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Old 12th Feb 2023, 3:32 pm   #410
regenfreak
Heptode
 
Join Date: Nov 2018
Location: London SW16, UK.
Posts: 655
Default Re: 6-gang FM stereo tuner heads

One of the most difficult challenges of making a multiple-gang varactor tuned broadcast receiver is the linearity and predictability of the tracking. I have done some measurements to characterise the Philips BB204B double varactor diode in terms of their frequency linearity, unloaded Qu in an LC tank and their actual performance in a tunable bandpass filter.

Based on the datasheet, I think its graph was measured with one of the two diodes. One diode Q is about 200 at 100MHz. In my case, I have measured diode capacitance with two diodes in series which would half the Q to about 100. The advantage of having the diode in series is that it minimises the effects of the fluctuating RF AC on the diode capacitance and less distortion products.

The mathematical model of the varactor is represented by the simple equation in attachment one. V is the sum of DC tuning voltage plus RF signal voltages. Phi is the contact potential of the diodes. By taking the logarithmic function of the C and V relation, it is possible to find the power index n using linear regression.

The varactor can be idealised as a capacitor (of high resistance depleted region) in series with a small value resistor (variable, low-resistance undepleted region+ constant contact resistance). Q increases with increasing reversed bias voltage, therefore its performance should be worst at the lower limit of the broadcast band.

Attachment 2 illustrates LogC vs log(V+phi), the power index n = 3.37 using linear regression. For ideal linearity, n should be 2 because the frequency is inversely proportional to capacitance squared. I have found there are variations of the measurements among different BB204B samples.

In the 3rd attachment, it shows the measurements of (1) frequency vs reversed voltage and (2) unloaded Q of LC resonator vs frequency for a single LC resonator (L =88nH). In this scenario here, the Q of the inductor is comparable in magnitude with that of the varactor diode (1/Q = 1/Qc + 1/QL). Usually, the Qc of the air gang capacitor is significantly bigger than the inductor QL.

AT 88Mhz, Qu = 55 and at Qu = 129, very drastic difference!


To evaluate the performance of the varactor diodes in a tunable FM bandpass filter with 50 ohms terminations, I have tried it with a Butterworth optimised at 100MHz. As you can see in attachment 4, it smashes at 50 ohms; bang on at the centre of the Smith chart. S11 = -45db, S21 = -2.5db which is very good (typo in my file name, it should be 98.8MHz and not 86.8Mhz)

Attachment 5, shows the changes in bandwidth and bandpass response at 88Mhz, 99Mhz and 108Mhz, respectively. At 88Mhz, the filter has about additional -2db insertion losses due to the lower Q of the varactor diodes at the low-frequency bottom end. At the top end of the broadcast 108Mhz, the selectivity of the bandpass degrades and therefore it is desirable to have multiple gangs of tunable bandpass filters in high-performance FM tuners.
Attached Thumbnails
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Name:	Q undepleted resistance.jpg
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Name:	BB204 logC vs log(V+phi) n=-3.37.jpg
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Name:	BB204 f and Q vs V.jpg
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Name:	BB204 86.8MHz -2.5db 50 ohm.jpg
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Name:	BB204 varactor tuned bandpass.jpg
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Last edited by regenfreak; 12th Feb 2023 at 3:56 pm.
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