Push-Pull Output Transformers - Part III, The Final Countdown:

Discussion in 'Amateur Radio Amplifiers' started by KD2NCU, Sep 28, 2017.

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  1. WA1GFZ

    WA1GFZ Ham Member QRZ Page

    OH I agree many T3 configurations have saturation issues because they are not balanced like T2. So WTH wind your output transformer balanced like T2 so problem is solved without adding more hardware that trashes the high end.
  2. ON4LDY

    ON4LDY QRZ Member

    I have read this discussion with a real interest.
    Now thta everybody has expresse his opinion on the subject, I would be very interested to read how a real exemple comes up.

    For instance :
    knwoing the frequency, the ouput power, the transistor,

    a) what core should be use for the bifilar trnasformer
    b) how to calculate the losses in the core if there is nearly no B field in it
    c) for what leakage inductance are we looking for
    d) how to calculate the number of turn to be winded
    c) ....

    answering all this questions with the corresponding physical expalnation is the key: go from the theory to the real practice.

    I propose this example to start :

    frequency : 30 MHz
    output power : 1.25 kW
    transistor : nxp 1k25

    who is candidate ?
  3. KD2NCU

    KD2NCU Ham Member QRZ Page

    Hello ON4LDY
    I think you are asking for someone to work through an entire example showing how to apply all this to a real problem which I will be happy to do.
    I need to ask you some questions first.
    If you've been following this all the way, you've seen there has been some nastiness on this thread. Now if you are genuinely interested I'd be very happy to work through an example for you. Please assure me that your motive here is learning and that you are not another troll looking for a battle or looking to try to prove me wrong with junk science. If your motive is genuine, then tell me a little about your background so I know what level to start and what tools I can use that you will be familiar with. IE; are you an electrical engineering graduate? If not, no problem, it just tells me where I need to start and I will be more careful to explain things fully rather than take it for granted that you know something that you might not have had formal training in.
    You may respond to me via private message or email if you prefer. Click on my QRZ Page in my icon at left and it should take you to my profile where you should be able see my email address and you should also be able to send me a private message by going to your profile page and clicking on conversations.
    Also, please send me your email address via private message.
  4. ON4LDY

    ON4LDY QRZ Member


    Im very serious, I'll send you an email...
  5. WA1GFZ

    WA1GFZ Ham Member QRZ Page

    ON4LDY You want to stay below 200g at the lowest operating frequency The wire should be sized to carry the current you are running. Calculate the flux density on 1 winding at the operating voltage so the FET saturation voltage just adds to margin. A 300 watt amplifier will have about 1 amp peak offset current so maybe a bigger device can just be scaled as a starting point. If the core gets hot add more turns or get a bigger core. Finally look at your second harmonic output (ON9CVD advice) This is a good indication of operating status. -30dBc or better is a good target. I'm using similar size and type of core as W6PQL, type 43 in my case. Check for temperature rise, my case my cores run stone cold 160 through 6 meters. Some of the cables warm up just a bit after a long AM transmission. Good luck with your project. I would use a pair of those type devices push pull parallel if I was starting over. The advantage of using two FETs is you can cascade two 1:2 transformers in the output and eliminate T2. A 1:3 transformer you will need the T2. Mark is the smart guy and I provided all my references that he can share. Helge's book talks about ferrite with some simple rule of thumb information.
  6. KD2NCU

    KD2NCU Ham Member QRZ Page

    Hello WA1GFZ & ON4LDY: Below is some additional analysis of what T2 brings to the table. I conclude that if the push pull amp is designed well with reasonably balanced and matched transistors, properly biased with only small DC drain/collector bias currents (biased just into class AB and not any more than necessary to eliminate crossover distortion) and the design of T3 is such that it has two or more turns on the primary winding, then the bifilar feed coil T2 brings nothing to the party and is of no use. If the circuit is poorly designed with excessive and unmatched collector/drain biased current that is forcing T3 to be larger than really necessary, then use of T2 can get T3 back down to the proper size but so could have designing the bias circuits and matching the transistors properly. In that case, T2 is a bandaid for a poor biasing and matching.
    Feel free to review the analysis below and provide feedback.

