35-year-old 3-way speaker
Electroacoustic evaluation, system geometry, directivity and listening positioning
LspCAD 6.20 pro simulation on .frd/.zma data from the three transducers: 27 cm woofer, 7.7 cm midwoofer and 5 cm tweeter, with paper+mica and paper cones. Crossover A: 5 components, three parallel ways, flat vertical baffle with the acoustic offsets adopted for the three transducers in the model. This version strictly distinguishes between model, calculation and pending measurement. The model is frozen as MR-A-01 before building the physical cabinet.
● CONFIRMED: 5 frozen components (L3 1.8 mH, C1 33 µF, R2 2.2 Ω, L4 0.82 mH, C2 2.7 µF), 3 parallel ways, no series R on the tweeter. Flat vertical baffle. ● LspCAD SIMULATED: ripple ±0.7–1 dB (400 Hz–4 kHz), horizontal directivity −2 dB at ±20°, vertical notches at 1 kHz (±60–70°) and 4.5 kHz (±25–30°), model minimum impedance ~4.9 Ω. ● PENDING: real sensitivity, real impedance, THD, baffle step, 3 m in-room response. Crossover A = working reference, not a validated design.
0. Executive summary
20-second read
Topology: 5 components, three parallel ways. Woofer: 1st-order low pass (L3 series). Midwoofer: C1 + R2 in series with the driver and L4 in shunt — together they form a 2nd-order high-pass electrical network. Tweeter: 1st-order high pass (C2 series, without deliberate series attenuation resistor). CONFIRMED
Geometry: flat vertical baffle (90° relative to the floor). The three drivers flush-mounted. The acoustic offsets adopted for the three transducers in the model (+0 mm tweeter, −5 mm midwoofer, −20 mm woofer relative to the baffle) are included in the simulation. PHYSICAL ASSEMBLY: CONFIRMED · ACOUSTIC OFFSETS: ADOPTED IN MODEL, PENDING MEASUREMENT
400 Hz–4 kHz ripple (model): ±0.7 to ±1 dB. VISUAL ESTIMATE
4–10 kHz ripple (model): ±1.5 to ±2 dB. The residual towards 4–5 kHz is compatible with a resonance or irregularity of the tweeter itself; its exact origin must be confirmed by measuring the real unit. VISUAL ESTIMATE PENDING MEASUREMENT
Horizontal directivity (model): cumulative loss of ~2 dB at ±20°; ~4–6 dB at ±30° in 6–10 kHz, with progressive narrowing above. In the vertical plane, two notches consistent with cancellation physics: one at ~1 kHz at ±60–70° (woofer-mid) and another at 4.5 kHz at ±25–30° (mid-tweeter). LspCAD PREDICTION
Impedance (model): provisional minimum ≈4.9 Ω at ~1.4 kHz, moderate phase. The model does not show the combination of very low Z and high phase that tends to be especially demanding for stages with appreciable output impedance. LspCAD PREDICTION PENDING MEASUREMENT
Listening: ear at the tweeter-midwoofer junction, speakers at 20–25° per side, 2.5–3.5 m distance, slight toe-in. INFERENCE FROM THE MODEL
General design thesis
Remove the woofer from the problematic band at the right moment and make its directivity compatible with that of the midwoofer in the transition zone. The design combines a first-order electrical filter on the woofer and tweeter with a second-order high-pass electrical network on the midwoofer, and with the acoustic offsets adopted for the three transducers included in the model. In the model, that ensemble produces a more uniform response than the electrical schematic, considered in isolation, would suggest. Experimental validation remains pending.
Epistemological state of the project
Three orthogonal axes. State of the object: what it is, whether it is closed or modifiable. State of the prediction: what the model said, with what degree of commitment. State of validation: what the measurement said, or whether there is one yet. They are not mixed.
| Element | State of the object | State of the prediction | State of validation |
|---|---|---|---|
| Crossover components (L3, C1, R2, L4, C2) | FROZEN | — | — |
| Woofer–mid crossover | PREDICTION ≈700–900 Hz | PENDING | |
| Mid–tweeter crossover | PREDICTION ≈4–5 kHz | PENDING | |
| Axial response | PREDICTION | PENDING | |
| Directivity (horizontal and vertical) | PREDICTION | PENDING | |
| Impedance and phase | PREDICTION | PENDING | |
| EPDR | MODEL ESTIMATE | PENDING | |
| Sensitivity | CALCULATION HYPOTHESIS: 89 dB/W/m (not LspCAD output) | PENDING | |
| Baffle step | INCOMPLETE MODEL | PENDING | |
| Driver THD and compression | ND — outside the scope of the model | NOT APPLICABLE TO MODEL |
FROZEN means the value must not be modified before obtaining physical measurements. It does not mean the value is optimal. ND means the model does not contain the phenomenon and therefore emits no prediction about it.
