Upload Tube Plate Curves and Derive Equations

Improved vacuum tube models for SPICE simulations

Part i: Models and example

past Norman 50. Koren

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Updated March xx, 2003

On to Part two: Listings and PSpice operation | Norman Koren Vacuum tube audio page
Finding SPICE tube model parameters .

Much of the material in here originally appeared in Drinking glass Audio, Vol. 8, No. v, 1996, p. 18.

Every bit my chief hobby interest is now photography and I piece of work crazy long hours at Imatest, I won't have much time to update this article or respond difficult questions.

James E. Lanier's PSPICE Triode Calculator is a promising plan for finding tube model parameters. It's still under development; he plans to aggrandize it to include tetrodes and pentodes.

LTspice can obviously be used for these models.

SPICE , an electronic circuit simulation program originally developed at the University of California at Berkeley, has found broad credence in the electronics and semiconductor industries. It can perform highly authentic time and frequency domain analysis of circuitous analog and digital circuits (including harmonic and IM baloney). Several commercial versions of SPICE run on personal computers, most notably PSpice from OrCAD. The downloadable PSspice student version (version 9.1 at terminal expect) has express capabilities past standards of solid-country circuit design, but it tin be amazingly useful in simulating vacuum tube amplifiers, which tend to have fewer components. Information technology was used for all examples in this article. It'south difficult to find on the OrCAD website. I had to get to the CadencePCB abode page and click on All Downloads. Other well-known SPICE implementations include Electronics Workbench, 800-263-5552, and ICAP/4, from Intusoft, P.O Box 710 San Pedro, CA 90733-0710; 310-833-0710. Duncan Munro's listing of SPICE vendors may contain some subconscious treasures. WinSpice is a free Spice3F4 Port for Windows 95, 98, 2000 & NT. Very intriguing. It will simulate much larger circuits than evaluation PSpice.

SPICE contains born models for passive devices (resistors, capacitors, inductors, etc.) and for most active semiconductor devices (bipolar transistors, FETs, Op Amps, etc.), just none for vacuum tubes. SPICE models and can exist downloaded from manufacturer's Websites.

Equations for vacuum tubes

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Scott Reynolds^one and Marshall Leachⁱⁱ model vacuum tubes every bit voltage-controlled current sources whose output electric current is a weighted sum of controlling element voltages raised to the 3-halves power. The decision-making elements are unlike for triodes and pentodes. (Since the suppressor grid has picayune effect on the transfer characteristics, pentodes are modeled equally tetrodes.) The plate electric current equation for triodes is I_P = (E_{One thousand} +Due east_P / �) ^3/2 / k_G1      for E_G +East_P / � >= 0
= 0     otherwise.

(1)

The plate current equation for pentodes is

I_P = (2/k_G1 p)(E_G +East_G2 / �) ^3/2 arctan(East_P / m_VB )      for E_G +E_G2 / � >= 0
= 0     otherwise.

(2)

where I_P is plate current, Eastward_G is control filigree voltage, E_P is plate voltage, East_G2 is screen grid voltage (all voltages with respect to the cathode), � is the amplification cistron, and m_G1 is a cistron used to fit the equation to information. The pentode equation differs from the triode equation in that the screen grid replaces the plate as a decision-making element, and an arctangent term (from Scott Reynolds' model) is added to model a response bend "knee" whose location is proportional to k_VB . Equations (ane) and (2) are forms of the Langmuir-Childs law, which tin be derived from primal physics.³ Plate curves for a 12AX7 triode with � = 93 (below the specified value but a good overall fit to equation (1)) are illustrated below in Figure 1.

The screen grid current equation for pentodes is

I_G2 = (East_G +Eastward_G2 / �) ^3/2 / grand_G2      for Due east_Thousand +Eastward_G2 / � >= 0
= 0     otherwise.

(three)

where I_G2 is the screen grid current and yard_G2 is a constant similar in function to k_G1 .

Figure 1. 12AX7 plate curve from the onetime model.