    What Does T2 Really Do For Us? - Some Truths, Some Myths:

    • This analysis looks into some of the statements that have been made regarding why T2 is sometimes used in addition to T3.
    • Statements have been made that using T2 rather than T3 alone, reduces the flux in T3, allows use of a smaller T3, reduces the risk of saturation of T3 and related claims.
    • If the transistors in a push pull output stage have been biased correctly and are reasonably well matched and the design of T3 calls for two or more turns on the primary, then T2 is not needed and brings nothing to the party and using T2 does not allow T3 to be smaller than if T2 were not used.
    • If however, the quiescent operating point collector/drain currents are not well balanced and one of the transistors has an abnormally large quiescent operating point collector/drain current unbalanced by the other transistor, then this creates a steady state DC flux in the core of T3. This alone will not cause the core to saturate but it leaves less headroom between this DC flux density and the core saturation flux density for the AC signal to operate without causing saturation. If the core has been oversized to compensate for this unbalanced DC flux, then the use of T2 can allow the core of T3 to be reduced back to its proper size. In this case, T2 is compensating for the poor design and transistor selection.
    • T2 does not reduce the risk of saturation of T3 due to unbalanced drive or other issues that result in the current and voltage pulses from one transistor being consistently larger than the current and voltage pulses from the other transistor. Unbalanced outputs from the transistors can still cause T3 core saturation even with the use of T2.
    Main Reason To Use T2:
    The main reason to use T2 is when operating at frequencies and impedances that would result in a T3 design with less than two turns on a center tapped primary winding. Two turns is the lowest practical number of turns that can be effectively center tapped whether using binocular cores or toroids. In this case, T2 provides the center tap and allows T3 to use a single turn on the primary winding if needed.

    Statements Made On This Forum About T2:

    1. “If the primary of T3 were center-tapped and its core could handle the DC current w/o saturating, T2 wouldn't be needed. IOW, T2 handles the DC current, and T3 handles the RF current. To prevent loading the output, the AC impedance of T2 will be much higher than that of T3.”
    2. “It's not so mysterious. Any current (AC or DC) causes lines of magnetic flux to be impressed into the medium. Ferrous media can accept a certain limit of AC+DC. By using a choke(s) to pass the DC current separately (decoupled from the AC path), the AC coupling device(s) can be smaller. It's that simple.”
    3. “The choke is used because in most cases if you feed the DC through the center tap of the output transformer the ferrite material will saturate. By providing a separate DC path to the output devices the common mode choke relives the additional stress.
    4. “The advantages of the use of separating the power feed through using T2, are that a smaller size T3 core can be used because of lower flux density and because the total number of windings can be less (e.g. only 1 winding for the primary and 4 for the secondary vs 2 windings for the primary and 8 for the secondary).”
    • The above statements make it sound like there are large DC currents in addition to large AC currents present in a push pull circuit and that by separating the two so that T3 only handles AC currents then T3 can be smaller with less risk of saturation.
    • In reality, there should be very little true DC current flowing anywhere in either circuit and there should be virtually no DC flux in the core of T3. The only true DC current that flows in either circuit is what should be a very small DC bias current flowing into both transistor’s collectors/drains. This current should be essentially insignificant compared to actual signal currents. If the transistors are well matched and properly biased, these two bias currents should be small, nearly equal, and will cause equal and opposite DC flux in the core of T3 in Circuit A thus tending to cancel. Other than these small bias currents, there are no other DC currents flowing anywhere in either circuit. The actual signal currents and voltages are all half sine pulses. Therefore, there should be very little true DC flux in T3 of Circuit A. If there is any significant DC flux in the core of T3 it is because of poor design, poor bias, or poorly matched transistors.
    • The first three statements above are only true if the circuit has been designed and built poorly forcing T3 to be much larger than it needs to be. In this situation, the use of T2 may allow a smaller T3 but so would proper design of the circuit to start with. If the circuit is well designed and balanced to start with, then T2 will not allow the use of a smaller T3 and the above statements are false.
    • Statement 4 above is false in almost all cases.
    Questions to be Answered:
    Does using T2 in circuit B allow use of a smaller core for T3?​
    Does using T2 in circuit B reduce the risk of saturating T3?
    Does using T2 allow T3 to handle only AC current while T2 handles the DC current?
    Does using T2 reduce the flux in the final transformer?