1. Crossover A configuration
3-way speaker with paper+mica and paper drivers, ~35 years old. The consolidated design consists of 5 components distributed across three parallel ways. The tweeter operates without a deliberate series attenuation resistor; its relative level is determined by the transducer sensitivity, C2 and the combined system response.
| Component | Value | Way | Function | Evidence |
|---|---|---|---|---|
| L3 | 1.80 mH | Woofer | 1st-order low pass (in series with the driver) | CONFIRMED |
| C1 | 33.0 µF | Midwoofer | High pass (in series with the driver) | CONFIRMED |
| R2 | 2.2 Ω | Midwoofer | Damping/level (in series with C1) | CONFIRMED |
| L4 | 0.82 mH | Midwoofer | Shunt, in parallel with the driver | CONFIRMED |
| C2 | 2.70 µF | Tweeter | 1st-order high pass (in series), no R1 | CONFIRMED |
Midwoofer topology
The combination C1 + R2 in series and L4 in shunt jointly form the 2nd-order high-pass electrical network of the midrange way. This formulation must not be decomposed into "two independent high passes that add up", nor should L4 be described as an autonomous shunt to ground of the driver.
- C1 and R2 are in series with the driver. At low frequency, C1 presents high impedance and limits the current towards the midwoofer.
- L4 is in shunt relative to the driver. At low frequency its impedance is low and reduces the voltage applied to the transducer.
- As frequency increases, C1 reduces its impedance and L4 increases its own, progressively allowing excitation of the midwoofer.
Unlike the woofer (real electrical low pass via L3) and the tweeter (real electrical high pass via C2), the midwoofer has no electrical low pass. In the model used, its upper cut-off is mainly determined by the driver's natural rolloff. The starting .frd shows a drop of ~87.6 dB at 5 kHz → 83.3 dB at 6 kHz → 78.0 dB at 10 kHz. READING OF THE STARTING FILE DESIGN INFERENCE
Decision: Crossover A remains frozen as an experimental reference. The next knowledge jump must come from the physical cabinet. INFERENCE
Why nominal Z and acoustic crossover do not coincide
A quick check with the 6 Ω nominal impedance may suggest that the filter values do not produce the expected crossover:
L3 1.80 mH with Z=6 Ω → f = Z/(2πL) ≈ 531 Hz C1 33.0 µF with Z=6 Ω → f = 1/(2πZC) ≈ 804 Hz L4 0.82 mH with Z=6 Ω → f = Z/(2πL) ≈ 1,164 Hz C2 2.70 µF with Z=6 Ω → f = 1/(2πZC) ≈ 9,824 HzHowever, LspCAD does not calculate with nominal Z, but with the starting .zma files:
- The midwoofer crossover around 700–900 Hz is defined by the combination of C1 + L4, not by a single component.
- The tweeter crossover around 4–5 kHz does not depend only on C2. With the model impedance, ~7–8 Ω around 5 kHz, C2 = 2.70 µF gives an electrical reference frequency of ~7.4–8.4 kHz. The acoustic transition begins earlier because the tweeter's own response already rises from ~2 kHz.
That is why the model's acoustic crossover (700–900 Hz woofer-mid, 4–5 kHz mid-tweeter) is consistent with the simulation even though the calculations with nominal Z give different figures. LspCAD PREDICTION
Component selection — specific specifications
Verifiable electrical specifications for each component. Supplier part numbers are not cited because they change between catalogs and countries; any distributor can locate the product by these technical references.
