# Colpitts oscillator analysis

A Colpitts oscillatorinvented in by American engineer Edwin H. Colpittsis one of a number of designs for LC oscillatorselectronic oscillators that use a combination of inductors L and capacitors C to produce an oscillation at a certain frequency.

The distinguishing feature of the Colpitts oscillator is that the feedback for the active device is taken from a voltage divider made of two capacitors in series across the inductor. The Colpitts circuit, like other LC oscillators, consists of a gain device such as a bipolar junction transistorfield-effect transistor, operational amplifier, or vacuum tube with its output connected to its input in a feedback loop containing a parallel LC circuit tuned circuitwhich functions as a bandpass filter to set the frequency of oscillation.

A Colpitts oscillator is the electrical dual of a Hartley oscillatorwhere the feedback signal is taken from an "inductive" voltage divider consisting of two coils in series or a tapped coil. L and the series combination of C 1 and C 2 form the parallel resonant tank circuitwhich determines the frequency of the oscillator.

The voltage across C 2 is applied to the base-emitter junction of the transistor, as feedback to create oscillations. Here the voltage across C 1 provides feedback. The frequency of oscillation is approximately the resonant frequency of the LC circuit, which is the series combination of the two capacitors in parallel with the inductor:.

The actual frequency of oscillation will be slightly lower due to junction capacitances and resistive loading of the transistor. As with any oscillator, the amplification of the active component should be marginally larger than the attenuation of the capacitive voltage divider, to obtain stable operation.

Thus, a Colpitts oscillator used as a variable-frequency oscillator VFO performs best when a variable inductance is used for tuning, as opposed to tuning one of the two capacitors. If tuning by variable capacitor is needed, it should be done with a third capacitor connected in parallel to the inductor or in series as in the Clapp oscillator. Instead of bipolar junction transistorsother active components such as field-effect transistors or vacuum tubescapable of producing gain at the desired frequency, could be used.

The capacitor at the base provides an AC path to ground for parasitic inductances that could lead to unwanted resonance at undesired frequencies. Selection of the base's biasing resistors is not trivial. Periodic oscillation starts for a critical bias current and with the variation of the bias current to a higher value chaotic oscillations are observed. One method of oscillator analysis is to determine the input impedance of an input port neglecting any reactive components. If the impedance yields a negative resistance term, oscillation is possible.

This method will be used here to determine conditions of oscillation and the frequency of oscillation. An ideal model is shown to the right. This configuration models the common collector circuit in the section above. For initial analysis, parasitic elements and device non-linearities will be ignored. These terms can be included later in a more rigorous analysis. Even with these approximations, acceptable comparison with experimental results is possible.

Ignoring the inductor, the input impedance at the base can be written as.A Colpitts oscillatorinvented in by American engineer Edwin H. Colpitts is one of a number of designs for LC oscillatorselectronic oscillators that use a combination of inductors L and capacitors C to produce an oscillation at a certain frequency.

The distinguishing feature of the Colpitts oscillator is that the feedback for the active device is taken from a voltage divider made of two capacitors in series across the inductor. The Colpitts circuit, like other LC oscillators, consists of a gain device such as a bipolar junction transistorfield effect transistor, operational amplifier, or vacuum tube with its output connected to its input in a feedback loop containing a parallel LC circuit tuned circuit which functions as a bandpass filter to set the frequency of oscillation.

A Colpitts oscillator is the electrical dual of a Hartley oscillatorwhere the feedback signal is taken from an "inductive" voltage divider consisting of two coils in series or a tapped coil. L and the series combination of C 1 and C 2 form the parallel resonant tank circuit which determines the frequency of the oscillator. The voltage across C 2 is applied to the base-emitter junction of the transistor, as feedback to create oscillations. Here the voltage across C 1 provides feedback. The frequency of oscillation is approximately the resonant frequency of the LC circuit, which is the series combination of the two capacitors in parallel with the inductor. The actual frequency of oscillation will be slightly lower due to junction capacitances and resistive loading of the transistor.

