Headphone Amplifier Design and Experiment

 Headphone Amplifier Design & Experiment.

So far my circuit -

Headphone Amplifier V0.1

 

 

LM 741 OP Amp at Buffer Stage

The slew rate of the LM741 is limiting the amplifier to about 40Khz sinewave, at about 2 volts (peak) into a 33 ohm load. 

This finding ties in nicely with the theory which states - the maximum frequency of a sine wave (before Slew Induced Distortion) delivered at the output is limited by the OP Amp's ability to dump charge Q into a load.

 The 741's quoted slew rate is 0.5v/us, or 500v/sec.

Applying the accepted guide of ...  SR = Vp·2𝝅·f

and rearranging for frequency f gives ... f = SR/[2𝝅·Vp], 

that is ...

f = 500,000/[2*3.142*2] = 39,788Hz.

DC Voltage Offset

The unwanted (although non-audio affecting) DC offset at the output of the bi-polar transistor designed LM741 was reduced by applying two same-valued resistors both at the output, and at the V+ input terminal. This DC offset is caused by internal bipolar transistor bias currents - the effects of which are to produce undesirable DC input to the OP Amp. The OP Amp amplifier section also 'sees' this DC offset at the input and amplifies it. To overcome this problem, creating an equal quiescent DC bias voltage (thanks to these resistors) at both V- and V+ then cancels out the undesired effect, or at least minimises it.

The LM741 DC output offset was reduced to less than 2mV, typically around 1mV or less.

And the output across the 33Ω 'power' load, we have a DC offset of much less than 1mV .... excellent, typically 100uV or less.

LF411CN or TL071 at Buffer Stage

Replacing the LM741 with a JFET LF411CN or TL071 resulted in instability - overshoot on the application of a square wave. and sometimes uncontrollable amplifier oscillatons.

 

 

Strong overshoot of a 4Khz Square Wave

Somewhere within the circuit we have a situation where negative feedback from the effective loop gain '𝜷·A' had a near 180 degree phase reversal at approximately unity gain - which is undesirable. 

Without the 1.5nF loading capacitor, the gain with feedback takes the form:

Aᵥ = A/(1+𝜷·A)

where A = Open Loop Gain of the OP Amp,

and  𝜷 = the feedback ratio from an impedance network, but 𝜷 =1 (not proven here) in this voltage follower configuration.

Instability in the form of heavy overshoot and/or oscillations are likely if a near 180° phase shift in the loop gain term 𝜷·A occurs, ie as 𝜷·A → -1.

With the 1.5nF capacitor present, the expression in the denominator changes (this will be studied in another article), and I suspect enough additional phase shift occured which induced instabilty, hence overshoot to square waves and eventual oscillations. Not so with the LM741 OP Amp, but I did note the LM741 still exhibited small, but significant overshoot (fast dying oscillations) on the application of a square wave or pulse.

Removal of the High Pass Filtering 1.5nF Capacitor

Now, removing the 1.5nF capacitor (part of the high pass filtering at midstage) eliminated all instabilities, and now we have a stable headphone amplifier which can deliver (if needed) 500mW into either 33Ω or 8Ω.

 

Slight overshoot at 4Khz, but the amplifier is very stable.

With the LF411CN in place, the unwanted, but non-distructive DC voltage offsets at ... 

(a) First OP Amp buffer output < 1mV, 

(b) Voltage across 33Ω or 8Ω load, < 1mV.

The amp is able to deliver more than 500mW into 8Ω if the regulated voltages are raised above ±12v respectively.

Frequency response is better than 15Hz .. 100Khz  ±1dB for 'clean' sinusoidal waves.

 

V0.2 of the Headphone Amplifier. (Mono)

 

Unfinished article, subject to changes. 5/10/2020

Update: 9/10/2020. 17/11/2020.

Sony TC-K35 Cassette Deck

 Sony TC-K35

 

An ebay purchase, and was in very good condition. Barely any head wear.

Recalibrated the azimuth to my full track ABEX 10Khz reference tape. The difference between previous setting and the reference tape was very small - approximately 90° to 180° degrees at 10Khz.

I also have calibrated the outputs to be equal, and read Dolby Level on playback of a full track ant-audio.co.uk Dolby Level reference recording. Internal record levels (ie, tape sensitivity) calibrated to be equal for both L/R channels, and set to match TDK FE cassette tapes.

 

8/8/2020.

Shockley Equation Verification

The 1N4148 Diode 

and the 

Shockley Equation.

