Capacitor Loading on OP Amps

Update, 21/10/2020: The TL071 OP Amp's open loop frequency response and phase shift was obtained from the TL071 data sheet online. It's frequency response resembles an amplifier with high DC gain, and with one low frequency pole, ie -3dB point.

My experimental headphone amplifier (Headphone Amp) has one TL071 in a non-inverting, unity gain configuration. On examining the data sheet, one can see that at unity gain, the TL071 has a bandwidth of approximately 4Mhz. Also, from a stability point of view, note the phase shift at 4Mhz at around -100°!

With the inclusion of a 1.5nF load capacitor CL, it is no surprize then that the amp was destabilizing. My temporary circuit layout must have also possessed sufficient parasitic capacitance to render the TL071 almost unuseable. Removing the 1.5nF additional load returned the amp to stability.

21/10/2020: Subject to corrections, and additions.

KEF 104-2 Floor Standing Speakers

 KEF 104-2 Floor Standing Speaker

Tweeter Replacements

 

 

Click on the images to magnify - applies to all.

 

By chance I spotted a youtube video showing one method to replace an ageing or blown dome KEF T33 tweeter on the KEF 104.2 floorstanders - this reminded me to do something about mine. The video here shows how one guy fixed his tweeter problem with a set of Morel MDT29s.  Morel MDT29 Tweeters

I've had my KEF 104.2s since about 2002/2004, and it wasn't long after I blew the tweeters. A temporary solution by my brother-in-law fixed the issue, a direct KEF T33 (SP1191) replacement was not easily available even at this time.

Yesterday, I mulled over several replacements, and finally decided on the french Audax TWO25A2 textile dome tweeter, since they seemed to have a similar spec to the T33s, and would probably fit without too much intervention?

 

 

KEF T33B tweeter specification - similar to the T33?

Audax TWO25A2: The sensitivity or output of the 4Ω tweeter from the official specs is stated at "93dB at 1W at 1 metre", although some sources quoted these Audax tweeters at 90dB? 

At 1 Watt input, I can only assume that Audax are using P=V²/R, where V is RMS volatge, and R is the 4Ω loading. This equates to: 1 = V²/4, or V² = 4, ie V = 2V rms.

Then for the Audax: 2V rms → 93dB output

Morel MDT40: The temporary fitted tweeters back in 2002/2004 were the Morel MDT40s: wired in twos, in parallel to mimic a 4Ω load to the amplifier and crossover unit. 

However, each MDT40 tweeter was still an 8Ω load and was sinking AC audio current as per specification - delivering the quoted "89dB at 1W, at 1metre" distance.   

So then, delivering 89dB loudness for 1W input suggests ...

from P=V²/R,  1=V²/8, or V=√8, 

ie V=2.83v.

 Then for the Morel: 2.83V rms → 89dB output

As a comparison then, by my calculation if the Morel was subjected to 'only' 2V rms, then the output would be less than the 89dB figure. If these specs are to be believed, the difference I experienced must have been at least -4dB, ie the Morel output was down. 

As a mathematical suggestion, I may have experienced a further drop from the Morel of 20·Log(2v/2.83v) or -3dB? In total then, perhaps approximately -7dB?

Perceptively, back in 2002/2004 I noticed the treble was down - but I simply got used to it.

The new Audax TWO25A2 4Ω Tweeter

 

And here again is the Audax TWO25A2 with its face plate removed, and plastic voice coil carefully fastened into place.

Note: flash photography may give the appearance that the dome is distorted - it is not.

 

Here the Audax TWO25A2 is ready to replace the old tweeter before soldering - my advice is to do the soldering first.

 

 

The countersunk screw heads may look a little 'proud', but the tweeters 'seated' nicely once installed, and indeed the screw heads acted as an additional grip. The locking plate in the background slides over and the tweeter can be centered and stabilized thanks to the fastening and centering screw. I may later devise a 'cushioning' interface between the Audax tweeter and the tweeter port on the 104/2 baffle?
 

Voice Coils

I think it's best to carefully solder with the voice coils removed - very easy and convenient.

 

Re-assembly

Not an issue, there was plenty of room to slide the Audax tweeters in. The depth of these tweeters is quoted at just over 23mm, not including the face plate.

 

 

There is a red marking on the tweeter to signify 'positive'. 

As it's AC we are concerned with in audio, 

can this only act as a guide so that we avoid 

phasing errors between left and right channels?

Remounting the Baffle on to the Main Cabinet

With the tweeters secured and centered it was time reassemble the driver unit.

And finally ...

 

In use the speakers have come to life - upper midrange and treble re-defining the sound image. So far, so good, I am very happy!

Unanswered Questions

(a) Flatness of Crossover  

There is a question concerning the original midrange driver frequency response merging with the Audax TWO25A2's response. At the intersection or crossover frequency - is there a rise, a fall, or is the frequency response reasonably flat?

(b) New Tweeter Power Handing

The power handling capacity of the Audax TWO25A2 is quoted at 55W RMS/DIN?, this is seemingly much less than the handling capabilities of the KEF T33? 

However, is that an issue? My Sony TA FB-940R amplifier can theoretically deliver up to 120W into 4Ω, but much of transient music spectral power (individual sinewave component powers) naturally fall off with frequency - something approximating to a 1/f power spectra, much like 1/f  'flicker noise'. 

Whats does this mean? Well, it means this - with a doubling of frequency, then expect approximately half the power to be present in the corresponding doubled frequency component.

As a small demonstration of the spectral power amplitudes in music, below is a 30 second Fast Fourier Transform from Elton John's "Philadelphia Freedom".

 

The frequency density plot from Audacity

seems to be based on (voltage) amplitude of each

spectral frequency component, not explicitly power.

In amplitude terms this is: 6dB drop per octave,
or if computed for power: 10dB per decade.

In truth, I'll never drive the KEF 104/2 hard on the TA FB-940R - about '10:30' on the volume dial and the room is starting to resonate!

Finally, here is an online video worth watching ... KEF 104.2 Full Service

 

Minor corrections and revisions ...

12/10/2020, 13/10/2020, 11/07/2022.

14/10/2020 (speaker sensitivity clarified)

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.)