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Patrick Turner Patrick Turner is offline
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Default Diode detector R and C value calculations.

The simplest detector of audio signals from amplitude modulated RF and
IF waves is done using the age old idea of a vacuum tube or germanium
diode used to charge a C usually from a winding on an IF transformer,
and there is a following R strapped across the C which discharges the
C constantly so that the average voltage across the C varies linearly
with the varying amplitude of the RF or IF AM wave envelopes.

The function is identical to to having a "1/2 wave rectifier" in a
power supply, except that the charging up of the C is done at RF or IF
frequencies, most commonly at 455kHz in AM radios, but F can be
10.7MHz in FM radios, or 4.5MHz in TV sets.
Instead of a "load" on a PSU, the detector load is a carefully chosen
R value to get a time constant with the chosen C value so that for a
nominated value of maximum expected audio voltage and maximum expected
audio frequency, there will be no slew distortions, and minimised
ripple voltage for good AC to DC conversion factor, and the load
imposed by the diode plus C plus R must not cause too much distortion
of the RF or IF individual carrier waves or load up the driving source
or cause reduction of the Q and hence selectivity of the tuned circuit
which usually drives most detectors in old radios without any sort of
buffer stage.

I always like to instal a triode cathode follower buffer stage between
the last IF transformer winding and detector in all old radios I
repair or restore. The envelope wave is preserved almost pefectly
intact and there is no loading of the LC tuned circuit, and no
reduction of Q or distortions. The CF I like to use is typically a 1/2
12AU7. This may be set up with Rk = 33k and taken to a -150V rail.
The anode is taken to the B+ rail used for the other radio tubes,
typically +200Vdc. The last IFT winding has one end to 0V, with the
live end taken to the 12AU7 grid.

So, we have the idle voltage at the cathode at about +6Vdc.

The output resistance of the CF = 1 / gm for the 12AU7, and this is
approximately 400 ohms.

The CF cathode feeds a diode anode with its cathode charging a C.
There can be a vacuum tube diode, say 6AL5 with forward voltage drop
of perhaps 0.05V, but with high Ra, or much easier, a germanium diode,
IN60 or other ge types with forward voltage drop of about 0.2V and
with low "on" resistance.

So how is the C value chosen? I like the reactance of C, XC = 4 x
Rout of the driving source which means in this case 4 x 400 ohms =
1k6.

In this case let us say the detector is in an old radio with IF =
455kHz.

If XC = 1k6, then C = 159,000 / ( XC x F ) = 159,000 / ( 0.00022uF x
455,000 ) = 220pF.

So what is the R value needed for the wanted audio bandwidth?

This depends on the audio voltages and undistorted frequency range we
want to obtain from the detection process.

There will always be a mimimum steady Vdc produced in a detector when
there is no modulation and just a carrier present in the case of
normal AM. ( With SSB or DSB envelopes, there is more to consider, but
I only deal now with ordinary full AM signals as used by main
broadcast band radio. )

We could drive a detector diode and C+R circuit directly from a
grounded winding on an IFT. Because the source driving impedance is
high, the C must be low value, typically 100pF maximum in many old
radios but C could be much higher if the source impedance were much
lower, and thus less prone to distortions, stray C effects and noise
generation.

But let us first assume that we are driving the detector from a low Z
source and from a winding with one end grounded and NO modulation.
With very low carrier levels the recovered or detected Vdc will be
low, and if the diode has a forward voltage drop of say 0.2V, then the
carrier peak voltage needs to be higher than 0.2V before any change in
Vdc might occur. And if the carrier peak voltage was 0.2V, and there
was any modulation, then the maximum peak and minimum peak carrier
voltage would be a maximum of between 0V and 0.4V because that's what
you'd get with 100% modulation.

But the audio voltage recovered will be very distorted because the
turn on character of the diode between 0V and 0.2V is causes little
audio signal recovery from on the bottom halves of the AF waves. To
try to keep well away from such non-linearity causing distressing
sound quality from such abysmally low level source signals in our
loungerooms, all sorts of other detectors have been invented, and I
won't even discuss the better of them such as the "infinite impedance
detector" or those using an opamp and NFB. In an old radio, we merely
have to remember the enormous dynamic capability of the tubes and we
will design the radio for much higher IF carrier signals than 0.2V pk
to appear at the detector.

We also want to be able to generate a decent AVC Vdc to control the
gain of RF, mixer and IF amp stages. It so happens the AVC needed is
often about -4Vdc. This may easily be gained from a seperate second
detector circuit working from the anode of the last IF amp tube with
small C, say 33pF feeding a diode and 1M load and 0.05uF C before the
recovered -Vdc is applied to RFT and IFT grid windings. Such an AVC
arrangement works well for least sibilance when tuning the strong
stations we want listen to.

But for the audio signal, we want a positive going audio signal,
especially if we are working from a cathode follower whose turn on
character is stronger than its turned off character..

But let us keep the focus on a carrier source from a grounded winding.
To avoid the distortions, carrier levels should be at least 1 peak
volts. From this and neglecting any diode resistance losses with a Ge
diode, and the very slight clipping of IF wave peaks, we might get the
steady V across C = carrier peak voltage.
Any audio detected will be only badly distorted by diode non-linearity
if the modulation levels are more than 70%.