My next project will be to design from scratch, a functioning and reliable high fidelity stereo headphone amplifier. Although based on a well established Class A-B model, in this project I will seek to derive all the related equations myself. But first there is a matter of investigating the 1N4148 diode (as one example), and its V-I characteristic.

There must be several such suitable diodes I could use to control the biasing of the eventual Class A-B push-pull headphone amplifier.

Below is a table showing forward bias I-V measurements I took, the input voltages varied from 0.575v to 0.835v.

I (mA)	0.393	0.644	1.060	1.747	2.680	4.160	6.340	9.520	13.900	19.540	26.485	30.614
V (volts)	0.575	0.600	0.625	0.650	0.675	0.700	0.725	0.750	0.775	0.800	0.825	0.835

Basic Diode Action

Under forward bias configuration (as shown) the
width of the contact potential is narrowed as electron current
is swept across the junction.

William Shockley Equation

According to the Shockley Equation, the relationship between forward bias diode voltage and diode current for a PN junction diode is ...

Where I_O = reverse saturation current,  Io = 25*10^-9 for the IN4148
V_T= KT/q ... thermal equivalant of voltage, 
K = boltzmann constant, T = absolute temperature, q = electron charge.  
And at 20C V_T ~ 0.025v

n= ideality factor, 
n=1 for a perfect diode, but often n = 1.. 2.5

From my empirical results, I wanted to establish n, and by ignoring the '-1' term, and rearranging I obtain ...

For the 1N4148 data above, I calculated the mean value of  n, that is ...

n = 2.351 

(to 4 significant figures)

With that I plotted the data vs the Shockley Equation model .... 

The correlation was remarkably good, better than I had anticipated! 

Matsushita DC Motor

AN6652 Matsushita 
DC Motor Circuit Investigation,
but No Modification.

I have another identical Matsushita motor where I decided to examine the motor controller circuit - this time based on the (later?) AN6652.

Before I took the back off, I had to de-solder a tag which connected the metal casing to the ground point. The casing is now electrically neutral to both ground (or -ve) and +Vcc. If in doubt, I would suggest we do this before attaching a similar motor to any cassette deck.

The circuit above is essentially the same as in the previous AN6651 configuration, except for: a signal diode, C=22uF, and here R1, R2, and R3 all effectively form part of Rs. 

Rs = R3+R1||R2 (R2 effective).

18/05/2020.

External Motor Controller Experiment

An External Motor Controller Experiment

Revised 15th May 2020.
(Apologies for the continual editing, the blogger has so many HTML editor bugs)

Traditionally, a brush-type DC 12v motor for a cassette deck has its controller tucked inside the housing of the motor assembly.

I hope to experiment again using the Panasonic or Matsushita AN6651 controller, and applying it to a stripped-out Matsushita DC motor, that is - remove the internal circuit and attempt to control speed externally.

All internal motor control components have been removed.

The motor in question here has the following measured internal parameters at approximately 2400rpm when under loaded conditions within the Sansui SC-1330 during Playback.

Vm=6.71v, Ra=18Ω, Ia=68.5mA

Vm = voltage across the motor brush terminals,
Ra = internal armature resistance, measured before loading.
Ia = armature current at approximately 2400rpm, under 'Play' loading conditons.

The widely accepted mathematical model is shown below.

Ea = generated 'back' electromotive force 'EMF' induced into the armature windings by the fixed internal field magnet. Note that Ea ∝ armature speed n.

From which Kirchoff's Voltage Law applied to the circuit, we have Vm=Ea+Ia*Ra, and from this I deduce that back-emf generated at approximately 2400rpm is Ea ~ 5.38v 

The AN6651 Block Diagram

Turning attention now to the AN6651 ...

Note: a series of 40 (in parallel?) output transistors, these will effectively restore the working or optimal Vm voltage across the brushes of the motor.

And in circuit ...

For the AN6651, the value of K is 40, this appears to be linked to the number of output transistors. Seemingly, every controller of this type has a value for K? The value of Vref for the AN6651, is nominally 1.0 volts - according to the datasheet.

Another similar motor controller is the LA5586, I examined its datasheet. As usual, the guides are very poorly written, but I believe I have managed to decipher how to calculate both Rt and Rs so as to get my Matsushita, or another similar DC motor working under the LA5586, or the AN6651. 

Note: The expression (Is+Ia)/K in the circuit diagram above is a guide and parameter that I have to use - it's highlighted in the LA5586 datasheet. I will assume that this can be applied to the AN6651.

