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Plate Resistance
On Jun 3, 10:39*am, Richard Clark wrote:
On Thu, 3 Jun 2010 04:59:24 -0700 (PDT), Keith Dysart wrote: But what exactly do you mean by 'real'? R=V/I? R=deltaV/deltaI? Heat is dissipated? Hi Keith, As demonstrated by Walt's data. 73's Richard Clark, KB7QHC Richard, you ask me where to begin. Well, I begin with Terman, where I quote him in Chapter 19, Sec 19.3, in Reflections 2. Since attachments are prohibited in this forum I'm going to try to copy Sec 19.3 here, which explains in detail why plate resistance Rpd is dissipative, while Rp is non-dissipative--it explains the difference between the two. In addition, I don't believe the diode is a correct model for describing the operation of a Class B or C amplifier. Now the quote: Sec 19.3 Analysis of the Class C Amplifier The following discussion of the Class C amplifier, which reveals why the portion of the source resistance related to the characteristics of the load line is non-dissipative, is based on statements appearing in Terman’s Radio Engineers Handbook, 1943 ed., Page 445, and on Terman’s example of Class C amplifier design data appearing on Page 449. Because the arguments presented in Terman’s statements are vital to understanding the concept under discussion, I quote them here for convenience: (Parentheses and emphasis mine) 1. The average of the pulses of current flowing to an electrode represents the direct current drawn by that electrode. 2. The power input to the plate electrode of the tube at any instant is the product of plate-supply voltage and instantaneous plate current. 3. The corresponding power (Pd) lost at the plate is the product of instantaneous plate-cathode voltage and instantaneous plate current. 4. The difference between the two quantities obtained from items 2 and 3 represents the useful output at the moment. 5. The average input, output, and loss are obtained by averaging the instantaneous powers. 6. The efficiency is the ratio of average output to average input and is commonly of the order of 60 to 80 percent. 7. The efficiency is high in a Class C amplifier because current is permitted to flow only when most of the plate-supply voltage is used as voltage drop across the tuned load circuit RL, and only a small fraction is wasted as voltage drop (across Rpd) at the plate electrode of the tube. Based on these statements the discussion and the data in Terman’s example that follow explain why the amplifier can deliver power with efficiencies greater than 50 percent while conjugately matched to its load, a condition that is widely disputed because of the incorrect assumptions concerning Class B and C amplifier operation as noted above. The terminology and data in the example are Terman’s, but I have added one calculation to Terman’s data to emphasize a parameter that is vital to understanding how a conjugate match can exist when the efficiency is greater than 50 percent. That parameter is dissipative plate resistance Rpd. (As stated earlier, dissipative resistance Rpd should not be confused with non-dissipative plate resistance Rp of amplifiers operating in Class A, derived from the expression Rp = delta Ep/delta Ip.) It is evident from Terman that the power supplied to the amplifier by the DC power supply goes to only two places, the RF power delivered to load resistance RL at the input of the pi-network, and the power dissipated as heat in dissipative plate resistance Rpd (again, not plate resistance Rp, which is totally irrelevant to obtaining a conjugate match at the output of Class B and C amplifiers). In other words, the output power equals the DC input power minus the power dissipated in resistance Rpd. We will now show why this two-way division of power occurs. First we calculate the value of Rpd from Terman’s data, as seen in line (9) in the example below. It is evident that when the DC input power minus the power dissipated in Rpd equals the power delivered to resistance RL at the input of the pi-network, there can be no significant dissipative resistance in the amplifier other than Rpd. The antenna effect from the tank circuit is so insignificant that dissipation due to radiation can be disregarded. If there were any significant dissipative resistance in addition to Rpd, the power delivered to the load plus the power dissipated in Rpd would be less than the DC input power, due to the power that would be dissipated in the additional resistance. This is an impossibility, confirmed by the data in Terman’s example, which is in accordance with the Law of Conservation of Energy. Therefore, we shall observe that the example confirms the total power taken from the power supply goes