    Effect of DC Collector/Drain Bias Current:
    • Both transistors will require a small collector/drain DC bias current. If the circuit is designed properly, this bias current will be very small compared to the collector/drain currents that flow at full signal power.
    • If the transistors are well matched and biased uniformly, then the DC flux from the DC bias currents tends to cancel one another in T3.
    • To the extent the transistors are mismatched or have an unbalanced bias, there can be a DC flux bias in the core. This alone does not cause saturation but does bias the core to some extent toward saturation eating into the headroom between operating flux density and saturation flux density. IE; there is no longer 50% margin between the peak flux density and the saturation flux density.
    • In Circuit A:, T3 is the recipient of this bias. In Circuit B:, T2 is the recipient and T3 does not receive any appreciable DC bias due to transistor biasing.
    Other DC Current?
    Other than the two small DC bias currents, there is no real DC current flowing anywhere. All other currents are in the form of half sine pulses of current that are stitched together to form a sinewave.​

    Analyze AC Operation of Circuit A:
    Calculate Turns Ratio: Each transistor wants to see 12.5 ohms when conducting.
    The load impedance is 200 ohms. So the impedance ratio of T3 is 12.5/200 or 1:16. ​
    So the effective turns ratio is 1:4.
    Since only one half of the primary is used at a time, the secondary must have 4X the turns of the active half of the primary or 4 turns.

    Calculate Currents:
    Secondary RMS current = sqrt(800 Watts / 200 ohms) = 2 amps.
    Primary RMS current = 8 amps.​
    Each transistor sees a peak current of 8 x 1.414 = 11.3 amps.
    Each transistor alternately “pulls” a half sine pulse of current with a peak of 11.3 amps.
    This current pulse is “pulled” directly through ½ of the primary winding and off of the DC bus.
    Other than what should be a small DC bias current, there is no actual steady state DC current flowing anywhere in T3 or anywhere else in the circuit. All signal currents are half sine pulses of current.
    Calculate Voltages: Secondary RMS voltage = sqrt(800 Watts x 200 ohms) = 400 Volts rms.
    Secondary peak voltage = 565.6 volts peak.
    Primary Peak Voltage = 565.6 / 4 = 141.4 volts peak across each single turn when that turn’s transistor is conducting.​
    During the half cycle when one turn is conducting, the RMS voltage will be 141.4 / 1.414 = 100 Volts RMS but this is occurring only half the time or with a 50% duty cycle on each turn.

    Flux Density:
    We’ve assumed that the selection of the core and number of turns on the primary results in a peak flux density (β) that is 67% of the saturation value of the core material.
    So now we know that 100 volts across 1 turn of the primary coil using the chosen core and at the given frequency will not saturate the core and will leave 50% headroom.
    Similarly, we know that 400 volts across 4 turns of the output winding will not saturate the core and will leave 50% headroom.
    Analyze AC Operation of Circuit B:

    • Based on previous analysis, T2 provides an extra 1:4 impedance transformation or an effective turns ratio of 1:2.
    • To maintain the same match between 12.5 ohms and 200 ohms, T3 must provide the remaining 1:4 impedance ratio or 1:2 turns ratio instead of 1:4 turns ratio in Circuit A. The total impedance transformation is still 1:16 as in Circuit A.
    Currents: Each transistor sees 11.3 amps peak or 8 amps RMS just as in Circuit A.
    • Based on previous analysis of T2, the primary of T3 will see one half of this or 4 amps RMS into 50 ohms or 200 volts.
    • The turns ratio of T3 is 1:2 so the secondary of T3 provides 2 amps into 200 ohms or 800 watts just like in circuit A.
    • It was shown previously that the currents in this circuit are also all half sine pulses of current. There is no actual constant DC current flowing anywhere in this circuit other than the previously mentioned small DC collector/drain bias current.
    Compare Peak Flux Density in the Two Circuits:
    • The equation for peak flux density in a coil core is given below.
    • The RMS voltage of the output is 400 volts in both circuits and the frequency is the same in both circuits.
    • If we assume use of the same core and same number of secondary turns for the moment, the peak flux density will be the same in both cases at 67% of the saturation value.
    • Looking at the equation below, if we try to make the area of the core smaller in either case, the peak flux density increases risking core saturation.
    • If we reduce the number of turns on the secondary, the peak flux density increases risking core saturation.
    • It’s already looking like T2 does not let us reduce the size of the core or reduce the secondary turns.
    Design of T3 for Circuit B:
    • T3 needs a turns ratio of 1:2. A design which satisfies the turns ratio of 1:2 would be 4 turns on the secondary and 2 turns on the primary.
    • We just verified that looking at the secondary winding of T3 indicates that this produces the same peak flux density (β) as the original T3 in Circuit A.
    Let’s check the primary windings of T3.

    Primary windings:
    Core area and frequency are the same in both cases.
    • First case: Vrms = 100 volts across 1 turn.
    • Second case: Vrms = 200 volts across 2 turns
    • The core area and the frequency are the same in both cases, and the ratio of Vrms to turns is the same in both cases, so Bmax is the same in both cases. Looking at the primary windings we get the same answer that the peak flux density (β) is the same in both circuits.
    So comparing final designs of the output transformers:
    Important Observations:
    1. In both cases we’re outputting 800 watts into 200 ohms so in both cases the RMS current in the secondary winding of T3 is 2 amps and the RMS voltage is 400 volts.
    2. If we use the same core in both cases, the peak flux density (β) will be the same in both cases except for the effects of DC bias current. We only have 50% headroom in both cases and assuming we want to keep this headroom, we cannot go to a smaller core. T2 is not reducing the AC flux in T3 and is not allowing us to use a smaller core.
    3. The secondary windings are identical and carry the same current in both cases so T2 is not allowing us to reduce the secondary windings.
    4. The primary current in circuit B is ½ that of circuit A. However the duty cycle of circuit B primary coils is 100% compared to 50% in circuit A. So the RMS current in each turn is the same in both circuits. The conductor size of the primary cannot be reduced. T2 is not allowing us to reduce the size of the primary conductor.
    5. Primary current waveform: In both circuits, the current through the primary coils is half sine pulses alternating polarity as each transistor turns on and off. In circuit A on each half cycle we have a peak current of 11.3 amps through 1 turn on the primary. In circuit B on each half cycle we have a peak current of 5.65 amps through 2 turns. Ie we have the same driving force in units of amp turns or MMF in both cases.
    6. No significant actual DC current flows through the primary of T3 in either case unless there is poor design, poor biasing, or poorly matched transistors. In both cases, the main currents that flow are alternating polarity half sine pulses.
    So nothing in the AC operation of these circuits is changed by the presence of T2 that lets us go to a smaller core, less windings, or smaller windings.

    The only situation in which T2 lets us go to smaller transformer is if poor design, poor biasing, or poorly matched transistors have artificially driven us to use a T3 core in circuit A that is larger than it really needs to be. IE; T2 is acting as a bandaid for poor design and transistor matching and will allow us to get T3 back down to a normal size if poor design has caused us to use a larger core for T3 than should have been needed.