The journey to find Rs begins with a voltage loop equation (from the datasheet) relating system parameters, Kirchoff's Voltage Law here states ...  

Eo + Ia*Ra = Rt(Is(1+K)+Ia)/K + Vref

(Vm = voltage divider/comparitor section)
 

where Is = current through Rs. 

Substituting Vm for Eo + Ia*Ra

and solving for Is gives ...

Is = (1/K+1)(K/Rt*(Vm-Vref) - Ia)

and since Rs = Vref/Is,  

Rs can be found.

The datasheeet also suggests that I must assign Rt < K*Ra otherwise the system will become unstable.

In this case: Rt < 40*18Ω or < 720Ω. Okay, so I'll go for Rt=680Ω or lower (I have plenty in stock!)

Calculating Rs 

According to the expression for Is, and setting Rt=680Ω, 

I obtain ..

Is = (1/41)(40/680*(6.71-1)-0.0685) = 0.00652 A.

Is ~ 6.50mA

As Rs = Vref/Is, and Vref=1v (for this controller), then

Rs ~150Ω

Okay, so I'll try Rs = 47Ω + 200Ω(variable)  or better try 100Ω + 100Ω(variable)?

I'll also set Vcc=12v, note that Vcc=Vm+V4.  

==========================================================

After putting this circuit into practice, I modified the ability to alter Rs by introducing a 'coarse' and fine' speed trimmer resistor.

AN6651 based circuit soldered on to 'stripboard'

Later the circuit was electrically isolated, moved away from the transformer and secured into place using plastic ties.

The good news is the motor controller works!, however - at this time other thoughts cross my mind...

Temperature Coefficient of Resistance?
There is another issue for me to factor in - an increase in motor resistance Ra with temperature as the motor begins to heat up! That is - what is the coefficient of temperature of Ra, and will this upset the running speed over a period of time?

Will I have to position Rs close to the motor so the ratio of Ra/Rs is maintained?, much like the wheatstone bridge principle. It doesn't appear so, but I'm not 100% certain.

Assuming Rs and the motor are not 'in close contact' - will I need to allow time for the motor to 'warm up' to calibrate its true stable speed? If so, then for how long?

Incidentally, I measured Ra ('cold'): 17.9Ω, and Ra (after 30 minutes of 100mA loading): 18.8Ω.

Findings, so far ...

Speed Calibration Using 3000Hz Test Tape

With a 3Khz test tape positioned at the middle of the tape,  I calibrated the tape speed.

At a 'cold' start up, I calibrated using my 'fine tune' trimmer for maximum stability, then noted the playback speed ... Playback frequency = 3000Hz ± 1, 2, 3Hz 

After 5, 10, and 15 minutes of running the motor in, so that Ra's temperature was effectively raised ... Playback frequency = 3000Hz ± 3,4,5,6 Hz. The median deviation in frequency was around 4Hz .. 5Hz. I didn't note if the motor was running fast or slow - just the steady difference.

Sometimes it would 'run' to about ± 8Hz/10Hz, but these were possibly down to wow and flutter wobbles, and that I was examining the deviations of speed for a longer period of time? The speed would soon run back to a stable difference of 3,4,5,6 Hz etc.

========================================

Later: I finally decided to have the motor running permantently, much like the Aiwa AD-F770. And after 20 minutes of warm up time, I aligned the speed of the motor to register 3000Hz ± 1,2,3 Hz etc. I am able to set the motor speed to playback exactly 3000Hz, but it is unrealistic to expect this to remain rigid throughout various tape positions. So far the Sansui SC-1330 and its 'new' motor/controller configuration is remaining within a ±0.5% tolerance of its motor speed target.   

Time will tell if having an 'external' ('offline') AN6651 motor controller works effectively?

Please note: Tape speed at the beginning, the middle, and at the end of a tape differ slightly. Calibrating at somewhere about the centre of the cassette tape is said to reduce overall errors. (I can't qualify the apparent speed variation from beginning to the end of a tape - it's based on general forum consensuses)

Power Consumption: The AN6651 is rated at 1.3 watts (1300mW) heatsinked on to conventional circuit board. At average use, the power consumed is largely through the output transistor stages which are employed to regulate Vm, and since Eo = Vm-Ia*Ra, then Eo and hence speed n is regulated. 

An estimation of the power dissipated by the AN6651 is approximately V4*Ia, or (12-6.71)*0.0685, that is 0.362w, and adding internal biasing into consideration, probably around 0.4W or 400mW.

