1: RL₁ = -20 log₁₀|S₁₁| dB
• Insertion loss for a passive forward path: IL = -20 log₁₀|S₂₁| dB
• Forward gain: G = 20 log₁₀|S₂₁| dB, when the network is active or has gain
• Reverse isolation: ISO = -20 log₁₀|S₁₂| dB

Limitations

S-parameters depend on the reference impedance. A two-port’s S-parameters at 50 ohms are not generally the same as its S-parameters at 75 ohms. Also, for strongly nonlinear devices, ordinary small-signal S-parameters are valid only around a specified bias point and signal level.

7. Scattering-transfer T-parameters: wave chain parameters

Definition used here

[ a₁ ; b₁ ] = [ [ T₁₁, T₁₂ ], [ T₂₁, T₂₂ ] ] [ b₂ ; a₂ ]

Why use scattering-transfer T-parameters?

• They allow cascaded RF networks to be multiplied directly.
• They are useful when measured networks are available as S-parameters but must be cascaded many times.
• They avoid repeated S-to-ABCD-to-S conversions in some microwave calculations.

If network 1 feeds network 2, and both are represented by compatible scattering-transfer matrices, then:

T_total = T₁T₂

Caution

Conversion from S to this T form requires S₂₁ ≠ 0. If S₂₁ is zero or extremely small, the T matrix becomes singular or numerically very large. This often happens near transmission zeros, which are common in filters. In such cases, a direct S-matrix cascade method or a different parameter set may be more numerically stable.

8. Reciprocity, symmetry, and losslessness

Reciprocity

For a reciprocal two-port under the conventions used here:

• Z-parameters: z₁₂ = z₂₁
• Y-parameters: y₁₂ = y₂₁
• ABCD-parameters: AD - BC = 1
• S-parameters with equal reference impedances: S₁₂ = S₂₁

Symmetry

A physically symmetric two-port has the same behavior looking into either port. Common tests include:

• Z-parameters: z₁₁ = z₂₂
• Y-parameters: y₁₁ = y₂₂
• ABCD-parameters: A = D
• S-parameters with equal reference impedances: S₁₁ = S₂₂

Losslessness

For a passive lossless two-port with real equal reference impedances, the S-matrix is unitary:

S^†S = I

where S^† is the conjugate transpose of S. This implies conservation of incident and reflected power. The unitarity property is one reason S-parameters are so useful in microwave engineering.

9. Notation for conversion formulas

The following determinants and abbreviations are used throughout the conversion tables:

Δ_Z = z₁₁z₂₂ - z₁₂z₂₁

Δ_Y = y₁₁y₂₂ - y₁₂y₂₁

Δ_h = h₁₁h₂₂ - h₁₂h₂₁

Δ_A = AD - BC

Δ_S = S₁₁S₂₂ - S₁₂S₂₁

Δ_T = T₁₁T₂₂ - T₁₂T₂₁

Z₀ is the real reference impedance for S and T parameters. Y₀ = 1 / Z₀.

All formulas assume that the displayed denominators are nonzero. If a denominator is zero, the conversion may not exist in that form.

10. Core conversion table

The table below gives explicit conversions among Z, Y, h, ABCD, S, and scattering-transfer T parameters under the conventions stated above. For compactness, some cells use an intermediate conversion. That is still an explicit formula: compute the intermediate quantities shown, then substitute them into the stated target formula.

11. Step-by-step method for using the conversion formulas

1. Identify the source parameter set. For example, determine whether your data are Z, Y, h, ABCD, S, or T parameters.
2. Verify the convention. This is especially important for ABCD and T parameters. Confirm the current direction and the ordering of variables.
3. Write down the known matrix elements. For example, if you have S-parameters, list S₁₁, S₁₂, S₂₁, and S₂₂.
4. Check the reference impedance. For S and T conversions, identify Z₀. Common values are 50 ohms and 75 ohms.
5. Compute any determinant or denominator. For example, when converting S to Z, compute D_SZ = (1 - S₁₁)(1 - S₂₂) - S₁₂S₂₁.
6. Check for singular or nearly singular denominators. If a denominator is zero or very small, the formula may produce a misleading result.
7. Apply the formula element by element. Keep complex arithmetic intact; phase matters.
8. Check units. Z elements are in ohms, Y elements are in siemens, B is in ohms, C is in siemens, while A, D, S, and T elements are generally dimensionless.
9. Validate the result with known physical properties. For a reciprocal passive two-port, check z₁₂ = z₂₁, y₁₂ = y₂₁, S₁₂ = S₂₁, or AD - BC = 1, as applicable.