| Component | Specification | DCR / Note |
|---|---|---|
| L3 (1.80 mH) | Preferably air core, 1.4 mm Ø wire (AWG15) — Jantzen Air Core or equivalent | DCR ≈ 0.42–0.43 Ω. Alternative: foil 14 AWG, DCR ≈ 0.36 Ω. The coil DCR is part of the series impedance of the bass way and modifies the filter level and Q; its real resistance must be introduced in the simulation. Iron core is not recommended due to its higher DCR (≈0.8 Ω). |
| L4 (0.82 mH) | Air core, 1.6 mm Ø wire (AWG14) — Jantzen Air Core or equivalent | DCR ≈ 0.21 Ω. Alternative: 1.2 mm Ø, DCR ≈ 0.34 Ω. In shunt; its DCR does not degrade woofer damping, but sets the slope of the midwoofer high pass. |
| R2 (2.2 Ω) | Non-inductive, 12–15 W (Mundorf MResist Supreme 15W, Mills MRA-12, Jantzen Superes 12W) | Will dissipate 3–5 W in peaks with compressed music. 10 W is marginal; 12 W minimum recommended. |
| C1 (33.0 µF) | MKP 250 V or higher. Mundorf MCAP EVO, Jantzen Cross Cap 400 V, ClarityCap CSA, Audyn Cap Plus. | If 33 µF exact is not found: 2× 15 µF + 2× 1.5 µF in parallel, same brand. Avoid bipolar electrolytic: ESR and non-linearity affect the mid-bass zone. |
| C2 (2.70 µF) | MKP 250 V or higher. Mundorf MCAP EVO Oil 450 V, Jantzen Superior Z-Cap 800 V, ClarityCap CSA 250 V. | With 40 W and 6 Ω it is <20 V peak at the terminals, so 100 V would already suffice. The 250–800 V are for dielectric construction, not for voltage. |
2. Frequency response and ripple (SPL)
Main model–measurement comparison band: ≈300 Hz–10 kHz. It is the band in which LspCAD emits a prediction and in which the planned measurement procedure can, in principle, compare. It is not called "validatable" because that would prejudge that the experimental method allows validation with sufficient uncertainty; it is only stated that it is the band where the comparison makes sense to attempt.
Within this band four contributions must be distinguished: the drivers' own response, the geometry and the offsets adopted, the action of the crossover, and possible reflections of the measurement environment. A discrepancy within this band does not automatically point to one of these four; that is what the causal diagnosis is for (section 7).
Band with greater dependence on the enclosure and measurement method: <≈300 Hz. Here the response depends on factors that LspCAD does not model in this simulation: real baffle step, enclosure dimensions and losses, woofer alignment, presence or absence of a port, room position and room gain. A measured discrepancy below 300 Hz must not be used to falsify the crossover. It is a different question.
Between 200 Hz and 10 kHz, the model's on-axis response stays in an approximate range of 88–91 dB. There are no deep holes at the two main transitions:
- Woofer → Midwoofer: ~700–900 Hz (model acoustic crossover).
- Midwoofer → Tweeter: ~4–5 kHz.
Above 10 kHz there is a progressive fall in the model — it must not be described as "flat to 20 kHz". Approximate reading: ~88–90 dB towards 10 kHz, ~85 dB towards 15 kHz, ~78–83 dB towards 20 kHz.
Estimated ripple 400 Hz – 10 kHz (model)
| Band | Estimated ripple |
|---|---|
| 400 Hz – 4 kHz | ±0.7 to ±1 dB |
| 4 kHz – 10 kHz | ±1.5 to ±2 dB |
The fall in the extreme treble is a characteristic of the model that must be verified by measurement and listening with the real cabinet. PENDING MEASUREMENT
3. Impedance and amplifier compatibility
| Parameter | Value | Evidence |
|---|---|---|
| Minimum impedance (model) | Provisional, close to 4.9 Ω at ~1.4 kHz | PREDICTION PENDING MEASUREMENT |
| Phase at that point | Moderate; the model does not show an accentuated reactive extreme in the minimum zone | PREDICTION |
| Operating band | The impedance modulus stays approximately in the 5–8 Ω zone over most of the modeled band | VISUAL ESTIMATE FROM GRAPH |
| Nominal impedance | ≈6 Ω | PREDICTION PENDING MEASUREMENT |
| Model EPDR | >≈3.5 Ω, estimate dependent on the predicted curve | ESTIMATED PENDING MEASUREMENT |
Characterization of the model: the model does not show the combination of very low impedance and high phase that tends to be especially demanding for stages with appreciable output impedance. The model suggests an EPDR above approximately 3.5 Ω, but this value must be verified from the measured impedance and phase of the finished cabinet. The specific compatibility with a given valve amplifier must be verified with the real impedance of the cabinet and the output impedance of the amplifier. INFERENCE PENDING MEASUREMENT
Output tap: neither 4 Ω nor 8 Ω is established in general as "the correct one". The tap that the manufacturer of each amplifier recommends for this nominal Z (~6 Ω) should be used, documented and kept constant between comparisons. With valves it can be informative to measure both taps and document how the frequency response changes due to the amplifier output impedance. INFERENCE
4. System geometry and directivity
Physical geometry of the acoustic centers
The speaker baffle is flat and vertical (90° relative to the floor). The three transducers are flush-mounted, with no step or tilt. The system reference point is the junction between tweeter and midwoofer, which constitutes the design axis and the listening axis.