    Effect of the Bifilar Coil T2 on Tendency of T3 to Saturate Due To Imbalance:
    Both cases have the same peak flux density (β), and the same peak MMF. Both have current and voltage impressed on them by alternate transistors. The presence of T2 does not reduce the tendency of T3 to saturate due to transistor imbalance. During any one transistor’s conduction cycle, the current in T3’s primary is driven to one half the value of the transistor current. If there is imbalance in the conduction cycles of the two transistors, this imbalance will be translated directly to T3’s primary resulting in the integral of the voltage and current in one direction being unequal to the integral of voltage and current in the other direction. This means there is a DC component present in T3’s primary resulting in flux staircasing toward saturation until some other effect limits the current or until actual saturation occurs. There is no difference in the tendency of T3 to saturate due to unbalanced transistor output with or without the use of the bifilar coil.

    Tendency to Saturate T2’s Core Due To Imbalance:
    T2 itself has less of a tendency to saturate due to imbalance between the transistors because it splits the current from any one transistor into equal and opposite currents producing very little flux in the core. If Q1 conducts more than Q2, the two currents in the bifilar coil are smaller during Q1’s cycle but they are still predominantly equal and opposite, thus cancelling flux. During Q2’s cycle, the two currents are larger but still equal and opposite thus cancelling. So imbalance between the transistors does not tend to cause T2 to saturate.

    Summary of Effect of Using T2 vs T3 Alone;
    1. T2 does not allow for the reduction in size of T3 unless the DC collector/drain currents are grossly and excessively large and unbalanced due to poor design or very poorly matched transistors.
    2. T2 does not reduce the AC flux seen by T3. T3 sees the same peak AC flux density in both cases.
    3. T2 does not allow the use of less turns on T3. T3 requires the same number of turns in both cases.
    4. T2 does not reduce the tendency of T3 to saturate if there is imbalance in the conduction cycles of the two transistors. T3’s primary winding sees half sine current and voltage pulses of alternating polarity from alternate transistors in both cases. In addition, the MMF and the peak flux are the same in both cases so the tendency to saturate due to imbalance is the same in both cases.
    5. T2 does allow T3 to handle only AC currents. However, there should not be any significant true DC currents in either case unless the collector/drain bias currents are excessive and mismatched. Other than the DC collector/drain bias currents, there are no true DC currents anywhere in either circuit. The signal currents in T3 are alternating polarity half sine pulses of current in both cases.
    Can the transformer size be reduced by using 1 turn on the primary and 2 turns on the secondary?
    Probably not. Notice that if we cut the turns in half, the peak flux density (β) doubles and we saturate the core.
    Notice that using a smaller core with smaller cross section also increases the peak flux density.
    The only way to offset the effect of the smaller turns is to increase the core cross section.
    Also, reducing the turns on the primary reduces the inductance of the primary by the square of the change in turns and now the inductance of the primary will be too small and the primary will draw a large inductive current reducing the transfer of power to the secondary

    Can the transformer size be reduced by using 4 turns on the primary and 8 turns on the secondary which would allow us to cut the core cross section in half?

    Probably not. This will probably change the primary inductance too much. Besides, if we can do this when using T2 then we could have doubled the turns in the first case as well and reduced the core size. So if we can do this, it’s not because of the presence of T2.

    Two Turns is the Lower Practical Limit for a Center Tapped Primary
    Typical RF output transformers are designed such that the open circuit inductive impedance of the primary winding is 4x to 6x or so times the properly matched resistive load impedance that will be presented by the primary winding. So if the primary is to present 50 ohms resistive load impedance, the primary winding will be designed to present 200 to 300 ohms inductive impedance at the lowest frequency of use with the secondary open circuited. This sets the no load or magnetizing current of the primary winding. The penalty for making this inductance too large is higher resistance in the windings and higher leakage reactance which degrades high frequency performance.
    • At higher design frequencies, the absolute number of turns on the primary and secondary must decrease to keep the magnetizing inductance reasonable at 4x to 6x the impedance seen at the coil.
    • The lowest frequency of use will determine the required inductance of the primary winding.
    • The geometry and core will determine how many turns are required for a given primary inductance.
    • The impedance ratio will determine the turns on the secondary.
    • At some combination of frequency and core geometry, the number of turns on the primary drops to 2. That’s the lowest practical number of primary turns that can accept a center tap using binocular cores or toroids.
    • If using beads or binocular cores going below 2 turns splits the transformer in half and bad stuff happens. See below.
    • If using a toroid, a single turn with a center tap would have the center tap pointing inward toward the center of the core. Keeping this center tap centered is impractical.
    • So two turns is the practical lower limit on the number of turns on the primary if using a center tap.
    • With a single turn center tapped primary coil using binocular cores, when Q1 is on, the primary current goes through only one side of ferrites. The other side has no current in the primary and the ferrites are acting like rf chokes to the secondary coil creating series inductance in the secondary.
    • This makes two turns the lower practical limit on the primary winding.