The difficulty with equations (one) and (2) is that they presume that the filigree has perfect control over the plate current, i.eastward., that there is no leakage current. The real world is, alas, not so kind, and these equations give a poor approximate of plate current for large positive plate voltage and large negative grid voltage,^v region (A) in Effigy i, above. Compare this with region (A) in Effigy 2, below, which is derived from the new model but matches published curves^iv extremely well.

The modeling error would not be serious if tubes did not operate in the region of greatest fault. Unfortunately they do, as illustrated in Effigy i by a typical load line for a 12AX7 with a 350V plate supply and a 150k W plate resistor. The load line crosses region (A), and operation may extend into this region for large signals. This problem is exacerbated in class AB push button-pull amplifiers, where the operation of each tube traverses the region of worst mistake as it moves from conduction to cutoff and back. An accurate estimate of distortion in button-pull amplifiers is impossible without an improved model.

New equations

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The new equations for tube characteristics are phenomenological equations, that is, equations that model the behavior of physical phenomena using a reasonable number of parameters, just are not derived from fundamental physics. They have been designed so that plate current I_P > 0 whenever plate voltage Eastward_P > 0 (for triodes) or screen grid voltage E_G2 > 0 (for pentodes). Both equations take advantage of the fact that log(i+exp(x)) approaches x when x >> 1 and 0 when 10 << 1.

The new plate current equation for triodes is

East ₁ = (Due east_P / k_P ) log(1 + exp(chiliad_P (1/ � + E_Yard /sqrt(thousand_VB + Eastward_P ^two))))
I_P = (E _i ^X / k_{G 1})(1 + sgn(E ₁))

(4)

The signum function, sgn(x) = one for x >= 0; sgn(10) = -ane for ten < 0, is used to prevent current flow when Due east_ane < 0. The new plate current equation for pentodes is like to that of triodes:

E _ane = (East_G2 / thousand_P ) log(i + exp(k_P (1/ �+East_G / E_G2 )))
I_P = (E ₁ ^X / k_{G 1})(ane + sgn(E ₁)) arctan(E_P / k_VB )

(5)

Equation (4) reduces to equation (1) when Eastward_P ^two >> m_VB and k_P (i/ � + E_G /Due east_P ) >> 1. Similarly, equation (v) reduces to equation (2) when yard_P (ane/ � + E_G / E_G2 ) >> ane. We proceed to use equation (3) for pentode screen filigree current for 3 reasons: 1. Screen current is not every bit critical to the tube operation as plate current. ii. Good data on screen current is scarce. 3. The model should be kept as simple equally possible for use with evaluation version of PSpice.

Figure 2. 12AX7 plate curve from the new model.

SPICE language and PSpice

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The SPICE language is an industry standard for describing electronic circuits (called netlists) and instructions for modeling them. PSpice is a commercial implementation of SPICE that features convenient schematics entry through a graphic interface. PSpice actually consists of 3 separate programs: Schematics for data entry, PSpice for running the SPICE simulation, and Probe for displaying the results.

If you lot plan to modify or add tube models yous'll need to know a bit most the SPICE language. Appendix A has listings of several SPICE files. The commencement line of a SPICE file contains a title. Data on this line is ignored. The terminal line consists of the .END argument. Netlist data lines have the general format,

Part node_1 node_2 {boosted nodes if applicable} value(s) ; optional comments

Comments may appear on lines that get-go with an asterisk (*) or on data lines post-obit a semicolon (;). Continuation lines begin with a plus sign (+), except for equations, where the portion to the right of the equal sign (enclosed in braces {...}) is restricted to 1 line. This limitation can present problems with long equations. To get around information technology, Due east ₁ in Equations (4) and (5) has been modeled as a voltage-controlled voltage source that controls I_P , which is a voltage-controlled current source. This makes 2 relatively brusque equations out of one long one.

I strongly recommend the first-class textbook by Paul Due west. Tuinenga,^x "SPICE, A Guide to Excursion Simulation & Analysis using PSpice." Information technology contains detailed descriptions SPICE commands and models, including how to perform frequency-domain assay (.AC), time-domain assay (.TRAN) and Fourier analysis (.4), which produces a detailed harmonic baloney analysis. In the PSpice Schematics programme these instructions are generated by clicking on Analysis, Setupwardly..., and then working with the appropriate boxes.

