The Kenwood KT-7500
Stereo FM/AM Tuner
I recently bought this to add to my interest in HiFi receivers and tuners.
The Kenwood KT-7500 is a beautifully engineered and finished piece of HiFi with a gorgeous fascia and controls, and of course high-end performance to match.
This particular version of the KT-7500 is slightly unusual in that there are two switchable de-emphasis configurations to choose from: 25µs and 75µs time constants; symbolically represented by 𝛕. If a tuner is going to give you a choice, then I would have expected both 50µs and 75µs time constants, not 25µs and 75µs!?
The time constant parameter 𝛕, is an accepted convention when describing 'corner frequencies' in the playback of a first-order, low-pass filter frequency response. Each time constant 𝛕 is directly linked to a corner frequency fc.
Here in the UK, the playback de-emphasis curve adheres to a time constant of 50µs, that is 𝛕 = 50/1000000 seconds, whereas, in the United States and Canada, they employ the 75µs time constant.
Therefore, it is quite possible that this KT-7500 was purchased in the US or Canada back in the late 1970s? I say this since 25µs was intended to be used for Dolby encoded broadcasts in the United States, possibly Canada too? For this to work correctly, a Dolby outboard would be required?
An explanation of de-emphasis, and the associated time constant will be explained at, or near the end of this article.
The KT-7500 in its Wooden Housing:
Opening up the KT-7500 reveals a beautifully laid out circuit.
Highlighted above in white is the final low-pass de-emphasis circuit that needs to be modified so that both 50µs and 75µs time constants are easily accessed, at present I've only 25µs (for a Dolby outboard?) or 75µs (United States) to choose from.
Observe below, a picture taken for the original advert by the seller, and the limited choice: 75µs (US or Canada) or 25µs (Dolby encoding) de-emphasis setting.
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Identifying De-emphasis Stages
Studying the schematic for the KT-7500, we are able to track down the output stages, and identify the de-emphasis low-pass circuit.
Both left and right channels have been highlighted for convenience: right in red, and left in blue.
Studying the circuit diagram reveals that a NJM4558 dual OP Amp has been used in the final stages of audio post-processing; that is FM de-emphasis.
The OP Amp appears to be configured in a non-inverting, first-order low-pass state. Similar to that shown below -
The derivation for the voltage gain for this non-inverting amplifier can be shown to be:
Av(ω) = 1 + Zf(ω)/R
Where Zf(ω) is the impedance of the parallel network containing the 33kΩ resistor and the 750pF (and, or the 1500pF) capacitance. The R is the 2kΩ resistance as shown above.
This voltage amplifier's gain is frequency dependent, but can easily act as a voltage follower if Zf→0Ω; in that case the gain is simply unity, ie 1.
However, returning to our low pass de-emphasis amplifier and filter - in terms of the resistive and capacitive components, the complex form of the voltage gain of the OP Amp in this non-inverting arrangement is:
Where Rf = 33000Ω, C = 750pF or 2250pF, and R1 = 2kΩ.
Note: In the KT-7500, C is actually switchable between 750pF and (750+1500)pF.
Also, be mindful that periodic frequency f (Hz) is related to angular frequency ω=2𝝿f (radians/second), or f=2𝝿/ω.
In the above 'complex' form, both voltage gain and input vs output phase shift can be analyzed.
In an attempt to keep this write up as simple as possible, the mathematical issues of derivation of formulae are going to be by-passed.
Computing OP AMP Gain Av(f) vs Frequency (Hz)
Applying a complex conjugate operator to the above expression, and we have ...
And so, the modulus or absolute value of the gain is ...
Mapped out, it will look like this ...
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| Frequency Response Curves for CR value of: C x R = 50µs |
If my calculations are correct, the plot in red would be the theoretical curve if the OP Amp was in an inverting configuration, and in blue is the theoretical plot for our non-inverting KT-7500.
Corner Frequency and Time Constant
The corner frequency is that frequency f, for which
2𝝿fCR = 1,
or
f = 1/{2𝝿CR} Hz.
The gain then becomes .....
Under these conditions, and without the '1' term, the gain is (Rf/R1)×(1/√2) or -3dB below its maximum value. However, because the gain for this OP Amp configuraton is Av = 1 + Zf/R, the '1' offsets this calculation a little.
The time constant 𝛕 mentioned earlier is generally derived from RC networks and their ability to charge or discharge, and in particular - the initial rate at which charging/discharging occurs on response to a voltage step function.
𝛕 definition: If this initial rate of charge were to be maintained, then the time taken for the capacitor to become fully charged or discharged is equal to: C x R seconds.
That is ...
𝛕=CR
The reader may have already deduced that frequency f and 𝛕 are related, that is, at the corner frequency fc: fc = 1/{2𝝿𝛕}.
UK FM De-emphasis
Here in the UK, the 50µs de-emphasis time constant 𝛕 is employed, it is directly related to a de-emphasis corner frequency.
fc = 1/{2𝝿ᐧ50µs} = 1000000/{2𝝿ᐧ50} = 3183Hz.
In the context of the KT-7500, and to obtain 𝛕=50µs, C needs to be 1500pF, neglecting component tolerances, the actual values of CR used above gives ...
𝛕=1500pF*33KΩ = 49.5µs
or
fc = 1000000/{2𝝿ᐧ49.5} = 3215Hz.
Now examine the above plot to confirm the -3dB drop at approximately 3183Hz. This equates to (1/√2)*17.5 at 3183Hz.
United States/Canadian De-emphasis
In the US and Canada, 𝛕=75µs, that is ...
fc = 1000000/{