Basic Colpitts Oscillator

One of the concepts which I’ve been exploring on my blog, concerns tuned circuits, and another concerns Voltage-Controlled Oscillators (VCOs). As one type of voltage-controlled oscillator, I have considered an Astable Multivibrator, which has as advantage a wide frequency-range, but which will eventually have as disadvantage, a limited maximum frequency, when the supply voltage is only 3V. There could be other more-complex types of VCOs that apply, when, say, 200MHz is needed, but one basic type of oscillator which will continue to work under such conditions, which has been known for a century, and which will require an actual Inductor – a discrete coil – is called the Colpitts Oscillator. Here is its basic design:

Colpitz_1.svg

In this schematic I’ve left out actual component values because those will depend on the actual frequency, the available supply voltage, on whether a discrete transistor is to be used or an Integrated Circuit, on whether a bipolar transistor is to be used or a MOSFET… But there are nevertheless certain constraints on the component-values which apply. It’s assumed that C1 and C2 form part of the resonant “Tank Circuit” with L1, that in series, they define the frequency, and that they are to be made equal. C3 is not a capacitor with a critical value, instead to be chosen large enough, just to act as a coupling-capacitor at the chosen frequency (:2) . R2 is to be made consistent with the amount of bias current to flow through Q1, and R1 is chosen so that, as labelled, the correct bias voltage can be applied, in this case, to a MOSFET, without interfering with the signal-frequency, supplied through C3.

I’m also making the assumption that everything to the right of the dotted line would be put on a chip, while everything to the left of the dotted line would be supplied as external, discrete components. This is also why C3, a coupling capacitor, becomes possible.

The basic premise of this oscillator is that C1 and C2 do not only act as a voltage-divider, but that, when the circuit that forms between L1, C1 and C2 is resonant with a considerable Q-factor (>= 5), C1 and C2 actually act as though they were a centre-tapped auto-transformer. If this circuit was not resonating, the behaviour of C1 and C2 would not be so. But as long as it is, it’s possible for a driving voltage, together with a driving current, to be supplied to the connection between C1 and C2, in this case by the Source of Q1, and that the voltage which will form where C1 connects with both L1 and the Gate of Q1 (that last part, through C3), will essentially be the former, driving voltage doubled. Therefore, all that needs to happen on the part of the active component, is to form a voltage-follower, between its Gate and Source, so that the voltage-deviations at the Source, follow from those at the Gate, with a gain greater than (0.5). If that can be achieved, the open-loop gain of this circuit will exceed (1.0), and it will resonate.

It goes without say that C1 and C2 will also isolate whatever DC voltage may exist at the Source of Q1, from the DC voltage of L1.


 

There is a refinement to be incorporated, specifically to achieve a VCO. Some type of varactor needs to be connected in parallel with L1, so that low-frequency voltage-changes on the varactor will change the frequency at which this circuit oscillates, because by definition, a varactor adds variable capacitance.

What some sources will suggest is that, the best way to add a varactor to this circuit will be, to put yet-another coupling capacitor, and a resistor, the latter of which supplies the low-frequency voltage to the varactor. But I would urge my reader to be more-creative, in how a varactor could be added. One way I could think of might be, to get rid of R1 and C3, and instead of terminating L1 together with C2 to ground, to terminate them to the supply voltage, thus ensuring that Q1 is biased ‘On’, even though the coupling capacitor C3 would have been removed in that scenario. What would be the advantage in this case? The fact that The varactor could be implemented on-chip, and not supplied as yet-another, external, discrete component, many of which would eat up progressively more space on a circuit-board, as a complex circuit is being created.

I should also add that some problems will result, if the capacitance to be connected in parallel with L1 becomes as large, as either C1 or C2. An eventual situation will result, in which C1 and C2 stop acting, as though they formed a (voltage-boosting) auto-transformer. An additional voltage-divider would form, between C1 in this case, and the added, parallel capacitance. And this gives more food for thought. (:1)

 

(Possible Usage Scenario : )

(Updated 7/29/2019, 14h45 … )

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Hypothetical Variable Gain Amplifier

What I find is that in recent years, the term ‘Variable Gain Amplifier’ has changed in meaning, to correspond more to a ‘Variable Attenuation Stage’, after a fixed-gain amplifier. And this seems especially true, when applied to ‘IF Stages’ – ‘Intermediate Frequency Stages’ – Of a radio receiver. I’ve also observed that low-distortion technologies are preferred in recent years, as opposed to the high-distortion technologies that manufacturers were limited to, say, in the 1970s, when ‘AGC’ was first being marketed to consumers.

Yet, even with the technologies that are now available, there are sometimes added constraints. For example, if one wanted the variable-resistance component either to be optical – for lowest distortion – or, for that to be a JFET – easier to implement – then, this component might need to exist externally to an IC, just because the IC itself may be engineered only to allow for two complementary types of transistors, those being, an enhancement-mode N-channel MOSFET and an enhancement-mode P-channel MOSFET. Further, The properties of such MOSFETs can sometimes be inconvenient, in the form of high Threshold voltage, named ‘VT0′, which is the voltage required to make the transistors start to conduct. Practical values of VT0 may be more suited to logic circuits, than to the processing of low-amplitude, analog RF or IF frequencies. A thinner oxide layer for the entire IC can reduce the required VT0.

Yet, the possibility exists for even a MOSFET to operate in ‘Triode Mode’, which is a mode in which it is Not ‘Saturated’. This mode is achieved when:

VDS < VGS – VT0

The problem in trying to reach this mode seems to arise in the fact that if, VT0 is already a higher-than-desired voltage, VGS-VT0 is likely to be a lower-than-desired voltage-range, since VGS is also limited by the supply voltage.

In Triode Mode, a MOSFET effectively behaves like a variable resistor, which decreases in value as the Gate voltage continues to increase.

And so to summarize what form the task might take, to make the Variable Gain Amplifier monolithic with a MOSFET-based IC, I constructed the following, hypothetical diagram, which does not explicitly nail down what VT0 is supposed to be, nor the supply voltage:

Serge_VCR_3b.svg

 

What I seem to have noticed however, in order for the suggested IF stage to work, is that the actual signal should not have a ‘Peak Amplitude’ at the Gate of the last amplifier stage, greater than (0.1V). Yet, the feedback-loop itself, that adjusts attenuation, could play a role in keeping that peak amplitude close to (0.1V).

(Corrected 7/7/2019, 11h05 … )

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