To perform a SPICE simulation with the MicroSim evaluation package, run the Schematics program, so click on File, Open... to open a Schematics data file using the usual Windows navigation techniques. (You tin can also create a new schematic.) We'll call information technology filename.SCH in this example. You lot may edit and relieve information technology if you wish. To perform the PSpice simulation, click on Analysis, Simulate. This creates two SPICE language files: filename.CIR containing simulation instructions and filename.Net containing the netlist. These files are then read into the PSpice simulator, which writes text results (voltages, currents, etc.) to filename.OUT and graphics data to filename.DAT for display with Probe, which is run automatically if y'all have the .PROBE statement in the information file. Probe displays fourth dimension and/or frequency-domain plots of voltages at selected nodes or currents through selected components. The format of the display is quite versatile. If V(n) is the voltage at node n, VDB(n) is the voltage in dB and VP(n) is the stage. Current display is similarly flexible.

To use the Schematics program I had to create symbols for tubes: a hard task you lot tin can avert by downloading the models and following the instructions in Appendix B for loading the symbol and SPICE model libraries into PSpice.

Parameters

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Tabular array 1 gives parameters for some familiar tubes. These parameters are used in the tube model library listed in Appendix A3. The showtime six are equivalent to �, X, m_G1 , k_G2 , k_P , and g_VB in equations (3)-(5).

TUBE	MU	EX	KG1	KG2	KP	KVB	CCG	CPG	CCP	RGI
6DJ8	28	1.iii	330		320	300	2.3P	2.1P	0.7P	2k
6L6CG	viii.7	ane.35	1460	4500	48	12	14P	0.85P	12P	1k
12AX7	100	i.4	1060		600	300	2.3P	2.4P	0.9P	2k
12AU7	21.5	1.three	1180		84	300	2.3P	2.2P	ane.0P	2k
6550	seven.9	i.35	890	4800	60	24	14P	0.85P	12P	1k
KT88	8.viii	1.35	730	4200	32	sixteen	14P	0.85P	12P	1k

Table 1.  Spice parameters for some popular tube models

Near parameters in Table i tin can exist determined from published graphs and tables. Small-indicate triode information was obtained from Tom Mitchell'south book.⁴ EL34 information came from the Audiomatica Sofia web page. Other sources were the Parts Connexion itemize (i-800-769-0747), which has a large collection of reprints, old copies of the Sylvania and RCA tube manuals, and the pages of Drinking glass Sound. The best places to discover tube data on the Web are Duncan's Amp Pages and Frank's Electron tube Pages. Published values for inter-electrode capacitance e'er give better high frequency response than experiment. I measured the capacitance of a tube socket with 2 inch leads, and found it to be effectually 0.7pF for adjacent pins and 0.5pF for others. I added these capacitances to the published values. Withal, false frequency response may be somewhat optimistic. Tubes of different origin (e.k., Chinese, Russian, and sometime British 12AX7s) tin differ markedly in their inter-electrode capacitances. This may explain some of the sonic differences. Of course, real circuits have devious capacitance, and y'all must specify it if you want to include it in SPICE simulations.

Finding parameters by trial and mistake

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The parameters in Table 1 can be constitute by a methodical trial and error process. To utilize this procedure, the programs in Appendix A1 through A3 must be employed. Listings A1 and A2 produce plate characteristic curves for triodes and pentodes, respectively. Listing A3 is a portion of the tube library referenced past the .LIB statement in listings A1 and A2. Tubes are modeled as subcircuits, starting with .SUBCKT and ending with .ENDS. .SUBCKT is followed by the model proper noun and then the element node names. We have chosen the order the element nodes to be plate, control grid, cathode, and (in pentodes) screen grid.

To find the parameter values for a new tube, information technology is all-time to first with values for a like existing tube, except for amplification factor MU (�), which is by and large close to the manufacturer's specification. MU is (minus) the alter of plate voltage for a given change of grid voltage at constant plate current. This is illustrated by line segment BC in Figure 2, which is a adept choice for determining MU because it is located in a region of tube operation far from region (A), where effective MU is reduced. In this case, plate voltage increases by 100V when grid voltage is decreased by 1V while plate electric current remains constant at 1.9 mA, resulting in MU = 100.