only to 1) the RF power delivered to the load RL, and 2) to the power dissipated as heat in Rpd, thus, proving there is no significant dissipative resistance in the Class C amplifier other than Rpd. Data from Terman’s example on Page 449 of Radio Engineers Handbook: (1) Eb = DC Source Voltage = 1000 v. (2) Emin = Eb - EL = 1000 - 850 = 150 v. [See Terman, Figs 76(a) & 76(b)] (3) Idc = DC Plate Current = 75.l ma. 0.0751a. (4) EL = Eb - Emin = 1000 -150 = 850 v. = Peak Fundamental AC Plate Voltage (5) I1 = Peak Fundamental AC Plate Current = 132.7 ma. 0.1327 a. (6) Pin = Eb x Idc = DC lnput Power = l000 x O.0751 = 75.l w. (7) Pout (Eb - Emin)/2 = ELI1/2 = Output Power Delivered to RL = [(1000 -150) x 0.1327]/2 = 56.4 w. (8) Pd = Pin - Pout = Power Dissipated in Dissipative Plate Resistance Rpd = 18.7 w, (9) Rpd = 18.7W/0.0751^2 = Dissipative Plate Resistance Rpd = 3315.6 ohms (10) RL = (Eb - Emin)/I1 = EL/I1 = Load Resistance = 850/0.137 = 6405 Ohms (6400 in Terman) (11) Plate Efficiency = Pout x 100/Pin = 56.4 x 100/75.1 = 75.1% Note that Terman doesn't even mention non-dissipative plate resistance Rp, and therefore it cannot be considered the source resistance. Note also in line (10) that RL is determined simply by the ratio of the fundamental RF AC voltage EL divided by the fundamental RF AC current I1, and therefore does not involve dissipation of any power. Thus RL is a non-dissipative resistance. (For more on non-dissipative resistance see Appendix 10.) Referring to the data in the example, observe again from line (10) that load resistance RL at the input of the pi-network tank circuit is determined by the ratio EL/I1. This is the Terman equation which, prior to the more-precise Chaffee Fourier Analysis, was used universally to determine the approximate value of the optimum load resistance RL. (When the Chaffee Analysis is used to determine RL. from a selected load line the value of plate current I1 is more precise than that obtained when using Terman’s equation, consequently requiring fewer empirical adjustments of the amplifier’s parameters to obtain the optimum value of RL.) Load resistance RL is proportional to the slope of the operating load line that allows all of the available integrated energy contained in the plate-current pulses to be transferred into the pi-network tank circuit. (For additional information concerning the load line see Sec 19.3a below.) Therefore, the pi-network must be designed to provide the equivalent optimum resistance RL looking into the input for whatever load terminates the output. The current pulses flowing into the network deliver bursts of electrical energy to the network periodically, in the same manner as the spring-loaded escapement mechanism in the pendulum clock delivers mechanical energy periodically to the swing of the pendulum. In a similar manner, after each plate current pulse enters the pi-network tank curcuit, the flywheel effect of the resonant tank circuit stores the electromagnetic energy delivered by the current pulse, and thus maintains a continuous sinusoidal flow of current throughout the tank, in the same manner as the pendulum swings continuously and periodically after each thrust from the escapement mechanism. The continuous swing of the pendulum results from the inertia of the weight at the end of the pendulum, due to the energy stored in the weight. The path inscribed by the motion of the pendulum is a sine wave, the same as at the output of the amplifier. We will continue the discussion of the flywheel effect in the tank circuit with a more in- depth examination later. Let us now consider the dissipative plate resistance Rpd, which provides the evidence that the DC input power to the Class C amplifier goes only to the load RL and to dissipation as heat in Rpd (Again, not Rp.) With this evidence we will show how a conjugate match can exist at the output of the pi-network with efficiencies greater than 50 percent. In accordance with the Conjugate Matching Theorem and the Maximum Power-transfer Theorem, it is well understood that a conjugate match exists whenever all available power from a linear source is being delivered to the load. Further, by definition, RL is the load resistance at the tank input determined by the characteristics of the load line that permits delivery of all the available power from the source into the tank. This is why RL is called the optimum load resistance. Thus, from the data in Terman’s example, which shows that after accounting for the power dissipated in Rpd, all the power remaining is the available power, which is delivered to RL and thence to the load at the output of the pi-network. Therefore, because all available deliverable power is being delivered to the load, we have a conjugate match by definition. In the following Sec 4 we will show how efficiencies greater than 50 percent are achieved in Class C amplifiers operating into the conjugate match. Walt, W2DU |