12. Practical application guidance

Use Z-parameters when:

• The circuit is low-frequency and naturally described by impedances.
• Series elements dominate.
• You are doing mesh analysis.
• Open-circuit test conditions are reasonable.

Use Y-parameters when:

• The circuit is naturally described by shunt admittances.
• Nodal analysis is convenient.
• Parallel connection of networks is being studied.
• Short-circuit test conditions are reasonable.

Use h-parameters when:

• You are analyzing transistor small-signal amplifier stages in classical low-frequency form.
• You want current gain and input impedance to appear directly in the model.
• You are working from older transistor data sheets or educational material.

Use ABCD-parameters when:

• The network is a cascade of two-port blocks.
• You are analyzing filters, attenuator pads, matching networks, or transmission-line sections.
• You want the total response of a chain by matrix multiplication.

Use S-parameters when:

• You are working at RF, microwave, or millimeter-wave frequencies.
• The network is measured with a vector network analyzer.
• You care about return loss, insertion loss, gain, isolation, or match.
• You are exchanging device data using Touchstone files.

Use scattering-transfer T-parameters when:

• You have S-parameter data but need to cascade multiple networks.
• You want wave-based cascade calculations.
• You are careful about transmission zeros where S₂₁ may approach zero.

13. Worked example: converting ABCD to S

Suppose a two-port has ABCD parameters A, B, C, and D and is used in a 50-ohm system. Let Z₀ = 50 ohms.

Step 1: Compute the common denominator:

D_AS = A + B/50 + 50C + D

Step 2: Compute input reflection:

S₁₁ = (A + B/50 - 50C - D)/D_AS

Step 3: Compute forward transmission:

S₂₁ = 2/D_AS

Step 4: Compute reverse transmission:

S₁₂ = 2(AD - BC)/D_AS

Step 5: Compute output reflection:

S₂₂ = (-A + B/50 - 50C + D)/D_AS

If the network is reciprocal, AD - BC = 1, so S₁₂ = S₂₁ for equal reference impedances.

14. Worked example: converting S to ABCD

Suppose measured S-parameters are available from a vector network analyzer and you want to cascade the device with other circuit blocks. Use the S-to-ABCD formulas.

Step 1: Confirm Z₀. If the measurement was made in a 50-ohm system, Z₀ = 50 ohms.

Step 2: Confirm S₂₁ is not zero. The standard S-to-ABCD formula divides by S₂₁.

Step 3: Compute:

A = ((1 + S₁₁)(1 - S₂₂) + S₁₂S₂₁)/(2S₂₁)

B = Z₀((1 + S₁₁)(1 + S₂₂) - S₁₂S₂₁)/(2S₂₁)

C = ((1 - S₁₁)(1 - S₂₂) - S₁₂S₂₁)/(2Z₀S₂₁)

D = ((1 - S₁₁)(1 + S₂₂) + S₁₂S₂₁)/(2S₂₁)

Step 4: Cascade by multiplying ABCD matrices in the physical order of the signal path.

15. Numerical and physical cautions

Singular conversions

A conversion may be singular even when the physical network is well-defined. Examples:

• Z to ABCD formula above requires z₂₁ ≠ 0.
• Y to ABCD formula above requires y₂₁ ≠ 0.
• ABCD to Z formula above requires C ≠ 0.
• ABCD to Y formula above requires B ≠ 0.
• S to ABCD and S to T require S₂₁ ≠ 0.
• T to S requires T₁₁ ≠ 0.

Near-zero denominators

If a denominator is very small, the conversion may amplify measurement noise. This is especially important when converting measured S-parameters near filter transmission zeros. In those cases, the converted ABCD or T values may become very large even though the original S-parameters are physically meaningful.

Reference impedance and renormalization

S-parameters must specify their reference impedance. If a device measured at 50 ohms is placed in a 75-ohm system, the S-parameters should be renormalized or converted through Z/Y parameters and then re-expressed at the new reference impedance. Modern RF tools implement this, but the underlying mathematics depends on the wave definition and reference impedance convention.

Complex reference impedances

The formulas in this report assume equal real Z₀. For unequal or complex reference impedances, use generalized formulas. This is not merely a cosmetic change: the definition of wave amplitude affects power normalization, conjugation, and passivity tests. Kurokawa’s power-wave paper is the classic reference.