To determine EX and KG1 (X and thousand_G1 ), run the appropriate plate curve program (Appendix A1 or A2), and observe plate current I(VP) using Probe. Adapt EX and KG1 so that curves for relatively low negative grid voltages (due east.g., Vg = 0 or -0.five for the 12AX7 in Figure two) friction match experimental data. Typical values of EX range from ane.three to 1.4. Line curvature increases with EX. The textbook value of 3/2 for EX is appropriate for equations (1) and (ii), where information technology gives a reasonable average representation of tube functioning, but is not really authentic in all regions. KG1 is inversely proportional to plate current for given filigree and plate voltages. Information technology ordinarily requires several runs to become a really good match for EX and KG1. MU may need to be adjusted slightly in the process.

For pentodes, the best estimates of MU, EX, and KG1 are obtained from triode-mode curves, i.e., curves taken with the screen grid continued to the plate. Such curves were bachelor for the pentodes listed in Table 1. It is very gratifying to see how parameters obtained from the triode curves (Effigy four) result in excellent fits to pentode and ultra-linear curves (Figures iii and 5). In running the pentode plate curve plan (Appendix A2), operating mode tin be set by adjusting parameter TRIMODE (0 for pentode, twoscore for ultra-linear (UL), and 100 for triode). VG2NOM (quiescent screen voltage) must also exist set appropriately.

KG2 is inversely proportional to pentode screen grid current (I(VG2) in Appendix A2) for given command and screen filigree voltages. Curves for pentode screen grid electric current are rarely published, but screen grid current is usually included in tables of typical tube operation. Information technology is adequate to match a point or two from these tables. KG2 does not need to be estimated with great accuracy to obtain skilful results in SPICE simulations.

KP (k_P ) dominates the behavior of the new model in region (A), which is characterized past large negative grid voltage, large plate voltage, and low plate current. Plate electric current is inversely proportional to KP in this region. Determining KP for a given tube is done entirely by trial-and-error. Triode-mode curves must exist used to obtain an accurate gauge of KP for pentodes because published pentode curves tend to have bereft resolution in region (A).

KVB (one thousand_VB ) relates to the "human knee" of the feature curves, and is defined differently in the triode and pentode equations. For pentodes, the knee is proportional to KVB, and is near visible in the pentode-way curves (Figure 3 for the 6550). Equation (five) does not requite an authentic judge of the knee for all levels of grid voltage, E_G . Fortunately, this is not a serious limitation because load lines for practical designs laissez passer close to the knee joint for E₁₀₀₀ = 0. (Otherwise there would exist a serious impedance mismatch.) The location of the knee for E_G = 0 was used to determine KVB in Tabular array 1. For triodes, the knee is proportional to the foursquare root of KVB, and is only apparent when the tube is operated with positive filigree voltage. Triode curves for positive grid voltage are published infrequently, for case, the 12AU7 in the Sylvania tube transmission.

Figure three. Excursion for obtaining triode characteristic curves.

RGI is the filigree-to-cathode resistance that controls grid current when E_G > 0. (No filigree electric current flows during normal operation, when Eastward_G < 0.) The numbers in Tabular array 1 are rough estimates based on measurements of similar tubes in onetime texts.³ Good up-to-appointment information is very scarce, and would be most welcome. Grid current flows in class AB₂ button-pull amplifiers, simply doesn't demand to be modeled precisely considering it does not contribute to the output signal. It should, still, exist modeled well enough to determine if the commuter tubes can supply the necessary current. Grid current presents a special problem in capacitively-coupled circuits: Since it only flows in one management, information technology charges the coupling capacitor, driving the tube closer to cutoff. This effect does not appear in SPICE small signal analysis or in transient (.TRAN) solutions for a single cycle of the input waveform: Many cycles are required. This effect tin be very audibly jarring.

Plate curves

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Effigy four. Excursion for obtaining triode characteristic curves.