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Plate Resistance
On Thu, 3 Jun 2010 12:08:42 -0700 (PDT), walt wrote:
Data from Terman’s example on Page 449 of Radio Engineers Handbook: (1) Eb = DC Source Voltage = 1000 v. From your own data Eb = DC Source Voltage = 800 v. (2) Emin = Eb - EL = 1000 - 850 = 150 v. [See Terman, Figs 76(a) & 76(b)] You do not supply context for me to apply to your data. (3) Idc = DC Plate Current = 75.l ma. 0.0751a. Idc = 260mA (4) EL = Eb - Emin = 1000 -150 = 850 v. = Peak Fundamental AC Plate Voltage You do not supply your minimum nor maximum plate voltage swing. (5) I1 = Peak Fundamental AC Plate Current = 132.7 ma. 0.1327 a. You do not supply your peak AC Plate current. (6) Pin = Eb x Idc = DC lnput Power = l000 x O.0751 = 75.l w. Pin = 208W (7) Pout (Eb - Emin)/2 = ELI1/2 = Output Power Delivered to RL = [(1000 -150) x 0.1327]/2 = 56.4 w. You report Pout, but we cannot use this formula for lack of data. Pout = 100W (8) Pd = Pin - Pout = Power Dissipated in Dissipative Plate Resistance Rpd = 18.7 w, From your report of Pin and Pout: Pd = 108W (9) Rpd = 18.7W/0.0751^2 = Dissipative Plate Resistance Rpd = 3315.6 ohms From what is reported by you: Rpd = 108W/(.260mA)² Rpd = 1597 Ohms (10) RL = (Eb - Emin)/I1 = EL/I1 = Load Resistance = 850/0.137 = 6405 Ohms (6400 in Terman) You do not report Emin but you report Load Resistance RL = 50 Ohms (11) Plate Efficiency = Pout x 100/Pin = 56.4 x 100/75.1 = 75.1% Plate Efficiency = 48% By all reckoning according to your reference from Terman, using what you report, it appears that you have exhibited a Conjugate basis Z match as you claim, and that the plate Rpd by the same reckoning is the same as we formerly arrived at Rp. It would appear that over the course of some dozen years between publications that Terman simplified the term Rpd to Rp which, according to you, is not found in your volume, and as such this migration of terms seems logical by the numbers agreeing in both volumes for different labels. Inasmuch as Rpd does not appear in Terman's later work, nor in any of the Tube specifications since that era, Rpd appears to be an orphan. You report your own Rp (now Rpd) or its equivalent by resistor substitution (a valid determination) to be on order of 1400 Ohms. This conforms closely to the value found above, and the data reported by RCA for Rp in a design of similar characteristics. The range of possible values taken from RCA: 900 Ohms to 1500 Ohms. Taking your low, the high from my range, and the higher computed through your supplied data using Terman's formula, the average is 1500 Ohms with a variation of roughly 6% which is about the limits of superlative accuracy for conventional bench equipment. What this means is that all three values are identical on the basis of accumulation of error. Having said that, this is not the end of analysis. However, at the first pass your data has demonstrated that the Plate serves as a real resistor dissipating half of the available power being supplied to a load that is conjugately matched. The only difference is that you state as much, but dismiss the plate dissipation as being a real resistor. Perhaps I mis-state you. If not, I take issue with that and ask once again, as this perception is unique to your hypothesis, do you have data that differentiates the resistance of steel absorbing and dissipating the impact of the electron stream as being different from carbon absorbing and dissipating the impact of the electron stream? Would it serve to replace the steel plate with a graphite one like the 845 (similar to the GM-70)? When I review the spec sheets for this tube, it reports an Rp of 1700 Ohms - hardly remarkable at 100 more Ohms than the computation above. Of course, there are compounding application differences, but still, graphite plates or steel don't seem to force a new conclusion. Materials don't seem to be an issue. Certainly the mechanisms of resistance differ in the kinetics of speed, but not in the product of heat. To my knowledge, no authority bases the concept of resistance upon the speed of the electron, but rather in the kinetics of its collision. 73's Richard Clark, KB7QHC |
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Plate Resistance
On Jun 3, 8:14*pm, Richard Clark wrote:
On Thu, 3 Jun 2010 12:08:42 -0700 (PDT), walt wrote: Data from Terman’s example on Page 449 of Radio Engineers Handbook: (1) Eb = DC Source Voltage = 1000 v. From your own data Eb = DC Source Voltage = 800 v.(2) Emin = Eb - EL = 1000 - 850 = 150 v. [See Terman, Figs 76(a) & 76(b)] You do not supply context for me to apply to your data.(3) Idc = DC Plate Current = 75.l ma. 0.0751a. Idc = 260mA (4) EL = Eb - Emin = 1000 -150 = 850 v. = Peak Fundamental AC Plate Voltage You do not supply your minimum nor maximum plate voltage swing.(5) I1 = Peak Fundamental AC Plate Current = 132.7 ma. 0.1327 a. You do not supply your peak AC Plate current.(6) Pin = Eb x Idc = DC lnput Power = l000 x O.0751 = 75.l w. Pin = 208W (7) Pout (Eb - Emin)/2 = ELI1/2 = Output Power Delivered to RL = [(1000 -150) x 0.1327]/2 = 56.4 w. You report Pout, but we cannot use this formula for lack of data. Pout = 100W(8) Pd = Pin - Pout = Power Dissipated in Dissipative Plate Resistance Rpd = 18.7 w, From your report of Pin and Pout: Pd = 108W(9) Rpd = 18.7W/0.0751^2 = Dissipative Plate Resistance Rpd = 3315.6 ohms From what is reported by you: Rpd = 108W/(.260mA)² Rpd = 1597 Ohms(10) RL = (Eb - Emin)/I1 = EL/I1 = Load Resistance = 850/0.137 = 6405 Ohms (6400 in Terman) You do not report Emin but you report Load Resistance RL = 50 Ohms(11) Plate Efficiency = Pout x 100/Pin = 56.4 x 100/75..1 = 75.1% Plate Efficiency = 48% By all reckoning according to your reference from Terman, using what you report, it appears that you have exhibited a Conjugate basis Z match as you claim, and that the plate Rpd by the same reckoning is the same as we formerly arrived at Rp. *It would appear that over the course of some dozen years between publications that Terman simplified the term Rpd to Rp which, according to you, is not found in your volume, and as such this migration of terms seems logical by the numbers agreeing in both volumes for different labels. *Inasmuch as Rpd does not appear in Terman's later work, nor in any of the Tube specifications since that era, Rpd appears to be an orphan. You report your own Rp (now Rpd) or its equivalent by resistor substitution (a valid determination) to be on order of 1400 Ohms. This conforms closely to the value found above, and the data reported by RCA for Rp in a design of similar characteristics. *The range of possible values taken from RCA: 900 Ohms to 1500 Ohms. Taking your low, the high from my range, and the higher computed through your supplied data using Terman's formula, the average is 1500 Ohms with a variation of roughly 6% which is about the limits of superlative accuracy for conventional bench equipment. *What this means is that all three values are identical on the basis of accumulation of error. Having said that, this is not the end of analysis. *However, at the first pass your data has demonstrated that the Plate serves as a real resistor dissipating half of the available power being supplied to a load that is conjugately matched. * The only difference is that you state as much, but dismiss the plate dissipation as being a real resistor. *Perhaps I mis-state you. *If not, I take issue with that and ask once again, as this perception is unique to your hypothesis, do you have data that differentiates the resistance of steel absorbing and dissipating the impact of the electron stream as being different from carbon absorbing and dissipating the impact of the electron stream? Would it serve to replace the steel plate with a graphite one like the 845 (similar to the GM-70)? *When I review the spec sheets for this tube, it reports an Rp of 1700 Ohms - hardly remarkable at 100 more Ohms than the computation above. *Of course, there are compounding application differences, but still, graphite plates or steel don't seem to force a new conclusion. *Materials don't seem to be an issue. Certainly the mechanisms of resistance differ in the kinetics of speed, but not in the product of heat. *To my knowledge, no authority bases the concept of resistance upon the speed of the electron, but rather in the kinetics of its collision. 73's Richard Clark, KB7QHC Richard, I'm totally shocked by what I've read above. I can't believe it! I can't believe you've distorted what I've written in my last post above to the extent that I can't possibly clarify or correct it--it's more than just misunderstanding. In addition, it's totally misleading to other readers of this thread, and makes me appear as a moron and an idiot. Sorry, Richard, I'm through with this thread. There's nothing I can do now to fix the situation. Walt, W2DU |
#4
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Plate Resistance
On Thu, 3 Jun 2010 18:15:12 -0700 (PDT), walt wrote:
I can't believe you've distorted what I've written in my last post Hi Walt, Can you give an example? 73's Richard Clark, KB7QHC |
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