Note: This article is finished, but subject to the correction of minor mistakes or amendments.
 

2/11/2020 - small addition.

***I tend to write in this www.blogger.com directly online, and not offline. The reason? - the blogger editor is full of software bugs, if I prepare and later paste a document into the blogger editor it is filled with formatting errors and colour quirks, hence it is easier to write this way.***
.......

Experiment only, not Recommended.

Aiwa AD-F770 Capstan Motor

Regulator Replacement
(Just an Experiment)

Quite recently I decided to return the original troublesome '12v 2400rpm CCW' capstan motor back to the Aiwa F770 cassette deck for further investigation. Previously, I had replaced it with a probable Chinese copy of a Mabuchi DC motor. 

I chanced my luck and replaced two internal electrolyic capacitors hoping that the onboard regulator would work correctly. It wasn't long before the transport (playback) speed of the deck began to show the same subtle variability as before - the very reason I replaced it!

Backplate of flywheel - note the regulator circuit inside the motor circuit.

Front view

I again examined the original regulator circuit and ordered some 2SA684 (PNP) transistors. There were also zener diodes in this old regulator circuit, and I soon realised that I may need to replace all the components to be sure this would work again!? 

While I waited for the transistors to arrive, I mulled over the idea of designing a simple, but highly stable voltage regulator, centered around the popular National LM317.    

The original voltage regulator sits on the back of the dc motor.

Desoldering the old regulator circuit from the original motor I needed to find out what voltage the motor operates at the 'correct speed'? - the result was approximately 5.5v. With this in mind, I built and tested a circuit to deliver trimmable motor voltages between 4.7 and 6.0 volts, approximately.

The LM317 Based Voltage Regulator Circuit:

Note: A tantalum capacitor was initially added across effective-R2 as recommended by National Semiconductor (to reduce ripple effect), but this made the output slightly unstable - approximate deviation of about ± 2% when stable, so I removed it. I also added a small 10uF tantalum capacitor at the output with the addition of a protection diode across the LM317, and another across the motor. Probably not needed, but I put them there.

 
Note that as Vout = 1.25(1+R2/R1), the effective value of R2 is given by ....

R2= 1200(1200+Rv)/[2400+Rv]

Where trimmer Rv is approximately 2600Ω (by measurement), at maximum setting.

Simulating the 'new' regulator circuit.

Using stripboard ("veroboard"?), the said circuit was then assembled, and tested again. Later the circuit was encased, and secured into a simple plastic insulating case. All connections to the F770 were resumed.

The motor needed to be returned to its casing - all previous regulator components (except an 8-pin chip) were removed, and a new lead was soldered in.

Correct Playback Speed Alignment: Using a full track width reference tape, and an external digital source I aligned the motor speed by listening to the two sine waves 'beating' together until there is zero, or a very slow drift between the two.  (17/04/2020)

 *************

18/4/2020 ... This morning I ran some more tapes through the F770, and again the speed began to wobble slightly - it's very subtle, but noticeable over a period of about 15 minutes.  It's so subtle that you can be forgiven for thinking "did I hear that pitch wobble?...".

Conclusion: Now that the regulator issue may have been eliminated, the motor is probably partially worn? I suspect brush-commutator contact is partially failing?

***************

New Mabuchi Motor Fitted EG-510ED-2B2 (18/4/2020)
After realising that the old motor was showing its age, I decided to discard with the idea of a new stable regulator - it worked well, but the motor wasn't behaving itself! 

I've now fitted a genuine Mabuchi motor into the Aiwa AD-F770, after putting the parts back together, the deck is now working very well.

The Aiwa supplies 12.5v to the dc motor, and the motor draws an average of about 58mA when in play mode, and a little less when just running free.  Of interest too, when the old motor was in circuit, it drew only around 40mA - perhaps there was an issue within the old motor were brush/commutator contacts were more resistive due to dirty or worn contacts?

The old motor dissasembled is shown below.

From close-up inspection, I could see why the motor was varying its speed - the commutator brushes had partially broken. There was also a small build up of carbon deposites on the commutator.

General Comment about the AIWA AD-F770

This is a very good performing machine, but personally I wouldn't recommend buying a F770 due to the complexity of the internal circuit layout. They are awkward to fix or service, so lot of patience required!

7/05/2020: Judging the feedback from another website, I think it is important for the reader to understand that the use of the LM317 voltage regulator (as stated above) is an *experiment* - it is not recommended. 