Plate curves (plate electric current as a role of plate voltage for a set up of filigree voltages) may exist obtained by running i of four files in the tube models file, which can exist downloaded past shift-clicking on Tubemods.zip. Schematics for Triotest.sch and Pent_P.sch are shown on the right.

1. Triotest.sch  Figs. 2, three.  Triode curves.
2. Pent_P.sch  Figs. 4, 5.  Pentode curves in pentode mode (screen filigree at a fixed voltage). VG2NOM should be set to the fixed screen voltage used in the data sheet.  EVALUE E2 aspect EXPR is prepare to V(%IN+, %IN-)*1+V(1P)*0 (could be simply V(%IN+, %IN-) ).
3. Pent_TR  Fig. half-dozen.  Pentode curves in triode mode (screen grid continued to plate). VG2NOM is non used. EVALUE E2 attribute EXPR should exist set to V(%IN+, %IN-)*.0+V(1P)*1 (or just V(1P) ) .
4. Pent_UL.sch  Fig. 7.  Pentode curves in Ultra-Linear (UL) mode (screen filigree on 40% output transformer tap). VG2NOM should exist set to the quiescent plate voltage. EVALUE E2 attribute EXPR should exist set to V(%IN+, %IN-)*.4+V(1P)*.six . Ultra-Linear way is a compromise betwixt pentode and triode mode that shares some of the all-time attributes of both: much lower output impedance than pentode fashion and much greater power output than triode style.

Command files and netlists for these files, likewise equally a earlier versions written in SPICE language, are shown in Appendices A1 and A2. Boosted instructions on using these files are well-nigh the stop of Part 2. Pentode, triode, and UL mode plots for the GE 6550A are shown below. The 6550A data sail is available from Frank'south electron tube pages. Information technology's gratifying to see the splendid understanding with information in all three modes.

Figure v. 6550A Pentode fashion plate curves.

Figure half-dozen. 6550A Pentode, Triode mode plate curves.

Figure vii. 6550A Pentode, Ultra-Linear (UL) mode plate curves.

Output transformers

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Output transformers take traditionally been surrounded by an aura of mystery, and hard data has been hard to observe. Plitron Manufacturing Inc. (601 Magnetic Drive #8, Toronto, Ontario, Canada M3J3J2, 416-667-9914) has improved this situation in a new line of toroidal output transformers that have an unusually complete set of specifications.⁹ They have also published an splendid book, "Transformers and Tubes in Power Amplifiers", by Menno Vanderveen, that describes these specs in particular.

Toroidal transformers take much lower leakage flux than traditional "EI" transformers (so-named after their core geometry). This results in an extremely big bandwidth. Their simply drawback is that their extremely depression magnetic excursion reluctance makes information technology necessary to balance the dc current in the two haves of the principal winding extra intendance. Table ii gives parameters for the PAT-4006-CFB output transformer relevant to SPICE simulation. The PAT-4006-CFB is a semi-custom version of the 100W PAT-4006, available on special order, designed for four 6550 or similar tubes in push button-pull-parallel. It has a 2 kohm master winding and 2 center-tapped secondary windings: a v ohm winding for the speaker and a 20 ohm winding for feedback.

PARAMETER	SYMBOL	VALUE
Total primary inductance	LP	392.5H
Master leakage inductance	LSP	0.972mH
Quality cistron = LP / LSP	Q	403600
Ultra-linear tap		40%
Turns ratio	NP /NS	20
Constructive master capacitance	CIP	342pF
Total main resistance	RIP	56 ohms
Full secondary resistance	RIS	0.one ohms

Tabular array 2. Parameters of the Plitron PAT-4006-CFB output transformer

To develop the SPICE model (Appendix A3), the center-tapped chief winding with ultra-linear taps is divided into four mutually-coupled segments that take {0.3, 0.2, 0.2, 0.three} of the total number of windings. The inductance of each segment is proportional to the square of the number of windings: {.09LP, .04LP, .04LP, .09LP} = {35.325H, 15.7H, xv.7H, 35.325H}. The ratio of primary to secondary inductance is (N_P / N_S )^two. The transformer's coefficient of common coupling, K_ALL , is entered into the SPICE data file:

K_ALL = sqrt(1-1/Q) ~= 1-1/(twoQ)   (The approximation holds for large Q.)