    Flux Walking/Staircasing To Saturation:
    It is a phenomenon in certain circuits that can lead to unexpected saturation of a core.
    Example: In a push pull amplifier the voltage waveform across the primary of the output transformer is actually alternate voltage pulses from the two transistors. If these voltage pulses are not equal and opposite and therefore do not average to zero, then there is a net DC voltage component present which will make the flux in the core climb steadily until the current is limited by some other effect or until the core starts to saturate possibly blowing transistors.


    Oversizing the core does not stop this from happening. An imbalance or net DC will still cause the flux to staircase upward until some other nonlinearity or effect takes over or saturation occurs.

    The usual effect is that on one half cycle, the core begins to saturate and the current on that half cycle is excessively large. It may reach the point where this large current on one half cycle drops enough extra voltage somewhere in the circuit that the process becomes self limiting and an equilibrium point is reached, however, the current is unnecessarily high on one half cycle and that transistor will run hot as will the transformer. In addition, the waveforms are most likely distorted creating harmonics and distortion in the transmitted signal. The linear amplifier is no longer linear. There are ways to mitigate this effect that won’t be covered here.

    The T2/T3 configuration does not stop this from happening. If the transistors are not conducting equally there will be a DC offset even with T2 present.

    Attached Files:

  7. WA1GFZ

    WA1GFZ Ham Member QRZ Page

    Mark, Why did you use a 200 ohm load impedance? Also when the primary is 12.5 ohms each device is driving 6.25 ohms. It would be easier to understand if you used common voltages like 50 volts and 50 ohms for the load. Interesting read with flux transformers.
    Now throw in transmission line transformers. The (2 X 2) 1:2 transformer in my case is 4 turns of cable shield center tap DC fed with the 4 turns of center conductors boot strapped to generate a 1:4 impedance step up.
    I need to wrap my head around the flux walking. Think about it, no two FETs are perfectly matched. So I wonder if the offset energy is just coupled to the secondary as a voltage offset to reset the core on each cycle???
    I agree with your comment about the primary 2 turn minimum rather than 1 turn center tap but add that it also maintains a balance in the core just like when you use a T2 choke.
    Clean this up and you have a great QST or QEX article to flush all the crap science out there down the drain where it belongs. I waded threw a lot of it getting to my understanding and design. gfz
  8. KD2NCU

    KD2NCU Ham Member QRZ Page

    Good evening GFZ:
    1. No particular reason for the impedances chosen. I recently reviewed a couple of App Notes that used those same impedances, so, ...
    I can make the numbers say anything you want them to say. ;)
    2. I don't agree with the 6.25 ohm statement. Here's some analysis.

    Circuit A:
    In circuit A, when Q1 conducts, Q2 is an open circuit for all practical purposes and the lower one turn of T3 is just acting like a secondary winding that is open circuited. It will have a voltage induced into it by the upper turn but there’s no current in the lower turn. It’s just a coil of wire open circuited at one end flapping in the breeze. It’s contributing nothing to the secondary.

    So during Q1’s half cycle, the transistor is placing a peak voltage across the upper turn of about 141 volts. It’s just lonely Q1, a one turn primary, and a 4 turn secondary, so the turns ratio that Q1 sees is 1:4 so the secondary voltage is 566 volts peak or 400 volts RMS.

    Essentially we’re only ever using one primary turn at a time so it’s really a 1:4 transformer. We just keep switching which turn we use in order to reverse the polarity.

