The series tuned Colpitts or Clapp oscillator used in the Viking Ranger is by and far the circuit of choice for this application. The circuit features a large inductance to capacitance (L/C) ratio which limits the current flowing in the main oscillator coil. Typical series-tuned Colpitts or Clapp oscillator circuit. The search for the very high inductance required often leads to the use of inductors supported on plastic strips. These coils not only have very large temperature coefficients, but also poor retrace characteristics.

• Clapp Oscillator Application
• Clapp Oscillator Circuit Diagram
• Yig Tuned Oscillator
• Common Collector Clapp Oscillator
• Clapp Oscillator Operation

A Colpitts oscillator, invented in 1918 by American engineer Edwin H. Colpitts,^[1] is one of a number of designs for LC oscillators, electronic 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.^[2][3][4][5]

• 1Overview
• 2Theory

Overview[edit]

The Colpitts circuit, like other LC oscillators, consists of a gain device (such as a bipolar junction transistor, field-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 oscillator, where the feedback signal is taken from an 'inductive' voltage divider consisting of two coils in series (or a tapped coil). Fig. 1 shows the common-base Colpitts circuit. L and the series combination of C₁ and C₂ form the parallel resonant tank circuit, which determines the frequency of the oscillator. The voltage across C₂ is applied to the base-emitter junction of the transistor, as feedback to create oscillations. Fig. 2 shows the common-collector version. Here the voltage across C₁ 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:

${\displaystyle f_0=\frac{1}{2\pi \sqrt{L\frac{C_1{C}_2}{C_1+C_2}}}.}$

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).

Practical example[edit]

Fig. 3 shows a working example with component values. Instead of bipolar junction transistors, other active components such as field-effect transistors or vacuum tubes, capable 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.^[6] 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.^[7]

Theory[edit]

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

${\displaystyle Z_{\text{in}}=\frac{v_1}{i_1},}$

where ${\displaystyle v_1}$ is the input voltage, and ${\displaystyle i_1}$ is the input current. The voltage ${\displaystyle v_2}$ is given by

${\displaystyle v_2=i_2{Z}_2,}$

where ${\displaystyle Z_2}$ is the impedance of ${\displaystyle C_2}$. The current flowing into ${\displaystyle C_2}$ is ${\displaystyle i_2}$, which is the sum of two currents:

${\displaystyle i_2=i_1+i_s,}$

where ${\displaystyle i_s}$ is the current supplied by the transistor. ${\displaystyle i_s}$ is a dependent current source given by

${\displaystyle i_s=g_m(v_1-v_2),}$

where ${\displaystyle g_m}$ is the transconductance of the transistor. The input current ${\displaystyle i_1}$ is given by

${\displaystyle i_1=\frac{v_1-v_2}{Z_1},}$

where ${\displaystyle Z_1}$ is the impedance of ${\displaystyle C_1}$. Solving for ${\displaystyle v_2}$ and substituting above yields

${\displaystyle Z_{\text{in}}=Z_1+Z_2+g_m{Z}_1{Z}_2.}$

The input impedance appears as the two capacitors in series with the term ${\displaystyle R_{\text{in}}}$, which is proportional to the product of the two impedances:

${\displaystyle R_{\text{in}}=g_m{Z}_1{Z}_2.}$

If ${\displaystyle Z_1}$ and ${\displaystyle Z_2}$ are complex and of the same sign, then ${\displaystyle R_{\text{in}}}$ will be a negative resistance. If the impedances for ${\displaystyle Z_1}$ and ${\displaystyle Z_2}$ are substituted, ${\displaystyle R_{\text{in}}}$ is

${\displaystyle R_{\text{in}}=\frac{-g_m}{{\omega }^2{C}_1{C}_2}.}$

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.