(6)

The primary leakage inductance, L_SP , should non be entered into the SPICE model. Its furnishings are calculated from K_ALL . Similarly, the full main inductance, L_P , is not entered. The effective primary capacitance, C_IP , is inserted between the stop terminals of the primary winding. The SPICE model of the PAT-4006-CFB in Appendix A3 matches Plitron's published data very closely. Primary and secondary resistances accept been omitted for the sake of simplicity (to avoid bumping into the limits of the PSpice evaluation package) and because they have very little effect on performance: They are only about 2.5% of their respective impedances. They can be easily added if required.

Example: The original PAS preamplifier

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Figure eight. Original PAS-three line amplifier schematic diagram.

Effigy ix. Original PAS-three line amplifier frequency response at start gain stage plate (3P)
and output (LINE_OUT). Generated by Probe.

The frequency reponse at the output meets the twenty-20,000 Hz �1dB specification with no problem, but in that location is a huge 0.five Hz tiptop at the first gain phase plate. Altough this peak is well outside the range of hearing it caused definite audible issues, specially on records, where the rotational frequency at 33.3 RPM is-- y'all guessed it-- almost exactly 0.5 Hz. It was a sort of grindy audio-- possibly an intermodulation distortion component. A redesign, discussed in Feedback and Allegiance and SPICE and the fine art of preamplifier design, fixed it beautifully. Listings and excerpts from the output files are in Appendix A4 in part two.

Output files PASorgTC.cir and PASorgTC.cyberspace were generated past schematics. Output file PASorgTC.out was generated by PSpice. Many of the lines in PASorgTC.cir are generated from Schematics by clicking on Analysis, Setup..., and then working with the appropriate boxes. .LIB is followed by the name of the library file that contains subcircuits referenced in the program. .PROBE instructs the program to generate data for the PROBE program, which displays graphs of time and/or frequency domain signals at each node. .ac calls for an ac (frequency-domain) analysis, i.due east., a frequency sweep with 20 points per decade from 0.01 Hz to 1 MHz. If nowadays, .TRAN calls for a transient (time-domain) analysis, which is required if a Fourier analysis is to be performed.

Appendix A4C shows some of the results of running PSpice, including the dc voltages at each node, the currents fatigued by the two voltage sources, and the full power consumption. The first tube is labelled TU3 considering TU1 and TU2 were in the phono preamplifier. For example, the plates of TU3 and TU4 are at 168 and 196 volts-- about where they should be (a fiddling over half the supply voltage). A Fourier analysis tin be performed for time domain simulations.

Lessons

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Audio myths die hard, just several wither under the brilliant light of SPICE simulation. Feedback loops, which generate plenty of controversy in audio circles, are well-suited for SPICE analysis. We can only touch them here- I discuss them in detail in Feedback and Fidelity.

Permit A be the open-loop (non-feedback) gain of an amplifier. Allow B be the fraction of the output voltage that the feedback circuit subtracts from the input. The closed-loop gain (with feedback) of the amplifier is

G = A/(1+AB)

(7)

T = AB is called loop proceeds. A 180 caste stage shift in open-loop gain A at any frequency where T > ane will cause oscillation. An RC network has a maximum phase shift of 90 degrees at frequencies well beyond its corner frequency (i/two p RC).

For a feedback loop to be stable, rolloff at both low and loftier frequencies must exist dominated by a unmarried RC network (known to the mathematically literate as a pole on the complex plane) at frequencies where T > 1. Instabilities (near-oscillation situations) announced equally peaks or irregularities in the frequency response curve. Such instabilities are shockingly common, even in very expensive high-terminate amplifiers. In Stereophile equipment reviews, they appear as supersonic peaks of up to 3dB between 50 and 150kHz in frequency response curves measured with 8 ohm resistive loads.⁶ In a particularly amusing case, an $eighteen,990 amplifier with such a top received a mixed review, drawing an angry long-winded response explaining how every detail of the setup (down to the power cord) had to be perfect for these incredible amplifiers to sound decent. Ridiculous! (Information technology was a Jadis; I didn't want to mention the brand when I kickoff published this article.)