    Given the turns ratio of 1:4 the impedance ratio is 1:16. The load is 200 ohms so the transistor is looking into 200/16 = 12.5 ohms.

    You might want to say that the transistors are in parallel, which is technically true but they are never on at the same time. There is always only one primary turn with a driving current in it and always 4 secondary turns getting lit up by it.

    Looking at the currents, the peak load current will be 566 volts/200 ohms or 2.83 amps.

    This 2.83 amps is being driven solely by the one turn primary and one transistor so the primary current (as well as the transistor current) will be 2.83 x 4 = 11.31 amps peak.

    The transistor is seeing a 141 volt swing in voltage and a 11.31 amp swing in current during its cycle. By definition then, the transistor is looking into an impedance of 141 volts/11.31 amps = 12.5 ohms. The AC impedance is the change in voltage divided by the change in current during the conduction cycle.

    Circuit B:
    In the case of circuit B, the transistor places 141 volts across the upper coil. This induces 141 volts in the lower coil with the polarity shown which IS connected to the output transformer. So in this case, the output transformer primary sees 282 volts peak and the secondary sees 564 volts peak.

    The load current again is about 2.8 amps peak.
    The T3 primary current will then be 5.6 amps peak.

    The two currents in the windings of T2 are equal and opposite so the transistor current is twice the T3 primary current or about 11.2 amps just like in circuit A.

    During its active half cycle, the transistor sees a 141 volt swing and a 11.2 amp swing in current so the impedance it is looking into is 141 volts/ 11.2 amps or 12.5 ohms.

    3. Wrap head around flux walking: Well said! When first introduced to this concept, I really had trouble with it. Most explanations get into convoluted discussions about the BH curve, minor loops, minor offset loops, and no two descriptions of the phenomenon seemed to agree or use the same BH diagrams and it just gave me migraine headaches. Here's how the light finally came on for me. If one transistor is consistently conducting more than the other, then there is definitely a bit of DC offset. Once I quit thinking about the BH curves and just started thinking about forcing a DC voltage onto an inductor, the light finally came on. If I apply a DC voltage to a resistor in series with an ideal inductor, the current will start to rise and then will level off when the voltage drop across the resistor equals the DC supply voltage. The initial rise in current looks somewhat linear at first. If I use a smaller resistor, the current rises to a higher level before leveling off. If I use an even smaller resistor it rises even further before leveling off. Eventually, if I use a small enough resistor in series, the current will look like it is ramping up linearly for quite a while before leveling off at some huge value. Theoretically, if I made the resistor zero, the current would ramp up linearly forever.

    Once I make the resistor zero, it's just the dc supply and the inductor.
    The physics of the inductor is such that V = L di/dt. So if I force a constant voltage across the ideal inductor, the rate of change of current has to be constant as well meaning a ramp. In reality, we can never actually force a constant voltage across an inductor because the inductor always has some resistance. So if we put a constant DC voltage across a real inductor, the current starts to ramp but levels off once the voltage drop across the resistance equals the DC supply unless the inductor has a core in which case we might saturate the core before the current levels off.

    Back to transformers. If we apply a sinewave of voltage with a bit of a DC offset to a transformer primary winding so the sinewave is floating on some small DC level, we are essentially putting a DC voltage (in addition to the AC voltage) across the inductor that is the primary winding.
    So just like the example above, a DC current will flow (in addition to the AC current) and the DC current will start to ramp up just like the inductor example above. This DC current is driving the flux in the core upward.

    How far and how long will the DC current and flux ramp up? Just like the inductor example above, as the DC current ramps up, there is a voltage drop growing in the resistance of the transformer primary windings as well as anywhere else this current is flowing through.

    So what happens?
    1. If there is enough series resistance in the windings of the transformer and elsewhere, then this might level off without saturating. When the DC voltage drop in the windings and any other series resistance equals the DC offset in the applied voltage waveform, the current and flux stop growing just like the inductor example above. But we now have a DC bias flux in the core so our AC voltages and currents are taking the core closer to saturation now given this offset.