Each transducer presents an effective acoustic center depth adopted in the model, related to its geometry, motor and acoustic behavior. These offsets must not be interpreted as invariant physical coordinates of the transducer: the acoustic center can vary with frequency and they constitute one of the main uncertainties of the model. ADOPTED IN MODEL
| Driver | dy vertical | Acoustic offset adopted in model | Note |
|---|---|---|---|
| Tweeter | +38.5 mm | 0 mm (reference) | System reference offset |
| Midwoofer | −38.5 mm | 5 mm behind the baffle | Adopted for the model |
| Woofer | −223.5 mm | 20 mm behind the baffle | Adopted for the model |
Constructional consequence: no step or baffle tilt is required. The acoustic offsets adopted by LspCAD are included in the model and are absorbed by the crossover design. Whether those offsets match the real ones of the physical units is a matter to verify by measurement. PHYSICAL ASSEMBLY: CONFIRMED · ACOUSTIC OFFSETS: ADOPTED IN MODEL, PENDING MEASUREMENT
Acoustic relevance: at 4.5 kHz (midwoofer-tweeter crossover), the wavelength is ~76 mm. The 5 mm difference between the acoustic offsets adopted for midwoofer and tweeter is equivalent to ~6.6% of a wavelength, about 24° of phase. At 750 Hz, the wavelength is ~457 mm. The 15 mm difference between the acoustic offsets adopted (woofer 20 mm, midwoofer 5 mm) is equivalent to ~3.3% of a wavelength, about 12° of phase. Do not confuse these 15 mm of offset difference with the 185 mm geometric separation between centers, which is used for the notch geometry. CALCULATED
Angles to the listening axis (at 3 m)
With the ear at the axis (tweeter-midwoofer junction) and at 3 m distance, the vertical angles to each acoustic center are:
| Driver | Vertical angle | State |
|---|---|---|
| Tweeter | arctan(38.5/3000) ≈ +0.73° | On axis |
| Midwoofer | arctan(−38.5/3000) ≈ −0.73° | On axis |
| Woofer | arctan(−223.5/3000) ≈ −4.27° | Within tolerance |
The critical mid-tweeter crossover (~4–5 kHz) occurs practically on axis, because the two drivers involved are only ±0.73° from the listening point. The woofer, at 4.3° below the axis, remains in the model within a small angle relative to its crossover with the midwoofer. CALCULATED
Horizontal directivity (model)
The cumulative loss is ~2 dB at ±20° and ~4–6 dB at ±30° in the 6–10 kHz band, with progressive narrowing above. PREDICTION
| Horizontal angle | Loss in 6–10 kHz |
|---|---|
| 0° (on axis) | 0 dB |
| ±10° | < 1 dB |
| ±20° | ~2 dB |
| ±30° | ~4–6 dB |
| ±60° | Very high attenuation |
Vertical directivity — the main compromise
In the model's vertical polar map two cancellation notches appear, one for each crossover between ways:
Midwoofer-tweeter crossover notch (~4.5 kHz)
With a relative dip of ≈18–20 dB with respect to the on-axis level, located at ±25–30° measured from the tweeter-midwoofer junction. It is the critical notch because it is closer to the vertical listening axis.
Geometric condition (independent calculation): the separation between tweeter and midwoofer acoustic centers is 77 mm. At 4.5 kHz the wavelength is ~76 mm. The total cancellation condition (d·sinθ = λ/2) gives sinθ = 38/77 ≈ 0.493 → θ ≈ 29.5°. At 3 m distance, ±29.5° corresponds to ±1.7 m of vertical displacement. CALCULATED
Position observed in the model: LspCAD reproduces that notch at ±25–30° with the stated dip of 18–20 dB. LspCAD PREDICTION
Woofer-midwoofer crossover notch (~1 kHz)
A second cancellation minimum exists in the ~1 kHz zone, corresponding to the crossover between woofer and midwoofer. With 185 mm separation between acoustic centers, the geometric condition (d·sinθ = λ/2) places the cancellation at ±60–70° vertical around 1 kHz. CALCULATED
Numerical verification: for θ = 65°, sinθ = 0.906 → λ/2 = 185 × 0.906 = 168 mm → λ = 335 mm → f ≈ 1,024 Hz. For θ = 70°, sinθ = 0.940 → λ/2 = 174 mm → λ = 348 mm → f ≈ 986 Hz. The notch therefore falls between 986 Hz and 1,024 Hz depending on the exact angle.
At 3 m distance, ±65° vertical corresponds to > 6 m of vertical displacement relative to the axis. It is completely outside any reasonable listening position.