Open questions / debates in the field

• ABCD and T convention differences: There is no single universal notation for chain matrices. Some authors define ABCD using I₂ instead of -I₂. Some define scattering transfer matrices with different wave ordering. This is not a scientific dispute, but it is a persistent source of engineering errors.
• Power waves versus pseudo-waves: For complex reference impedances, different wave definitions can give different-looking S-parameters. The correct choice depends on whether the goal is power accounting, measurement calibration, or mathematical convenience.
• Numerical stability in cascades: Cascading many networks using ABCD or T matrices can lead to very large or very small numbers, especially for long lossy lines or high-rejection filters. Engineers debate and develop more stable algorithms, including Redheffer star products and state-space approaches.
• Passivity and causality enforcement: Measured broadband S-parameters often contain small errors that violate passivity or causality. Correcting those data without distorting the real device behavior is an active topic in RF/microwave modeling and signal-integrity work.
• Linear versus nonlinear behavior: Ordinary two-port matrices describe linear small-signal behavior. Power amplifiers, mixers, varactors, and switching devices may require X-parameters, large-signal S-parameters, harmonic-balance models, or time-domain nonlinear models.
• De-embedding and fixture removal: Converting among matrices is straightforward in theory, but real measurements include fixtures, launches, connectors, and calibration standards. The best de-embedding method depends on the frequency range, substrate, calibration quality, and device geometry.

Sources cited and useful references

• David M. Pozar, Microwave Engineering, Wiley. Standard academic microwave engineering text covering S-parameters, transmission lines, and two-port networks.
• Keysight Technologies, S-Parameter Design Application Note. Industry reference for S-parameter concepts and measurement usage.
• Rohde & Schwarz, Understanding S-Parameters. Industry tutorial on scattering parameters and RF measurement interpretation.
• Qucs Project, Technical Documentation on Network Parameter Conversions. Open technical documentation containing two-port conversion formulas and circuit-simulation conventions.
• scikit-rf Project, Network Tutorial Documentation. Practical open-source RF/microwave network-analysis documentation.
• David M. Pozar and other microwave engineering texts commonly derive ABCD-to-S and S-to-ABCD formulas using equal real reference impedance; the same relationships are also summarized in many RF CAD tool manuals.
• Kaneyuki Kurokawa, “Power Waves and the Scattering Matrix,” IEEE Transactions on Microwave Theory and Techniques, 1965. Classic paper on power-wave definitions for scattering matrices.
• Michael Steer, Microwave and RF Design: Networks, Two-Port Networks, LibreTexts. Open educational reference on two-port network descriptions.

Final practical advice

For hand analysis, choose the parameter set that matches the circuit structure: Z for series behavior, Y for shunt behavior, ABCD for cascades, and h for classical transistor models. For RF measurement, begin with S-parameters because they are what the instrument directly measures. Convert only when the target representation gives a clear advantage, and always check the sign convention, reference impedance, and singular denominators before trusting the result.

This content was generated primarily with the assistance of ChatGPT (OpenAI), and/or Gemini (Google), and/or Arya (GabAI), and/or Grok (x.AI), and/or DeepSeek artificial intelligence (AI) engines. Review was performed to help detect and correct any inaccuracies; however, you are encouraged to verify the information yourself if it will be used for critical applications. In all cases, multiple solicitations to the AI engine(s) was(were) used to assimilate final content. Images and external hyperlinks have also been added occasionally - especially on extensive treatises. Courts have ruled that AI-generated content is not subject to copyright restrictions, but since I modify them, everything here is protected by RF Cafe copyright. Many of the images are likewise generated and modified. Your use of this data implies an agreement to hold totally harmless Kirt Blattenberger, RF Cafe, and any and all of its assigns. Thank you. Here is Gab AI in an iFrame.

AI Technical Trustability Update

While working on an update to my RF Cafe Espresso Engineering Workbook project to add a couple calculators about FM sidebands (available soon). The good news is that AI provided excellent VBA code to generate a set of Bessel function plots. The bad news is when I asked for a table showing at which modulation indices sidebands 0 (carrier) through 5 vanish, none of the agents got it right. Some were really bad. The AI agents typically explain their reason and method correctly, then go on to produces bad results. Even after pointing out errors, subsequent results are still wrong. I do a lot of AI work and see this often, even with subscribing to professional versions. I ultimately generated the table myself. There is going to be a lot of inaccurate information out there based on unverified AI queries, so beware.

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