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Stephen A. “Jack” Dyer’s final installment moves beyond SPICE simulations to bench measurements of one physical Philbrick (GAP/R) K2-W vacuum-tube operational amplifier. The results offer a useful check on the model and a set of concrete directions for further work—but they describe one unit under particular test conditions, not the performance of every K2-W.
What Part 6 adds to the K2-W model
In the preceding installment, Dyer compared LTspice simulations of a proposed K2-W model with values in the amplifier’s data bulletin and described the agreement as generally excellent. Part 6 changes the question: what does a physical K2-W do on the bench, and how might those measurements inform the model?
Dyer’s approach reflects a broader purpose of simulation: “one of the principal purposes of a model is to foster insight into what’s being modeled.” The measurements are not a comprehensive validation of the model. They provide observations from one amplifier, under configurations that vary by measurement, and a starting point for more detailed modeling and experiments.
How Dyer set up the measurements
Fixture and connections
The test platform used a 10 × 6 × 2 inch aluminum chassis and a plugboard. The chassis held an octal socket for the K2-W and banana-jack connections for the inputs, output, grounds, high-voltage rails, heater supply, voltage and supply-current measurements, and safety ground. The plugboard was 0.062-inch pad-per-hole FR-4, with input, output, and ground connections; selectable versions of the measurement circuits from the previous installment; a selectable output-load resistor; and test points.
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Dyer designed the chassis-and-plugboard arrangement to keep the setup organized, make it easier to switch between configurations, and reduce parasitic effects as practicable. That matters because the measured result can depend on the test circuit and its components, not just on the amplifier.
Equipment used
Dyer reports using two variable regulated Kepco KR4 M supplies capable of 300 V for the required positive and negative 300 V rails; a Heath 2718 variable supply for approximately 1.5 V input bias; an HP 33120A function/arbitrary waveform generator; a Siglent SDS 1202X-E oscilloscope; an Agilent U1272A true-RMS multimeter; a PrismSound dScope Series III audio analyzer; an HP 3575A gain-phase meter; a laptop interface; and the custom fixture. These are the instruments used in his measurements, not a recommendation that readers need these particular models.
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What unit was measured—and what the results can establish
The unit under test contained two GAP/R-labeled 12AX7 tubes. Dyer inferred from the labels that they had been hand-selected for high gain (high μ). He also checked resistor values that could be measured through external pins and found them within tolerance. Those observations apply to this specimen only; there was no multi-unit sample from which to estimate unit-to-unit variation.
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Open-loop gain is especially sensitive to measurement technique. Dyer warns that noise can be a major problem, particularly at the summing junction, and that both circuit configuration and component values affect the result. A simple measurement arrangement depends on assumptions; obtaining a precise value with low uncertainty can require arduous setup work. For this article’s purpose, he considered errors of several decibels acceptable.
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What the single K2-W measured on the bench
The measurements below are Stephen A. “Jack” Dyer’s 2025 results from one physical K2-W. Specifications are manufacturer figures quoted in his article from a K2-W data bulletin; the bulletin version is not dated there. The measured figures should be read with their test conditions, not as universal K2-W ratings.
| Measurement | Dyer’s result and conditions | Specification or comparison cited |
|---|---|---|
| Open-loop gain and frequency response | 60,000 open-loop gain at 2 Hz, measured from 2 Hz through 100 kHz with a 1 MΩ effective output load and measurement-network values R1 = 12 kΩ, R2 = 22 kΩ, R3 = 8.2 kΩ, and R4 = 2.2 kΩ. The response showed an approximately 50 Hz dominant pole; it first fell faster than 20 dB/decade after the pole, then declined at 20 dB/decade between 1 kHz and the 100 kHz measurement limit. Gain was about 4.6 dB at 100 kHz. | The quoted manufacturer figure was 15,000 dc open-loop gain. The different stated frequency and measurement conditions matter when comparing it with the 2 Hz bench result. |
| Output impedance | 0.17 Ω at 1 Hz, measured with feedback. | The article quotes less than 1 kΩ open loop and below 1 Ω fully fed back. |
| Voltage range | A 54 V voltage-range measurement with a 47 kΩ resistive load, using an inverting amplifier with Ri = 10 kΩ and Rf = 100 kΩ. | The quoted specification was −50 Vdc to +50 Vdc at the output and both inputs. The reported 54 V result is a measurement in the stated loaded inverting configuration; it should not be recast as a symmetric output-swing specification. |
| Supply current | After a 15-minute warmup, with the unit at quiescence in a gain −1 inverting configuration, Dyer measured 3.57 mA at +299.8 Vdc and 3.47 mA at −299.7 Vdc. | The quoted specification was 4.5 mA per rail at ±300 Vdc. |
| Step response | With gain −1, a 1 Vrms input for the response sequence, a 44.9 kΩ output load, and no input-offset compensation, Dyer measured a 1.6 μs rise time, a 1.6 μs fall time, and 47% overshoot. | The quoted specification was a 2 μs rise time. The overshoot is an important part of the measured response, not captured by rise time alone. |
| Frequency response | With the response dependent on Rb and, to some extent, Rload, the measured response was essentially flat at 0 dB below about 50 kHz, about +0.5 dB at 100 kHz, peaked near +6.6 dB around 280 kHz, and reached −3 dB near 440 kHz. | No directly comparable manufacturer value is stated for this response in the article. |
| Input-bias adjustment | A positive input bias of 1.41 V produced 0.0047 V at the output. | The manufacturer guidance quoted by Dyer was approximately 1.5 V positive input bias at balance. A version of the bulletin gave an adjustable 0.9–1.7 V range between pins 1 and 2. |
How to interpret the bench results
The open-loop gain is not a simple pass-or-fail comparison
The measured gain of 60,000 at 2 Hz is higher than the quoted 15,000 dc specification, but the figures are not a clean like-for-like test. One is a bench measurement at a stated frequency and with a particular network and effective load; the other is a manufacturer specification identified as dc open-loop gain. Dyer also emphasizes noise, summing-junction readings, circuit topology, and component values as sources of difficulty. The difference alone does not establish that either figure is wrong.