Vertical variation according to the model at 3 m
| Vertical offset relative to axis | Resulting angle | Behavior in the model |
|---|---|---|
| 0 mm | 0° | Optimal |
| ±100 mm | ±1.9° | Region of small variation |
| ±250 mm | ±4.8° | Region of small variation; matches the recommendation in section 6 |
| ±500 mm | ±9.5° | Changes in the response begin to be visible from here |
| ±700 mm | ±13° | Visible degradation in 4–5 kHz |
| ±1,090 mm | ±20° | Approximation to the region where the dip associated with the mid-tweeter notch begins to become significant |
| ±1,600 mm | ±28° | Complete mid-tweeter notch |
| > 6 m | ±65–70° | Woofer-mid notch (purely theoretical, outside any real position) |
Correct formulation: the model shows a region of relatively small variation around the design axis; at 3 m it spans approximately ±25 cm (±4.8°). The degradation becomes progressively more visible as one moves away from the axis. It must not be stated as "without audible effect" because the real cabinet response, the real notch width and the room acoustics are not yet characterized. CALCULATED PREDICTION PENDING MEASUREMENT
Green blotch at 1 kHz off-axis: in the model's vertical map a greenish zone appears in the 1 kHz band at intermediate angles. It must not be interpreted as cone breakup. The most parsimonious cause in this model is the residual contribution of the woofer above its crossover, favored by the first-order electrical slope of L3. INFERENCE
Joint reading of figures 4 to 8
The five figures cover the same phenomenon from two complementary perspectives. Figures 4, 5 and 6 are discrete cuts: Figures 4 and 5 show the response at specific angles, and Figure 6 shows it at specific frequencies (1, 2, 4, 6, 8 and 10 kHz). Figures 7 and 8 are continuous views: color maps on the frequency-angle plane.
- Figure 6 (polar diagram): shape of the lobe modeled at each specific frequency.
- Figure 7 (horizontal map): summarizes the entire horizontal behavior of the model in a single image.
- Figure 8 (vertical map): the most critical of the three. It makes visible the two notches described in the text.
Taken together, the five figures are consistent with what the report maintains by calculation: horizontal directivity with ~2 dB loss at ±20° and ~4–6 dB at ±30°; small vertical variation within ±25 cm at 3 m (±4.8°); two cancellation notches consistent with the geometric physics of the system. They do not "confirm" the real cabinet: they confirm the behavior of the model built with those .frd/.zma. LspCAD PREDICTION CALCULATED PENDING MEASUREMENT
5. Sensitivity and required power (under explicit hypotheses)
SYSTEM SENSITIVITY: ND
89 dB/W/m — CALCULATION HYPOTHESIS, NOT LspCAD OUTPUT
The real sensitivity of the finished cabinet will not be known until it is measured. The value 89 dB/W/m is a working hypothesis, not a property of the cabinet. The following calculations must be read conditioned on that hypothesis and on a free-field scenario. PENDING MEASUREMENT
Three levels of treatment of a numerical value
This document explicitly distinguishes three levels for any numerical value of the system (89 dB, impedance, EPDR, 95 dB SPL, 200 Hz–10 kHz response):
- Level 1 — Prediction. "The working hypothesis is approximately 89 dB/W/m."
- Level 2 — Validation. "The measurement gives X; the comparison with the prediction is made according to the pre-registered criterion."
- Level 3 — Specification. "The cabinet is characterized as X dB/W/m."
One does not pass directly from level 1 to level 3. The distance between them is the measurement, and that distance cannot be jumped without losing traceability.
Modeled scenario: 80 dB SPL continuous + 15 dB crest = 95 dB peak, at 3 m, free field. To maintain a conservative criterion, the following calculations consider the SPL produced by a single cabinet. With two cabinets reproducing the same signal, the ideal stereo sum provides approximately 3 dB additional at the listening point.
20·log₁₀(3) = 9.54 dB → 1 W gives ≈79.46 dB per cabinet at 3 m. 95 dB SPL with one cabinet: 10^((95−79.46)/10) ≈ 35.8 W. 80 dB SPL continuous with one cabinet: 10^((80−79.46)/10) ≈ 1.13 W. Stereo equivalent at the listening point (two cabinets, +3 dB): ≈17.9 W/channel for 95 dB peak.In the modeled scenario, maintaining 80 dB SPL continuous + 15 dB crest at 3 m requires approximately 1.1 W of average power and peak capability of ~36 W in one cabinet (or ~18 W/channel in stereo with the ideal sum). These figures are a calculation conditioned on the sensitivity hypothesis and the free-field scenario, not a specification of the cabinet.