For the example oscillator above, the emitter current is roughly 1 mA. The transconductance is roughly 40 mS. Given all other values, the input resistance is roughly

${\displaystyle R_{\text{in}}=-30\mathrm{\Omega }.}$

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.^[8] The low-frequency gain is given by

${\displaystyle A_v=g_m{R}_p\ge 4.}$

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

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${\displaystyle R_{\text{in}}=-g_m{\omega }^2{L}_1{L}_2.}$

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.^[9] Equivalence can be shown by choosing the junction of the two capacitors as the ground point. An electrical dual of the standard Pierce oscillator using two inductors and one capacitor is equivalent to the Hartley oscillator.

Oscillation amplitude[edit]

The amplitude of oscillation is generally difficult to predict, but it can often be accurately estimated using the describing function method.

For the common-base oscillator in Figure 1, this approach applied to a simplified model predicts an output (collector) voltage amplitude given by^[10]

${\displaystyle V_C=2I_C{R}_L\frac{C_2}{C_1+C_2},}$

where ${\displaystyle I_C}$ is the bias current, and ${\displaystyle R_L}$ is the load resistance at the collector.

This assumes that the transistor does not saturate, the collector current flows in narrow pulses, and that the output voltage is sinusoidal (low distortion).

This approximate result also applies to oscillators employing different active device, such as MOSFETs and vacuum tubes.

References[edit]

1. ^US 1624537, Colpitts, Edwin H., 'Oscillation generator', published 1 February 1918, issued 12 April 1927
2. ^Gottlieb, Irving Gottlieb (1997). Practical Oscillator Handbook. US: Elsevier. p. 151. ISBN0750631023.
3. ^Carr, Joe (2002). RF Components and Circuits. US: Newnes. p. 127. ISBN0750648449.
4. ^Basak, A. (1991). Analogue Electronic Circuits and Systems. UK: Cambridge University Press. p. 153. ISBN0521360463.
5. ^Rohde, Ulrich L.; Matthias Rudolph (2012). RF / Microwave Circuit Design for Wireless Applications, 2nd Ed. John Wiley & Sons. pp. 745–746. ISBN978-1118431405.
6. ^University of California Santa Barbara Untitled Publication, p. 3.
7. ^S. Sarkar, S. Sarkar, B. C. Sarkar. 'Nonlinear Dynamics of a BJT Based Colpitts Oscillator with Tunable Bias Current'Archived 2014-08-14 at the Wayback Machine. IJEATISSN2249-8958, Volume-2, Issue-5, June 2013. p. 1.
8. ^Razavi, B. Design of Analog CMOS Integrated Circuits. McGraw-Hill. 2001.
9. ^Theron Jones. 'Design a Crystal Oscillator to Match Your Application'Archived 2015-01-22 at the Wayback Machine. Maxim tutorial 5265 Sep 18, 2012, Maxim Integrated Products, Inc.
10. ^Chris Toumazou, George S. Moschytz, Barrie Gilbert. Trade-Offs in Analog Circuit Design: The Designer's Companion, Part 1.

Further reading[edit]

• Lee, T. (December 2003). The Design of CMOS Radio-Frequency Integrated Circuits. Cambridge University Press. ISBN978-0521835398.
• Rohde, Ulrich L.; Poddar, Ajay K.; Böck, Georg (May 2005). The Design of Modern Microwave Oscillators for Wireless Applications. New York, NY: John Wiley & Sons. ISBN0-471-72342-8..
• Vendelin, George; Pavio, Anthony M.; Rohde, Ulrich L. (May 2005). Microwave Circuit Design Using Linear and Nonlinear Techniques. New York, NY: John Wiley & Sons. ISBN0-471-41479-4..
• Rohde, Ulrich L.; Apte, Anisha M. (August 2016). 'Everything You Always Wanted to Know About Colpitts Oscillators'. IEEE Microwave Magazine. 17 (6): 59–76. doi:10.1109/MMM.2016.2561498.
• Apte, Anisha M.; Poddar, Ajay K.; Rohde, Ulrich L.; Rubiola, Enrico (2016). Colpitts oscillator: A new criterion of energy saving for high performance signal sources. IEEE International Frequency Control Symposium. doi:10.1109/FCS.2016.7546729.