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Configuration matters across the measurements
The output-impedance result was taken with feedback, whereas the cited specification distinguishes open-loop from fully fed-back impedance. The voltage-range result came from a loaded inverting amplifier. The step-response test used a specific load and omitted input-offset compensation. Dyer also notes that the higher-frequency response depends on Rb and, to some extent, the output load. These conditions limit direct comparisons between measurements and prevent treating any one result as an unconditional property of every K2-W.
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The previous installment’s generally strong agreement between simulated values and data-bulletin specifications is a different comparison from Part 6’s physical measurements. Dyer reports similarities in character between some bench and simulation results, but the available measurements concern one specimen and use metric-specific setups. They are useful for asking what the model captures and what it omits, not for claiming a complete simulation-to-hardware validation.
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18 directions for further K2-W work
Dyer’s proposed projects span tube modeling, circuit analysis, and experiments with real amplifiers. They are suggestions for future work, not experiments completed in Part 6.
Improve the 12AX7 and K2-W models
- Add heater behavior. Extend the 12AX7 model or the complete K2-W model to include heater behavior.
- Make tube parameters heater-dependent. Investigate whether 12AX7 parameters such as μ should vary as functions of heater voltage.
- Model a high-μ 12AX7. Adjust other nonlinear-model parameters as needed and likely make measurements to characterize the tube.
- Improve positive grid-current behavior. Try a 12AX7 model that better describes positive grid current; Dyer describes Koren’s model as approximate and suggests considering Nakabayashi’s model.
- Model the offset-null bias source. Explain how nonzero internal resistance in the external input-offset-null bias source affects inverter frequency response and step response.
- Include resistor voltage coefficient. Model the voltage coefficient of resistance in the Allen-Bradley carbon-composition resistors used in the K2-W.
- Build a compact one-pole model. Develop a small model that includes input and output impedance, finite dc open-loop gain, input bias current, and input offset voltage, then compare it in SPICE with the Part 4 model.
Measure hardware and compare circuit behavior
- Build a test setup. Create a K2-W measurement fixture and make selected laboratory measurements.
- Try alternative components. Build a K2-W using precision metal-film resistors and Zener diodes in place of NE-2 neon lamps.
- Compare internal DC voltages. Compare SPICE predictions with measurements from a physical amplifier. Dyer flags that some units are radioactive through references cited in his article; that warning is not device-specific handling guidance, and it does not establish that every K2-W is radioactive.
- Measure common-mode rejection. Determine common-mode rejection ratio (CMRR) in simulation and on hardware, and compare the results with Pease’s estimate.
- Measure supply rejection. Determine power-supply rejection ratio (PSRR) in simulation and on hardware, comparing the results with Pease’s estimate.
- Build standard circuits. Use the Philbrick applications manual to implement configurations such as an inverter or integrator.
- Assemble a small analog computer. Gather multiple K2-W units and two 300 Vdc supplies for the project.
Explore internal circuit topology
- Use a small-signal gm model. Create a small-signal transconductance equivalent-circuit model for the 12AX7s and compare its simulated performance with published K2-W specifications.
- Make the differential pair symmetric. Evaluate a symmetric version of the K2-W differential pair in SPICE.
- Replace the tail resistor. Substitute a vacuum-tube constant-current sink for the differential-pair tail resistor, focusing especially on PSRR and CMRR.
- Analyze the second stage. Compare open-loop gain and frequency response for the common-cathode second stage with and without its positive-feedback loop.
Why these proposals matter
The projects turn the bench results into questions that can be tested: whether tube heater conditions or tube selection should change model parameters; how real component behavior affects frequency and transient response; and how internal circuit changes alter gain, CMRR, or PSRR. Some projects require a physical K2-W and suitable high-voltage laboratory equipment, while others can be explored in simulation. The central opportunity is to connect circuit-level explanations to measurements without treating one specimen as a population-wide standard.
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