As with any oscillator, the amplification of the active component should be marginally larger than the attenuation of the capacitive voltage divider, to obtain stable operation. Thus, a Colpitts oscillator used as a variable frequency oscillator VFO performs best when a variable inductance is used for tuning, as opposed to tuning one of the two capacitors. If tuning by variable capacitor is needed, it should be done via a third capacitor connected in parallel to the inductor or in series as in the Clapp oscillator.

Template:Expand section. Instead of bipolar junction transistorsother active components such as field effect transistors or vacuum tubescapable of producing gain at the desired frequency, could be used.

The capacitor at the base provides an AC path to ground for parasitic inductances that could lead to unwanted resonance at undesired frequencies. Periodic oscillation starts for a critical bias current and with the variation of the bias current to a higher value chaotic oscillations are observed .

One method of oscillator analysis is to determine the input impedance of an input port neglecting any reactive components. If the impedance yields a negative resistance term, oscillation is possible.

This method will be used here to determine conditions of oscillation and the frequency of oscillation. An ideal model is shown to the right.

This configuration models the common collector circuit in the section above.

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For initial analysis, parasitic elements and device non-linearities will be ignored. These terms can be included later in a more rigorous analysis. Even with these approximations, acceptable comparison with experimental results is possible. Ignoring the inductor, the input impedance at the base can be written as. If an inductor is connected to the input, the circuit will oscillate if the magnitude of the negative resistance is greater than the resistance of the inductor and any stray elements.

The frequency of oscillation is as given in the previous section.Remember Me? Colpitts oscillator stability analysis. Colpitts oscillator stability analysis Hi, I "designed" a collpits oscillator in base configuration according to a textbook  depicted in Fig.

Bild 1a it's in german, sorry. Concerning the loop gain of about 10, which is significantly larger than 1, the circuitry should certainly start oscillating. My question is, is there an analytical way to determine the stability in any way?

Further, is there a way to determine the turn-on time, which the oscillator needs until reaching steady state? The analysis should preferable include the correct transistor, if possible. I'm also curious about the graph in the right of Fig. Bild 2 in , where the hatched region is "The area in which experience has shown that optimum quality values can be achieved for the coil and the oscillating circuit no-load quality ".

Where do I get such an information, except from this textbook? Re: Colpitts oscillator stability analysis Ulrich Rohde has an in-depth analytical textbook about oscillators.

I recommend it to follow. Rohde But I'd rather say that analytical approximations are very tedious and mostly erroneous. Because oscillators are chaotic and nonlinear behaving devices therefore calculation will not set its place as wanted.

Re: Colpitts oscillator stability analysis A high L:C ratio takes more cycles to grow to a steady state from power-up. It also rings for a longer time after shut-off. The reason is that it usually has higher Q and greater 'inertia'.

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When L:C is low, or ohmic resistance is considerable, then it takes fewer cycles to reach steady state. Voltage amplitude tends to be reduced. Oscillations die out quickly if gain is insufficient. Re: Colpitts oscillator stability analysis Yes, there it is, looking at the graph in the Elemente book link looks like page The graph relates frequency to Zo The dotted lines seem to indicate that 1MHz suits a Z value ofand therefore L:C ratio of 1 million. Where a schematic contains an LC tank, or LC filter, etc.

Re: Colpitts oscillator stability analysis Hi, thank you for your replies! BigBoss: Thank you for the book suggestion, it is available in my university library. I will have a look. Until now I used LTspice for the simulations.An oscillator is a mechanical or electronic construction which produces oscillation depending on few variables. Various types of metal detectors, computers where microcontroller and microprocessors are involved use oscillators, especially electronics oscillator which produces periodic signals.

We discussed few oscillators in our previous tutorials:. The Colpitts oscillator was invented by American engineer Edwin H. Colpitts in Colpitts oscillator works with a combination of inductors and capacitors by forming an LC filter. Same as other oscillators Colpitts oscillator consists of a gain device, and the output is connected with an LC circuit feedback loop.