Response peaks are indicative of poor phase margin- the amount of additional phase shift that can be tolerated earlier oscillation begins. Since reactive loads tend to increase phase shift, poor stage margin can make an amplifier particularly sensitive to cables and loudspeakers. (Of form, some audiophiles might regard sensitivity to speaker cables as a virtue!) Stage margin should exist a standard specification in audio amplifiers: It is one of those seldom-mentioned factors that affect sonic quality. One of the reasons for the electric current popularity of triode amplifiers without feedback may be that they have no phase margin problem.

Some instability is inevitable when feedback is applied to tube amplifiers with output transformers because the high frequency rolloff of transformers is dominated by a complex pole pair. This necessitates some course of bounty, i.e., an RC network that rolls off response at frequencies lower than the transformer cutoff. The near mutual technique is to place a capacitor in parallel with the global feedback resistor. Beware of this technique: It works in the near-audio range, but SPICE shows that it can cause response irregularities at extremely high frequencies (likewise every bit inserting RF interference from speaker cables into the amplifier input).

A better approach to compensating feedback loops to add a capacitor betwixt the grid and plate of the tube to which the feedback returns (usually the input tube). The RC network formed by this capacitor and the input grid-finish resistor (a 2k to 10k resistor which should be added if not present) then becomes the dominant frequency-limiting network. The effective capacitance in this RC network is the sum of this capacitor and the tube inter-element capacitance multiplied past the proceeds of the stage (which is reduced by feedback). This is known equally the Miller effect. The proper capacitor value (a few picofarads) must be determined by trial-and-error: The calculations are not simple. This is where SPICE really shines. You tin endeavour a new capacitor value and examine its effects in about a infinitesimal.

Tube response extends well across 1MHz. The .AC sweep in SPICE makes information technology easy to observe extremes of frequency: I routinely examination 0.01Hz to 100MHz. To determine the correct compensation capacitor, observe the signals at the amplifier output and the plate of the input (feedback return) stage at frequencies upwards to 100MHz. Do this without and with capacitors across the load, which ever degrade stability. (Instabilities are visible as high frequency peaks.) Increasing the compensation capacitor rolls off high frequencies just increases stability. If your excursion and output transformer are well-designed, you should be able choose a value for the bounty capacitor that extends your amplifier'south frequency response well-beyond the limits of audibility (20kHz) while maintaining stability with the largest shunt capacitance likely to arise from cables and speakers. If you plan to use electrostatic speakers, y'all will probably need actress compensation capacitance. The final value must be determined experimentally, but it should be shut (within xxx%) to the SPICE-determined value.

Few of us have signal generators that become down to 0.5Hz, but SPICE shows upwardly a resonance at that frequency in the line phase of the venerable PAS^seven (40 dB or more at the input stage plate), which tin be quite serious because 0.5 Hz is close to the frequency of record warps. SPICE makes information technology easy to discover the response at intermediate proceeds stages besides as the output.

Using SPICE to investigate circuits has been nothing short of a revelation for me. I've been able to try out and rapidly debug new designs that I wouldn't accept otherwise risked, and I've answered many nagging questions. I hear a strong correlation between SPICE results (in areas such equally stability and RF susceptibility) and subjective sound quality. I fiund SPICE to be far more beneficial than "floobie dust" (extremely expensive premium components declared to produce magical results).

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Part ii: Listings and PSpice operation | Norman Koren Vacuum tube audio folio
Finding SPICE tube model parameters .

This folio created December 8, 2003

Images and text copyright (C) 2000-2012 by Norman Koren. Norman Koren lives in Boulder, Colorado. Since 2003 most of his time has been devoted to the development of Imatest. He has been involved with photography since 1964.  Designing vacuum tube audio amplifiers was his passion between about 1990 to 1998.

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Source: http://www.normankoren.com/Audio/Tubemodspice_article.html

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