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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Variable-Gain Amplifier, adapted for etching into silicon.

One of the subjects which I’ve blogged about before was, The design of a variable-gain amplifier stage, that was really a variable-attenuation stage. This stage was neither suited for direct implementation with discrete components, nor on an IC. The reason for the latter detail was, that that circuit still contained coupling capacitors. Those are difficult to implement on an IC. However, I’ve done my best to do so now, in order to design a stage, which can be etched onto an IC.

My strategy for implementing a coupling capacitor was, that I’d tie the Source, Drain and Bulk electrodes of a P-channel MOSFET together on the side of the input, and use the Gate as output. However, since the N-doped well of a P-channel MOSFET also has capacitance to the substrate, I added a schematic component, that would be a ‘Semiconductor Capacitor’ according to ‘NG-SPICE‘, and the rectangular dimensions of which would just be slightly larger in each direction, than those of the MOSFET. This is meant to simulate the added, unwanted bypass-capacitor, which the preceding transistor-stage would need to be able to overpower.

This is the schematic:

Default_NM_Gain_IF_6

These are the model-cards used:

http://dirkmittler.homeip.net/text/NMOS2.mod.txt

http://dirkmittler.homeip.net/text/PMOS2.mod.txt

http://dirkmittler.homeip.net/text/JUNCCAP1.mod.txt

And this was the Net-List that defines both the circuit, and one of the simulations:

http://dirkmittler.homeip.net/text/Default_NM_Gain_IF_6.net.txt

Obviously, on an actual IC, the capacitor ‘C1′ would not exist either. Instead, a presumed preceding stage would have another transistor, that does what ‘MC1′ does in this stage.

The concept behind this circuit was, that ‘M1′ is a working inverting amplifier with reasonable voltage gain – in the ballpark of ~18, if there was no circuitry designed to make it attenuate a signal. Simply because the voltage-divider exists between ‘R2′ and ‘R3′ at the input, that goes down to ~9. Additionally, the fact that ‘R5′ follows ‘MC1′, brings the voltage-gain down to ~6, when the control-voltage is 3.0V. But, as ‘M3′ starts to conduct, it starts to feed the inverted signal from the coupling-capacitor back to the Gate, where the feedback competes with the current being fed by ‘R2′. The higher the gain of ‘M1′ is, the better the negation of the signal is, that results.

All outputs should have some sort of load indicated, so I added ‘R5′. In fact, I get the impression that NG-SPICE runs into difficulty simulating an output-voltage, if there is no load resistor. But in reality, the current that flows from the Source to the Drain of ‘M3′ will also see to it that any following, chained stages are biased as this stage was biased. (:1)

This circuit has a surprising, simulated behaviour, in that it will regulate the output voltage down, almost to zero, as the control voltage increases between 4.1V and 4.25V…

(Updated 7/30/2019, 10h20 … )

Continue reading Variable-Gain Amplifier, adapted for etching into silicon.

The secret, to obtaining high-performance monolithic MOSFETs, under NG-SPICE.

One fact which I already blogged about in This Posting and This Posting, had to do with my frustration, at getting poor transistor behaviour, with enhancement-mode, N-channel MOSFETs, using the circuit simulation program called NG-SPICE.

For people who do not know, ‘SPICE’ stands for “Simulation Program, with Integrated Circuit Emphasis”. And NG-SPICE just happens to be the open-source version of it. Under Payware there are also ‘LT-SPICE’ and ‘P-SPICE’, to name a few.

Apparently, the default values which NG-SPICE puts, for the channel-length and channel-width of these MOSFETs, are just not suited for any purpose. Those are, 100μ x 100μ . And, NG-SPICE has as added drawback, that the power-user cannot just insert his customized parameters into the model-card – that defines a certain transistor-type – where they get ignored, but must put them at the end of every model-line, where the component is included in the circuit. It ‘kind of makes sense‘, since, with real ICs, the layout can be changed with every instance, but not the oxide layer thickness. But it’s also difficult to work with.

Apparently, the way to overcome that problem is, to keep the channel-widths at 100μ  , but to shorten the channel-lengths to 1μ . It gives much better results.

If the user has done this, then of course he must also recompute the optimal bias for the entire circuit, meaning the regulating resistor-values, if the goal is to keep bias-current the same. Apparently, VT0 was always a decent value (formerly ~1.8V), but the gate voltage needed to exceed this parameter by too many volts (with the  default parameters), to obtain appreciable current-flow.