Note on baffle step: LspCAD with a piston model does not include the baffle step effect of the real cabinet. In the band <≈300 Hz, the response additionally depends on enclosure dimensions and losses, woofer alignment, presence or absence of a port, room position and room gain. A measured discrepancy in this band must not be used to falsify the crossover. PENDING MEASUREMENT DO NOT DECIDE YET
Important caution: the above numbers are a calculation conditioned on seven assumptions that are not yet verified: (1) real sensitivity, (2) driver thermal behavior, (3) driver THD at those levels, (4) compression, (5) real listening distance, (6) room gain, (7) crest level actually demanded. They must not be presented as a demonstrated property of the cabinet. INFERENCE PENDING MEASUREMENT
Precaution: if one amp goes into clipping while another keeps margin, the difference is available dynamic capability, not proof that one has a superior timbral quality. INFERENCE
6. Listening positioning
Recommended configuration
| Parameter | Optimal value | Calculation basis |
|---|---|---|
| Ear height | Tweeter-midwoofer junction | System design axis |
| Listening distance | 2.5 – 3.5 m | Directivity and SPL of the model |
| Horizontal angle per side | 20–25° | Off-axis ~2 dB up to 20° in the model |
| Separation between tweeters (at 3 m) | 2.2 – 2.8 m → 20–25° per side. Central working zone: 2.4 – 2.6 m → approx. 22–23.5° per side. | 2 × 3 × tan(θ) |
| Toe-in | Slight, aiming at a point between the head and 30 cm behind | Off-axis symmetry |
| Preferred vertical listening region | Around the design axis; at 3 m, ±25 cm correspond to ±4.8° | Within the small-variation region of the model |
Coherent vertical scale (at 3 m distance):
- ±25 cm → small-variation region of the model.
- 40–50 cm → still relatively close to the axis, but may already produce changes in the response around 4–5 kHz.
- ±70 cm → clearly visible variation.
- ±1.1 m → approaching ±20°, the region where the dip associated with the mid-tweeter notch begins to become significant.
What to avoid
- Do not lower the cabinet "so the tweeter aims at the ear": the design axis is the tweeter-midwoofer junction, not the center of the tweeter.
- Do not separate the cabinets to the classic equilateral triangle (30°): the model predicts 4–6 dB less treble energy at that angle.
- Do not tilt the cabinet forward or backward: the baffle is designed vertical; tilting it changes the relative vertical angles between drivers.
- Do not obstruct the tweeter-ear path with armrests, low reflective tables or high backrests between cabinets.
- Keep listening vertically reasonably close to the design axis: displacements of 40–50 cm correspond approximately to 7.6–9.5° at 3 m and can modify the response around 4–5 kHz. PENDING MEASUREMENT
Practical verification
- Measure the height of the tweeter-midwoofer junction in the finished cabinet.
- Measure the height of your ears while seated at the listening point.
- Adjust chair or stand until they coincide.
- With 3 m distance, separate the tweeters 2.2–2.8 m (20–25° per side); 2.4–2.6 m correspond to 22–23.5° as the central working zone.
- Apply slight toe-in until the axis of each cabinet aims at a point between your head and 30 cm behind.
- Verify there are no obstacles between tweeters and ears.
7. Evidence classification and validation protocol
CONFIRMED
Values of the five components, parallel topology (C1 + R2 in series, L4 in shunt), physical geometry of the assembly (dy and physical position of the geometric centers of the three drivers on the baffle) and acoustic offsets adopted in the model. Also that certain .frd/.zma files were used as input data.
PREDICTION / SIMULATED
Everything LspCAD produces from those files: transfer functions, on-axis response, resulting impedance, phase and modeled directivity. The polar maps (Figures 6, 7 and 8) are the graphical representation of the predicted directivity, not a confirmation of the physical cabinet.
CALCULATED
Physical separation between geometric centers of the drivers, geometric angles at 3 m, vertical displacements, geometric cancellation conditions of the two notches, required power under explicit hypotheses (working sensitivity of 89 dB/W/m, free field, 3 m) and associated arithmetic.
INFERENCE
Choice of 20–25° per side as the preferred listening zone; listening height at the tweeter-midwoofer junction; convenience of slight toe-in; practical consequences derived from the model. Also the interpretation of the 4–5 kHz residual, the reading of the off-axis blotch at 1 kHz and the characterization of the expected behavior of the ensemble with valve stages.
PENDING MEASUREMENT
Real sensitivity, exact Zmin, nominal impedance of the finished cabinet, exact phase, THD at 80–95 dB, thermal compression, maximum clean SPL, real directivity, real in-room response, real baffle step. In particular:
- The crossover simulation does not demonstrate that the midwoofer reproduces 95 dB peak with low distortion — excursion, THD and compression are not modeled.
- The real baffle step of the cabinet can introduce an imbalance below 300 Hz that the simulation does not reflect.
- The coincidence between the acoustic offsets adopted in the model and the effective offsets of the physical units must be verified by measurement.
- The model EPDR (>≈3.5 Ω) must be verified from the measured impedance and phase of the finished cabinet.