Dedicated DC motor controllers typically sample the change in motor shaft speed due to a change in armature current, or terminal voltage.

If the load torque 'T' increases during an interval of time 𝚫t, the motor will slow down, the back EMFwill decrease (since EMF∝ speed) , and so armature current increases. 

(Note: T ∝ armature current). 

The controller then (typically an AN6651 in circuit) increases the terminal voltage by a proportion so that constant speed is maintained.  The reverse is true if the load decreases.

8/05/2020: I have just ordered some AN6651 controller chips after managing to decipher the AN6651 (and other similar) datasheets. I hope to devise a general solution to the problem of ageing DC motors in cassette decks by using and modifying third-party DC motors that can run at 2400rpm.

I have begun a new article here ... https://cassettedeckman.blogspot.com/2020/05/external-motor-controller-experiment.html

Over the next few weeks I hope to establish a reliable working modification that can be used for other third party DC motors. 

***********************************************

(Note: www.blogger.com has editing/software bugs, and so I may need to revise or edit the articles without notice. It's very irritating for me to do, and for you to read - so apologies.)

Line Signal Muting

Line Signal Muting

While studying my Sony TC-K61 cassette deck, I was intrigued how the muting transistor action works? After sketching out a similar circuit of my own to analyse and assemble, I think I may now understand how this muting is achieved.

Here is Sony's muting circuit for the TC-K61 cassette deck for both recording and at Line Out - marked in green.

After sketching out my own generalised circuit, I had some components easy-to-hand, and so put this simple circuit together.

Here we have - an external signal generator shown to the left with its own internal resistance of around 600 ohms. Then I just added a simple, non-specific RC network to simulate general external circuitry. After that there is a load resistance of 20,000ohms. An oscilloscope was connected across the load RL.

The muting transistor here is simply a S9014 NPN which is about to be switched 'on'. A sine wave signal voltage of 1Khz across RL was set to 2 volts peak-to-peak with no interference from the S9014. Once I had switch the S9014 'on', the output completely muted. 

The results ..

VL (before muting) = 2v.
VL (during muting) = 5mv.

This gave me an effective reduction of 20Log(0.005/2) or -52dB.

So why does this work?
Firstly, note that - the transmission line is effectively dc decoupled. Secondly, the S9014 is not experiencing any external one-directional electric field (hence voltage) to motivate charges across the collector-base-emitter junctions. 

So how does forward biasing the base-emitter junction result in an efficient -52dB muting reduction?

My theory: Both base-emitter, and base-collector junctions are forced into forward biasing modes.

There is no, or very little dc current running through RL, but since both forward biased junctions are now offering a conduction path, and in particular to an ac signal - it is this ac signal voltage component that gets shunted through both junctions as both junction slope resistances 𝚫V/𝚫I (thanks to biasing) are very small.

Effectively, the source ac signal (component only) voltage drop, almost entirely occurs across the 600Ω, and 670Ω+j/𝛚C impedances since the slope resistances (collector-base, base-emitter) are so low in comparison. It's basically potential divider law, the ac signal voltage at the two junctions is 'lost' earlier across the said impedances. *

(To understand slope resistance 𝚫V/𝚫I or slope conductance 𝚫I/𝚫V in this context, you'll need to study transistor NPN junction characteristics, and in particular the Ic vs Vbe (or even Ie vs Vbe) curve which are not always illustrated in datasheets) *

Shunting of the ac signal works in both directions, only one direction shown above.

Can we expect a forward biased base-emitter junction to offer a better conduction path than that of a forward biased base-collector junction?, probably, but I haven't investigated this.

I noted that during this electrical state, there was a very small dc potential across RL (collector-emitter) of 6.9mV, and again 6.9mV when I completely removed the circuit to the left of the S9014. This suggests that while one junction (probably base-emitter) was approximately 0.7v (forward biased), the other PN junction was at around 0.7v-0.0069v; effectively the same!

One final note - efficient muting was also realised when I reversed both emitter and collector.

23/03/2020.

2nd revision, 24/3/2020.
** 3rd revision: 20/03/2024

 

********************************************************************************

I also later simulated the circuit in https://www.falstad.com/circuit/circuitjs.html

The results were different concerning muting ability - this simulation was less efficient for some reason?, but the remaining analysis was reasonably accurate. You can see that both PN junctions were effectively forward biased and the slope resistance very low.

 
25/03/2020.