    2. If there is not enough series resistance to limit this effect, then the current and flux keep growing until the core just begins to saturate on one of the half cycles but not the other. This results in a larger current on that half cycle which drops even more voltage in the series resistance and maybe this now reaches equilibrium with the core going just into saturation on alternate half cycles and causing a little bit of signal distortion but everything continues to work. The core probably gets hot and so does one of the transistors.

    3. If the slight saturation did not drop enough voltage to limit the growth of the flux, now we go into hard saturation and burn stuff up.

    They call this flux walking or flux staircasing because I suppose on a micro level it occurs in steps as each new pulse comes through.

    Here's a very important point: This only happens when we are completely controlling the voltage across the inductor or transformer primary at all times. Ie; we are NEVER letting go of the inductor to let it reset the core on its own. If we were feeding the T3 primary with alternate polarity narrow pulses with a "rest period" between the pulses and we gave the inductor a current path to discharge, the inductor would "discharge" during these rest periods and the core would never flux walk. The problem with push pull linear amps is that we have to control or force a voltage across T3's primary at all times and it never gets a chance to discharge on its own.

    I've seen push pull switching power supplies that provide these rest periods between pulses and provide elaborate paths using diodes and extra windings and such to allow the core to reset during the rest period.

    There are a number of ways of dealing with this. One way is to put capacitors in series with T3's primary. You've probably seen this. I've not analyzed this approach but it bothers me a little bit and seems like nothing comes for free so I bet this practice has some downside to it. I've read a few other approaches. In the case of push pull switching circuits for power supplies, some designs actually monitor the peak current on each cycle of each transistor and in real time adjust the transistor drive to keep the two transistor outputs precisely balanced.

    Now there have to be millions of push pull amps out there that don't have any compensation whatsoever for this effect and they are not burning up. What explains this? I would say that in most cases, there is some offset but it is small due to good design and transistor matching so the resistance of the circuit is enough to limit this flux growth to an acceptable level.
    I would also think that there are scads of circuits that are just barely going into saturation and self limiting there so transformers are running hot as well as transistors, but not badly enough to burn stuff up.
    I would also bet that people have prototyped circuits, burned up T3 several times along with one transistor, then out of desperation screwed around empirically until they ended up with enough resistance somewhere to limit the effect to just hot transformers and transistors but no fire.

    4. Now throw in transmission line transformers.
    Do you have some diagrams you can send me? By now you can tell I'm a diagram kinda guy!o_O
    I do know a fair amount about TLT's but if there is a specific design you want me to look at send me a diagram. I think you have explained the design you are interested in above, and I'll see if I can follow the description, but a diagram would help.

  9. KD2NCU

    KD2NCU Ham Member QRZ Page

    Here's a very common application of using DC blocking capacitors C7 and C8 to keep any DC offset completely out of T3.
    Obviously, if T2 somehow kept DC out of T3 then these blocking capacitors would not be needed.
  10. ON4LDY

    ON4LDY QRZ Member


    tank you for your answer but is not exactly what i am focusing on and what I was expecting.
    May be i was not very clear but my question is only on the syzing of the bifilar core, the rest I can take care of it.
    I tell you what I think and may be you confirm or not.
    The core and the number of the turns must be such that it is equivalent to T3. The field in the T2 core must be very close to what it is happening in T3 Something else would lead to something inadequate or unefficient. T2 is there to create the a correct voltage in order to generate a current in T3 in the branch oposite to the active transistor.
    The question that I am asking to my self is : why is it not the case in the publication that I read on in the realization that I saw. The core of T2 looks always is smaller with number of turn not related with the number of turne of T3

    I repeate my questions with a clear focusing on T2

    a) what core should be use for the bifilar T2 trnasformer
    b) how to calculate the losses in the T2 core if there is nearly no B field in it
    c) for what leakage inductance in T2 are we looking for
    d) how to calculate the number of turn to be winded on T2

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