DO NOT DECIDE YET
Changes whose direction depends on data that does not yet exist. Any decision here without measuring is speculation:
- Tweeter R1 (attenuation or level adjustment).
- Change of L3 (for example to 2.0–2.2 mH).
- Change of C1 (reduction towards 27–22 µF or another variation).
- Modification of R2.
- Any component presented as a sonic improvement without verification.
- Driver replacement.
Freeze of the reference model — MR-A-01
Crossover A v2.4 is frozen as Reference Model MR-A-01. The freeze is not limited to the five crossover values: it covers all elements that, if modified, invalidate the comparison between prediction and subsequent measurement.
Frozen elements:
- LspCAD version and exact build.
.frdfiles used: name, date, origin and SHA-256 checksum of each..zmafiles used: name, date, origin and SHA-256 checksum of each.- Assumed geometry: positions and separations between geometric centers.
- Adopted acoustic offsets: the three values, with date of adoption.
- Crossover components: nominal values and real DCR introduced in the model.
- Simulation conditions: range, resolution and window type if applicable.
- Date and author of model closure.
If at any later time one of these elements must be modified, MR-A-01 is not edited. MR-A-02 is created and what changed and why is documented. Comparison with measurements is always made against the model that generated the prediction, not against a later version that already knows the result.
Interaction with the amplifier — separate later experiment
The amplifier Zout sweep is not part of the crossover validation. It is a later experiment, with its own design. First: cabinet → crossover → drivers → real response → real impedance. Later: amplifier Zout → interaction with Zspk(f). The two questions remain separate.
Objective: quantify ΔSPL(f) produced by the Zout,amp ↔ Zspk(f) interaction. Sweeps are performed with Zout = 0.1 / 0.5 / 1 / 2–3 Ω, keeping everything else constant. The search is not for "better sound"; it is to quantify the interaction. Consistent with the project's valve objective.
Interpretation and diagnosis criterion
When the physical measurement arrives, the comparison between prediction and measurement is evaluated on two orthogonal axes. They are not mixed.
Axis 1 — Comparison state
- CONFIRMED / COMPATIBLE
- DISCREPANCY
- INCOMPATIBLE / FALSIFICATION CANDIDATE
- NOT DECIDABLE
Axis 2 — Diagnosis
- SUFFICIENT MODEL — there was an applicable prediction and the result confirms.
- INSUFFICIENT MODEL — the model does not contain the evaluated phenomenon. Applicable to THD, compression and, in part, baffle step.
- EXCESSIVE UNCERTAINTY — the procedure does not allow discrimination.
- PENDING CAUSE — there is a discrepancy but the cause is not determined.
Four causes of discrepancy
- Definition error. The prediction was not formulated with sufficient precision to be compared.
- Input error. The prediction was well defined, but the model inputs do not represent the physical system.
- Model error. Correct inputs, phenomenon not contained.
- Experimental error. The measurement does not have sufficient resolution or is contaminated by the procedure.
The first question before any discrepancy is not "did the model fail?", but "was the prediction I am comparing against comparable?". The second is "what is the difference attributed to?".
Note on FALSIFIED. The word FALSIFIED is reserved for the case in which six conditions are simultaneously verified: the prediction was correctly defined, the model contains the evaluated phenomenon, the model inputs are correct, the experimental procedure is valid, the uncertainty is correctly estimated, and the discrepancy persists. In this project it will probably not be used; the operational vocabulary is CONFIRMED / DISCREPANCY / INCOMPATIBLE / NOT DECIDABLE, with causal diagnosis as accompaniment.
Validation protocol
Revised sequence. Order matters: first the real cabinet, then any adjustment.
- Measure impedance of each driver installed in its enclosure (woofer, midwoofer, tweeter). This is the base measurement, not the isolated T/S.
- Measure individual response of each way with its real physical geometry and current impedance. If deemed necessary, additional characterization of the driver parameters.
- Measure impedance of the original cabinet, if the old crossover still exists, to have a comparative reference.
- Build exactly Crossover A (5 components, C1 + R2 in series, L4 in shunt) with the flat vertical baffle.
- Measure the new cabinet with Crossover A in the same measurement configuration as the original, so as to compare: original → Crossover A → subsequent modifications.
- Determine the effective baffle step by combining near-field woofer measurement and gated far-field measurement, joining both curves by the appropriate measurement procedure. The direct difference between a 10 cm measurement and a 1 m measurement must not be interpreted as the baffle step: distance, acoustic geometry, relative contribution of each transducer, near-field/far-field conditions and interaction with the enclosure all change.
- Measure on-axis response at 1 m (with gating or appropriate technique), with the microphone at the tweeter-midwoofer junction.