So far, I have assumed the IF carrier source is low Z, and C = 220pF,
and that we want at least +1Vdc generated with no modulation. We also
would want the 455kHz ripple voltage at C to be between 1/10 and 1/20
of the maximum possible peak audio voltage which will also be 1Vpk if
the carrier is 1Vpk, ( at 100% modulation ).

So what about R???

Well, considering all things, I came up with a formula developed from
others used for PSU designs and calculations of ripple voltage.

R = 10 to the 12th / ( 8 x highest slew free audio F x CpF )

10 to the 12th is a constant.

Suppose we want highest non slewed audio F = 10kHz, and Cpf = 220pF,
then R = 1,000,000,000,000 / ( 8 x 10,000 x 220 ) = 57,818 ohms, in
fact a standard 56k would be OK.

Suppose the carrier level was a more healthy level of 2Vpk from out
lowZ winding. We should see about 2Vpk at C without any modulation.

Average 455kHz ripple voltage at C depends on the current drain from C
through R.

But after each time a carrier wave charges the C, the C voltage begins
to decline along a curve known as the time constant decay curve. We
have C, and we have R, so we can calculate their time constant.

TC in seconds = R in ohms x C in Farads = 56,000 x
220/1,000,000,000,000

Expressed in uS, TC = 56,000 x 220/1,000,000 = 12.3uS

If you draw one 10kHz sine wave lasting 100uS, and plot a time decay
curve from the peak of the sine wave, you shoud see the slope of the
decay curve is never flatter and is always slightly steeper than the
steepest part of the 10kHz wave.
This indicates slew distortion is impossible, and regardless of the
sine wave voltages.

Now using a grounded winding for our source, and carrier at 2Vpk, the
recoverable max audio voltage is at 100% modulation and varies between
2Vpk and 0V. ( approx, with perfect diode) The ripple voltage will be
highest when audio Vpk is highest, and where Vpk is minimal so to is
the Vripple, and the varying Vripple gives an audio output voltage
slightly less then the envelope shape and causing some distortion but
it is mild, and may be neglected for the general concept.

We would be intersted in the average Vripple, or Vripple with no
modulation.

The time constant we have = 12.3uS, which means the +2Vdc at C would
fall to 0.37 x +2Vdc after 12.3uS and so on. But because the initial
voltage drop is small, and much less than 2Vpeak, if the current was
constant to initial the V drop would be 2V in 12.3uS. draw a graph of
this if you are unsure.

The time between each charge of the C = 1 / IF = 455,000 seconds =
2.2uS.

So the Vdrop at C between charge pulses = 2.2 / 12.3 x 2V = 0.36 V.
This equals the peak to peak voltage of the sawtooth shaped ripple
voltage.

Vripple in Vrms = Vp-p / 2.82 = 0.36/2.82 = 0.13V approx. The maximum
audio Vrms =Vpk x 0.707 = 2 x 0.707 = 1.414Vrms, so Vripple is
approximately 1/10 of the maximum audio.
It is easily filtered down, and we might actually see 1.3Vrms max from
the detector.

At the average Vripple level where there is no modulation, initial
current drain from C = Carrier Vpk / R = 2V / 56k = 0.036mA.

We need to calculate this because we need to move on to using a
cathode follower buffered IF signal source.

Say we have the CF = 1/2 12AU7 and with grounded winding grid feed so
bias voltage at cathode = Ek = +6Vdc. Now if the carrier at the
cathode is 2Vpk, with no modulation the V across C will be +6Vdc +
2Vdc = +8Vdc.

To obtain the same ripple voltage average we need only maintain the
same initial current as voltage sags from C between charge pulses. so
we have another formula...

R = ( Cathode BIas Vdc + Carrier Vpk ) / current calculated above for
where bias = 0V.

= 8V / 0.036 = 222k, or 220k, standard value.

The Vripple will not change much even when audio voltage is maximum.

I have used the cathode follower with 33k Rk between cathode and 0V
and fed the grid which has one end biased and bypassed at +30Vdc, with
anode at about +200Vdc, and so Vdc across the C with Carrier Vpk at
2Vpk is about +38Vdc. With current = 0.036mA, R becomes 38 / 0.036 =
1.05Mohms,
or 1M, standard value.

Such a scheme gives extraordinarily low audio distortion right up to
about 95% modulation where there is a tendency for a slight flat spot
to appear on audio wave troughs because of the Vripple restriction as
the envelope voltage change declines below about a 0.3Vpk to 0Vac at
0% modulation.
In practice, the sound of the detector is excellent.

One has to worry about the following network of R and C used to filter
the Vripple, lest it cause cut off distortions but the CF + diode + C
+ R so far calculated is a low Z source of audio, and a typical filter
will be say 100k used with a C calculated for the wanted audio F pole.
Say F was 10kHz, R = 100k, then C uF = 159,000 / ( 10,000 x 100,000 )
uF = 159pF, or standard value = 150pF.
The ripple would be reduced to about 3mV, and lost in the following
audio amp bandwidth restrictions.
In practice, 100pF would be OK.

Patrick Turner

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