 

If in saturation mode, the resulting N-channel MOSFET is to keep conducting 3.75μA, then the correct bias-voltage is ~1.7V. And the amount of available voltage-gain then, at a 3V supply voltage properly bisected, is around 18 (-). This does imply that with the new parameters, VT0 has improved by becoming smaller.

Yet, I’m still detecting an active-circuit Gate capacitance of 0.7pF. This could continue to make the design of very-high-frequency VCOs difficult. But, lower resistance values can now be chosen as components of such a VCO (at the Drain of the transistor), such as with an Astable Multivibrator, due to the better transconductance, aka ‘KP’. The constancy of the Gate capacitance strikes me as logical, since I haven’t changed the channel-width. This capacitance is usually more, with respect to the Drain, than it is, with respect to the Source or Bulk. The capacitance with respect to the Drain is likely to have been amplified, by the (inverted) voltage-gain of the stage. If that was taken out of the equation, a total of ~106fF would be apparent.

Dirk

 

The Simplest Possible Mixer, using MOSFETs.

When a curious person searches the Internet for the circuit diagrams of (electronic) mixers, there is a certain complexity of what he or she will find. Just for people who might not know, the type of mixer I’m referring to is a component which does not add two signals together – which is what the naming might seem to suggest – but rather, which multiplies two signals. In certain cases the mixer will produce output, that contains an additive component as well as a multiplied component. But it’s the multiplied component circuit designers are interested in, because that can be used:

  1. In order to produce ‘mixed frequencies’, between two input frequencies, such as between a local oscillator and a Radio Frequency, resulting in an Intermediate Frequency,
  2. In order to act as a phase discriminator, the output of which will be maximally positive or negative, when two input signals are in-phase, but the output-voltage of which will be some neutral voltage, when the input waves are 90⁰ out-of-phase with each other. In this latter case, two reasonably constant input amplitudes are assumed.

What search results will often show, is somewhat complex mixers, that require either one or two balanced inputs – meaning inputs conditioned such, that they each appear differentially between two input electrodes – and which have as advantage for being designed that way, low distortion of the wave-form(s) supplied differentially in this way.

But sometimes, low distortion is not required. For example, in the case of a PLL – a “Phase-Locked Loop” – It’s assumed that the feedback voltage changes the frequency of a VCO – a “Voltage-Controlled Oscillator” – but with the intended result that two outputs lock in some phase-position, so that the two frequencies that are inputs to the phase-discriminator will be exactly the same frequency. This latter need often arises in the design of ICs. This latter application does not require that the phase-discriminator be particularly linear, nor that its output-voltages, that become feedback voltages, be in any range other than the range which the VCO requires as input.

And so the question can arise, what the simplest way might be to design a mixer, with the added detail that both inputs are unbalanced inputs – i.e., that each input appears at one terminal, and not in an opposing way, at two terminals – and for the sake of argument, our IC might be limited to using enhancement-mode, N-channel MOSFETs as the main active component. And this would be my solution:

Coinc-Det_1.svg

The concept is very simple. If Vin1 and Vin2 are at 180⁰, then M1 and M2 don’t conduct simultaneously. Therefore, R1 and Vcc (the supply voltage) achieve maximally positive average output-voltage. If Vin1 and Vin2 are at 0⁰ phase-position, the two transistors will become conductive in a way that coincides. Therefore, this is actually a Coincidence Detector. And the average  output-voltage will be maximally negative in that case. And, if Vin1 and Vin2 are at a 90⁰ phase-position, then the average output-voltage will be somewhere between the two values mentioned before.

I suppose it should be mentioned that, if the circuit designer knows ahead of time that one of the two inputs has a much higher amplitude than the other, or a more predictable amplitude, then this usually stronger input should be fed to Vin1.

As part of a feedback loop, the output needs to be followed by a low-pass filter, that emulates an integrator over the time-constant which is the fastest, with which that feedback loop is supposed to be able to react to a change in one of the frequencies. The simplest low-pass filter consists of a resistor followed by a capacitor… (:1)

And so, when looking for a way to implement a phase-discriminator, the curious person needs to choose which of the following has greater priority:

  • The simplest circuit-design, or
  • The lowest amount of distortion.

The circuit above will certainly give the highest amount of distortion. :-P

(Updated 7/9/2019, 16h55 … )

Continue reading The Simplest Possible Mixer, using MOSFETs.