The Clapp oscillator or Gouriet oscillator is an LC electronic oscillator that uses a particular combination of an inductor and three capacitors to set the oscillator's frequency. LC oscillators use a transistor (or vacuum tube or other gain element) and a positive feedback network. The oscillator has good frequency stability.

History[edit]

Clapp Oscillator Application

The Clapp oscillator design was published by James Kilton Clapp in 1948 while he worked at General Radio.^[1] According to Vačkář, oscillators of this kind were independently developed by several inventors, and one developed by Gouriet had been in operation at the BBC since 1938.^[2]

Circuit[edit]

Clapp Oscillator Circuit Diagram

The Clapp oscillator uses a single inductor and three capacitors to set its frequency. The Clapp oscillator is often drawn as a Colpitts oscillator that has an additional capacitor (C₀) placed in series with the inductor.^[3]

The oscillation frequency in Hertz (cycles per second) for the circuit in the figure, which uses a field-effect transistor (FET), is

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${\displaystyle f_0=\frac{1}{2\pi }\sqrt{\frac{1}{L}\left(\frac{1}{C_0}+\frac{1}{C_1}+\frac{1}{C_2}\right)}.}$

The capacitors C₁ and C₂ are usually much larger than C₀, so the 1/C₀ term dominates the other capacitances, and the frequency is near the series resonance of L and C₀. Clapp's paper gives an example where C₁ and C₂ are 40 times larger than C₀; the change makes the Clapp circuit about 400 times more stable than the Colpitts oscillator for capacitance changes of C₂.^[4]

Capacitors C₀, C₁ and C₂ form a voltage divider that determines the amount of feedback voltage applied to the transistor input.

Yig Tuned Oscillator

Although, the Clapp circuit is used as a variable frequency oscillator (VFO) by making C₀ a variable capacitor, Vačkář states that the Clapp oscillator 'can only be used for operation on fixed frequencies or at the most over narrow bands (max. about 1:1.2).'^[5] The problem is that under typical conditions, the Clapp oscillator's loop gain varies as f ⁻³, so wide ranges will overdrive the amplifier. For VFOs, Vačkář recommends other circuits. See Vačkář oscillator.

References[edit]

1. ^Clapp, J. K. (March 1948). 'An inductance-capacitance oscillator of unusual frequency stability'. Proc. IRE. 367: 356–358.
2. ^Vačkář, Jiri (December 1949). LC Oscillators and their Frequency Stability(PDF) (Report). Prague, Czechoslovakia: Tesla National Corporation. Tesla Technical Report. Archived from the original(PDF) on 2009-01-24. Retrieved 2008-12-20.
3. ^Department of the Army (1963) [1959]. Basic Theory and Application of Transistors. Dover. pp. 171–173. TM 11-690. Modification of the Colpitts oscillator by including a capacitor in series with winding 1–2 of the transformer results in the Clapp oscillator.
4. ^Clapp 1948, p. 357
5. ^Vačkář 1949, pp. 5–6

Further reading[edit]

• Ulrich L. Rohde, Ajay K. Poddar, Georg Böck 'The Design of Modern Microwave Oscillators for Wireless Applications ', John Wiley & Sons, New York, NY, May, 2005, ISBN0-471-72342-8.
• George Vendelin, Anthony M. Pavio, Ulrich L. Rohde ' Microwave Circuit Design Using Linear and Nonlinear Techniques ', John Wiley & Sons, New York, NY, May, 2005, ISBN0-471-41479-4.
• A. Grebennikov, RF and Microwave Transistor Oscillator Design. Wiley 2007. ISBN978-0-470-02535-2.

External links[edit]

Common Collector Clapp Oscillator

• Media related to Clapp oscillators at Wikimedia Commons
• EE 322/322L Wireless Communication Electronics —Lecture #24: Oscillators. Clapp oscillator. VFO startup

Clapp Oscillator Operation