The Colpitts oscillator is a linear oscillator which produces a sinusoidal waveform. The main oscillation device in Colpitts oscillator is created using the tank circuit. The tank circuit consists of three components- a inductor and two capacitors.

Two capacitors are connected in series, and these capacitors are further connected in parallel with inductor. In the above image, three components of the tank circuit are shown with proper connections.

The process starts with charging of two capacitors C1 and C2. Then inside the tank circuit, these two series capacitors discharge into the parallel inductor L1 and the stored energy in the capacitor transferred to the inductor. Due to the capacitor connected in parallel, the inductor now discharged by the two capacitors and the capacitors start to charge again. These charging and discharging in both of the components continues and thus providing an oscillation signal across it.

Below formula is to determine the oscillation frequency:. During this oscillation phase in the tank circuit, some energy loss is occurred. To compensate this lost energy and to sustain the oscillation inside the tank circuit, a gain device is required.

There are many different types of gain devices are used to compensate the loss of energy inside the tank circuit. The most common gain devices are transistors and operational amplifiers.

In the above image, the Transistor based Colpitts Oscillator is shown where the main gain device of the oscillator is an NPN transistor T1. In the circuit, resistor R1 and R2 are required for the base voltage. Resistor R3 is used as an emitter resistor. This resistor is very useful to stable the gain device during the thermal drift. The capacitor C3 is used as an emitter bypass capacitor which is connected in parallel with the resistor R3.

If we remove this C3 capacitor, the amplified AC signal will be dumped across resistor R3 and results in a poor gain. So, the capacitor C3 is provided an easy path for the amplified signal. The feedback from the tank circuit is further connected using the C4 to the transistor T1's base. The oscillation of the transistor based Colpitts oscillator circuit is depended on the phase shift. This is well known as barkhausen criterion for the oscillator.

As per the Barkhausen Criterionthe loop gain should be slightly greater than the unity and the phase shift around the loop needs to be degrees or 0 degrees. So, during this case, to provide the oscillation across the output, the total circuit needs 0 degrees or degree phase shift.A Colpitts oscillatorinvented in by American engineer Edwin H.

Colpitts is one of a number of designs for LC oscillatorselectronic oscillators that use a combination of inductors L and capacitors C to produce an oscillation at a certain frequency.

The distinguishing feature of the Colpitts oscillator is that the feedback for the active device is taken from a voltage divider made of two capacitors in series across the inductor. The Colpitts circuit, like other LC oscillators, consists of a gain device such as a bipolar junction transistorfield-effect transistor, operational amplifier, or vacuum tube with its output connected to its input in a feedback loop containing a parallel LC circuit tuned circuitwhich functions as a bandpass filter to set the frequency of oscillation.

A Colpitts oscillator is the electrical dual of a Hartley oscillatorwhere the feedback signal is taken from an "inductive" voltage divider consisting of two coils in series or a tapped coil.

L and the series combination of C 1 and C 2 form the parallel resonant tank circuitwhich determines the frequency of the oscillator. The voltage across C 2 is applied to the base-emitter junction of the transistor, as feedback to create oscillations.

Here the voltage across C 1 provides feedback. The frequency of oscillation is approximately the resonant frequency of the LC circuit, which is the series combination of the two capacitors in parallel with the inductor:. The actual frequency of oscillation will be slightly lower due to junction capacitances and resistive loading of the transistor. As with any oscillator, the amplification of the active component should be marginally larger than the attenuation of the capacitive voltage divider, to obtain stable operation.

Thus, a Colpitts oscillator used as a variable-frequency oscillator VFO performs best when a variable inductance is used for tuning, as opposed to tuning one of the two capacitors. If tuning by variable capacitor is needed, it should be done with a third capacitor connected in parallel to the inductor or in series as in the Clapp oscillator.

Instead of bipolar junction transistorsother active components such as field-effect transistors or vacuum tubescapable of producing gain at the desired frequency, could be used. The capacitor at the base provides an AC path to ground for parasitic inductances that could lead to unwanted resonance at undesired frequencies.