- Measure THD of the 7.7 cm midwoofer at 90 dB and at 95 dB SPL measured at the reference position between 800 Hz and 4 kHz. With L4 in shunt, the midwoofer has a 2nd-order high-pass electrical network and should not excursion as much as with a 1st order. If THD exceeds 3% at 95 dB SPL measured at the reference position, reducing C1 from 33 µF towards 27–22 µF may be considered and the measurements repeated. The decision must not be taken on THD alone: the acoustic woofer–midwoofer sum, response and phase in the 500 Hz–1.5 kHz zone must be verified simultaneously, because the objective is not only to protect the driver but to preserve system integration.
- Measure horizontal directivity (0°, ±10°, ±20°, ±30°, ±45°, ±60°) to compare with the polar map of Figure 7.
- Measure vertical directivity (0°, ±5°, ±10°, ±20°, ±30°) to compare with the polar map of Figure 8 and check the position of the two notches.
- Measure overall THD at 80 dB, 90 dB and 95 dB SPL at the reference position.
- Measure at 3 m at the real listening position in the room of use.
- Only then, decide whether the crossover needs additional modification. Any change of L3, C1, R2 or R1 must be simulated with the real DCR of the new component and verified in response, impedance and woofer–midwoofer sum before being accepted.
On tweeter protection during the first tests: known and stable amplifier, verify absence of DC, initially minimum volume, first measurement at low level, progressive increase, THD/SPL monitoring, and avoid any power test before knowing the real response. INFERENCE
On the future driver change
Crossover A must not be designed with a future replacement of the midwoofer and tweeter already in mind. The correct sequence is:
- Phase 1 — original drivers: 27 cm paper+mica + 7.7 cm paper + 5 cm paper → Crossover A → measure → listen.
- Phase 2 — modernization (if decided): if the midwoofer and tweeter are replaced with modern equivalents, the crossover will have to be redone from the new measurements. It would not be valid to automatically keep 33 µF, 0.82 mH, 2.2 Ω, 2.70 µF: Re, Le, Fs, impedance, sensitivity, response and directivity would change.
The possible later transformation into a FAST-type system (27 cm + paper full-range of ~4") is a different line of research, not a modification of Crossover A. It must not be mixed into this document.
8. Conclusion
Crossover A is an experimental reference mature enough to move from simulation to construction. It is not yet a crossover validated on the physical units.
- Model on-axis response reasonably uniform in the main band (±0.7 to ±1 dB up to 4 kHz; ±1.5 to ±2 dB from 4 to 10 kHz).
- Woofer-midwoofer transition placed sufficiently low in the model to reduce the woofer contribution in the region where its directivity begins to narrow.
- Plausible tweeter integration with a 1st-order filter (C2 2.70 µF) and without a deliberate series attenuation resistor in the model.
- Midwoofer with a 2nd-order high-pass electrical network (C1 + R2 in series, L4 in shunt). In the model, the midwoofer uses its natural rolloff as the upper band limit, without an additional electrical low pass.
- Flat vertical baffle with the three drivers flush-mounted: the acoustic offsets adopted in the model (+0 mm tweeter, −5 mm midwoofer, −20 mm woofer relative to the baffle) are included in the simulation.
- Model horizontal directivity with ~2 dB loss at ±20° and ~4–6 dB at ±30° in 6–10 kHz, progressive narrowing above, consistent with the polar maps (Figures 6, 7 and 8).
- Model vertical directivity with small variation around the axis up to approximately ±25 cm at 3 m (±4.8°), with two cancellation notches consistent with physics: mid-tweeter at 4.5 kHz at ±25–30°, and woofer-mid at ~1 kHz at ±60–70° (the latter completely outside any real listening position).
- Model impedance with a provisional minimum close to 4.9 Ω and moderate phase; no simultaneous combination of very low impedance and high phase appears in the model. The estimated model EPDR (>≈3.5 Ω) must be verified from the measured impedance and phase of the finished cabinet.
Under the modeled scenario of 80 dB continuous + 15 dB crest at 3 m, and with the working sensitivity of ~89 dB/W/m: maintaining that SPL requires approximately 1.1 W of average power and peak capability of ~36 W in one cabinet (or ~18 W/channel in stereo with the ideal sum). These figures are a conditioned calculation, not a demonstrated property.
The relevant question is no longer a fine adjustment of C2 on the model. It is: what is the real sensitivity? The real impedance? How does the cabinet respond at 3 m in the room? How much THD does it produce at 90–95 dB SPL? Where is the real baffle step? Until those answers are obtained, Crossover A must be treated as a working reference, not as an acoustically validated design — and precisely for that reason it is worth building and measuring it.
The next step is no longer to keep optimizing the simulation: it is to build and measure MR-A-01.