Periodic oscillation starts for a critical bias current and with the variation of the bias current to a higher value chaotic oscillations are observed.

## Analysis of Common-Collector Colpitts Oscillator

One method of oscillator analysis is to determine the input impedance of an input port neglecting any reactive components. If the impedance yields a negative resistance term, oscillation is possible. This method will be used here to determine conditions of oscillation and the frequency of oscillation.

An ideal model is shown to the right. This configuration models the common collector circuit in the section above. For initial analysis, parasitic elements and device non-linearities will be ignored. These terms can be included later in a more rigorous analysis. Even with these approximations, acceptable comparison with experimental results is possible.

Ignoring the inductor, the input impedance at the base can be written as. If an inductor is connected to the input, then the circuit will oscillate if the magnitude of the negative resistance is greater than the resistance of the inductor and any stray elements.

The frequency of oscillation is as given in the previous section. Given all other values, the input resistance is roughly. This value should be sufficient to overcome any positive resistance in the circuit. By inspection, oscillation is more likely for larger values of transconductance and smaller values of capacitance. A more complicated analysis of the common-base oscillator reveals that a low-frequency amplifier voltage gain must be at least 4 to achieve oscillation.

If the two capacitors are replaced by inductors, and magnetic coupling is ignored, the circuit becomes a Hartley oscillator. In that case, the input impedance is the sum of the two inductors and a negative resistance given by. In the Hartley circuit, oscillation is more likely for larger values of transconductance and larger values of inductance.

The above analysis also describes the behavior of the Pierce oscillator. The Pierce oscillator, with two capacitors and one inductor, is equivalent to the Colpitts oscillator. An electrical dual of the standard Pierce oscillator using two inductors and one capacitor is equivalent to the Hartley oscillator.Analysis of Common-Collector Colpitts Oscillator.

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H R Pota May 20, To be honest, all the different conditions one can use to check for sustained oscillations are different versions of one solid criterion. Figure 1: Feedback System.

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The above idea can be illustrated with the help of the feedback system shown in Figure 1. In this note the above mentioned three versions of the criterion for sustained oscillations are demon- strated. In the second version we break the feedback loop at a point in the circuit; set up an input voltage source at that point and then see the output voltage at the break-point.

Obviously the two. An ideal LC oscillator is shown in Figure 2. Figure 2: Idealised Colpitts Oscillator Analysis. Writing the KVL around the loop in Figure 2. The general solution to the differential equation 1 can be written as. With these initial conditions the general solution is. Now one can see that the voltages v x and v o in Figure 2 can be written as.

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The ratio of the maximum values of v o and v x can be written as:. The gain in equation 6 is greater than one.

The above analysis shows that in an ideal LC circuit in. Figure 2 there will be sustained oscillations at the frequency. Note that this circuit will not have sustained oscillations if any of the three elements is not ideal, i. Small-signal equivalent circuit of a common-collector Colpitts oscillator [3, Section ] is shown in Figure 3. Figure 3: Common-collector Colpitts oscillator small-signal equivalent. A simple analysis can be performed on this circuit to see if it will work as an oscillator and if yes.

### Colpitts Oscillator-Tank Circuit,Applications

In practice the gain needs to be larger than unity why? To do this analysis the feedback loop in Figure 3 is broken at the base of the transistor as shown in Figure 4 and a relationship between v i and v o is dervied to investigate if the conditions for oscillation are met or not. Figure 4: Open-loop CC Colpitts oscillator small-signal equivalent. After replacing the transistor with its Thevenin. Figure 5: Open-Loop Colpitts Oscillator. Writing KCL at the node 1 in Figure 5 we get.

Also note that. The resonant frequency is then given as:. This is because the gain or the transfer function V o s. Substituting the value of the resonant frequency in the equation 10 we get. A General Analysis. In a general case where the resonant circuit is not a simple combination of LC 1and C 2the above analysis can be repeated by replacing them with general impedances Z 1Z 2and Z 3.

Following an analysis similar to the one done for Figure 5 the transfer function for the circuit in. Figure 6 is given as, V o s.

The analysis in [2, Section 8. Here we analyse the entire circuit in one go and see what we get. The voltage source Li 0 is due to the initial current in the inductor. The KVL at the two nodes can be written as:.An oscillator is used to produce electronic signal with oscillating periods. Eg: Sine wave, square wave etc. Oscillators are broadly classified into two — linear oscillators and non-linear oscillators. As the name implies, linear oscillators are used to produce linear or sinusiodal waveforms.

Whereas, non-linear oscillators are used to produce non-linear non-sinusoidal output waveforms. All types of electronic oscillators use their input voltage to control the oscillation frequency.

Colpitts Oscillator is an electronic oscillator which uses an inductor and capacitors to form an LC oscillator circuit. Colpitts oscillator was invented by American scientist Edwin Colpitts in It is another type of sinusoidal LC oscillator and is basically a harmonic oscillator, which has a lot of applications.

The Colpitts oscillator can be realized using valves, transistors, FETs or op-amp. It is much similar to the Hartley oscillator except the addition of tank circuit.

In Colpitts oscillator the tank circuit consists of two capacitors in series and an inductor connected in parallel to the serial combination. The frequency of the oscillations are determined by the value of the capacitors and inductor in the tank circuit. Thus the main difference between a Colpitts Oscillator and a Hartley Oscillator is that the former uses tapped capacitance, while the latter uses tapped inductance.

In Colpitts oscillator, the capacitive voltage divider setup in the tank circuit works as the feed back source and this arrangement gives better frequency stability when compared to the Hartley oscillator which uses an inductive voltage divider setup for feedback. The circuit diagram of a typical Colpitts oscillator using transistor is shown in the figure below.

In the circuit diagram resistors R1 and R2 gives a voltage divider biasing to the transistor. Resistor R4 limits the collector current of the transistor. Cin is the input DC decoupling capacitor while Cout is the output decoupling capacitor. Re is the emitter resistor and its meant for thermal stability.

### Colpitts Oscillator

Ce is the emitter by-pass capacitor. Job of the emitter by-pass capacitor is to by-pass the amplified AC signals from dropping across Re. The the emitter by-pass capacitor is not there, the amplified AC signal will drop across Re and it will alter the DC biasing conditions of the transistor and the result will be reduced gain. Capacitors C1, C2 and inductor L1 forms the tank circuit. Feedback to the base of transistor is taken from the junction of Capacitor C2 and inductor L1 in the tank circuit.

When they are fully charged they starts discharging through the inductor L1.

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When the capacitors are fully discharged, the electrostatic energy stored in the capacitors gets transferred to the inductor as magnetic flux. The the inductor starts discharging and capacitors gets charged again. This transfer of energy back and forth between capacitors and inductor is the basis of oscillation. Voltage across C2 is phase opposite to that of the voltage across the C1 and it is the voltage across C2 that is fed back to the transistor. The feedback signal at the base base of transistor appears in the amplified form across the collector and emitter of the transistor. The energy lost in the tank circuit is compensated by the transistor and the oscillations are sustained. That means the input and output are in phase and it is a necessary condition of positive feedback for maintaining sustained oscillations.

The frequency of oscillations of the Colpitts oscillator can be determined using the equation below. Where L is the inductance of the inductor in the tank circuit and C is the effective capacitance of the capacitors in the tank circuit. By using ganged variable capacitors in place of C1 and C2, the Colpitts oscillator can be made variable.

all about colpotts oscillator --BE--OU EDUCATION

Main advantage of Colpitts oscillator over Hartley oscillator is the improved performance in the high frequency region. This is because the capacitors provide a low reactance path for the high frequency signals and thus the output signals in the high frequency domain will be more sinusoidal. Due to the excellent performance in the high frequency region, the Colpitts oscillator can be even used in microwave applications.

The circuit diagram of a Colpitts oscillator using opamp is shown in the figure above.