Colpitts circuit

The Colpitts circuit , also called the Colpitts oscillator , is an oscillator circuit for generating a periodic alternating voltage ( sinusoidal oscillation ). The oscillation frequency is largely determined by the values ​​of the oscillating circuit components . The Colpitts circuit is a capacitive three-point circuit . An oscillator for VHF or UHF frequencies often uses the Colpitts circuit with a transistor in base or gate circuit.

There are different variations of the Colpitts circuit, for example the Clapp , Seiler and Vackář circuit and the Pierce circuit used in digital technology .

history

Figure 1: Figure from the Colpitts oscillator patent

Fig. 2: Electron tube RE064, characteristic curve

The Colpitts oscillator was filed for patent by Edwin H. Colpitts in 1918. An electron tube (triode) in a basic cathode circuit was used as the amplifier . 7 is the cathode, 9 is the grid and 8 is the anode of the tube. The resonant circuit consists of the variable capacitors 13, 16 and the primary winding 20 of the transformer 22. The operating voltage of the battery 11 is supplied via the HF choke 12, which prevents the high-frequency voltage from being short-circuited. (The connections 23 and 24 are required in the description of variants). The vibration generated is picked up at the winding 23.

The frequency-determining network consists of an oscillating circuit with divided capacitance (13 and 16 in patent drawing). At the resonance frequency of the oscillating circuit, the phase shift between the two connections of the inductance is 180 ° (20 in the patent drawing). The triode in the cathode base circuit also has a phase shift of 180 ° between input and output. The sum of the phase shifts is 360 °, and thus the phase condition of the Barkhausen stability criterion is fulfilled. The loop gain must be greater than 1 so that the circuit starts generating oscillations after switching on . When the circuit delivers the desired amplitude, the loop gain has to go back to 1 in order to generate a sine wave with few harmonics . Electron tubes with a tungsten hot cathode can be controlled up to their saturation current. In this area, the slope decreases , as shown by the characteristic curve of the RE064 electron tube in Figure 2 with high grid voltage and high anode voltage. The working point of the triode is chosen so that the loop gain goes back to 1 at the desired amplitude. As a result, the circuit works with current saturation.

Transistor circuit

Fig. 3: Colpitts oscillator with FET

Figure 4: Gate circuit: Frequency-determining network

Figure 5: Practical Seiler circuit ( VFO ) for shortwave receivers (with SSB / CW) with a high first IF of 40 MHz. This VFO is built with a low-noise JFET , has an AFC input and a subsequent amplifier with a 50 Ω output (50 Ω technology).

The resonant circuit in the Colpitts oscillator circuit in Figure 3 consists of the two capacitors C ₁ , C ₂ , the optional capacitor C ₃ , and the inductance L ₁ . The amplifier J ₁ works in a gate circuit and does not rotate the phase between input and output, i.e. by 0 °. The high-frequency voltage at the drain (output) is divided by the capacitive voltage divider C ₁ , C ₂ and fed to the source (input). The gain of J ₁ is adjusted by R ₁ . Due to the component tolerances, it is often necessary to make R ₁ adjustable in order to achieve both goals, reliable oscillation and low harmonics . With C ₄ the output signal of the oscillator is decoupled. The capacitor C ₃ is a variable capacitor for frequency adjustment. The RC element R ₂ , C ₅ sifts the operating voltage .

The load resistance R _L does not belong to the oscillator, but simulates the load on the oscillator through the following stages. The parallel resistance R _P reduces the quality factor of the resonant circuit to Q = 100. The values ​​of load resistance and quality factor are important for the dimensioning or the circuit simulation . The auxiliary resistor R _T is necessary so that the simulator correctly processes the parallel and series connection of capacitors.

The frequency-determining network in Figure 4 consists of a parallel resonant circuit ( L ₁ - C ₁ - C ₂ ), which is fed via the non-visible differential output resistance r _{a of} the gate circuit. You can see the resonant circuit if you consider that the capacitor C ₅ in Figure 3 represents a short circuit for alternating currents and thus the upper end of the coil is connected to earth in terms of alternating currents. The invisible differential input resistance r _{e of} the gate circuit loads the resonant circuit. Since this small resistance is only applied to a partial voltage of the resonant circuit voltage due to the capacitive voltage divider, the attenuation is correspondingly reduced.

Equivalent circuit

The oscillation begins due to the heat noise at the input of the amplifier. The amplification of these minimal voltage fluctuations is well described with the small-signal model of the transistor. The amplitude of the alternating voltage on the resonant circuit increases until the amplitude limitation occurs due to current saturation or voltage saturation. The amplifier now works in large-signal mode. The calculation presented can be used for resonance frequencies up to the shortwave range. Complex numbers are not required for the calculation. At the resonance frequency, the reactances of capacitors and inductances in the resonant circuit cancel each other out. In the gate circuit, the Miller capacitance between the amplifier input and output only acts as an additional resonant circuit capacitance and is therefore also neglected.

For the calculation, the resistors at the amplifier input and the resistances at the output are combined in the Colpitts oscillator with FET circuit . The capacitive voltage divider in the oscillator circuit operates as an impedance converter , and has a voltage transmission ratio of . Resistance values with a resistance transmission ratio of transfer from one side of the capacitive voltage divider to the other. The resistance at the amplifier output is converted into a resistance at the amplifier input using the resistance transmission ratio . All resistors are now at the amplifier input. The amplifier output is connected to the input via the capacitive voltage divider. The amplifier must precisely compensate for the resistance losses in order to meet the amplitude condition. The amplification effect of the JFET is described by the slope . The transformation ratio of the capacitive voltage divider is a dependent variable which is calculated with the quadratic solution formula in order to meet the amplitude condition. ${\displaystyle R_{E}}$ ${\displaystyle R_{A}}$ ${\displaystyle N}$ ${\displaystyle N^{2}}$ ${\displaystyle R_{A}}$ ${\displaystyle R_{A}'}$ ${\displaystyle g_{m}}$ ${\displaystyle N}$

At the amplifier input (source) are the resistances , and the amplifier input resistor in parallel. After is . The equivalent resistance is ${\displaystyle R_{1}}$ ${\displaystyle R_{L}}$ ${\displaystyle R_{i}}$ ${\displaystyle R_{i}={\frac {1}{g_{m}}}}$ ${\displaystyle R_{E}}$

${\displaystyle {\frac {1}{R_{E}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{L}}}+{\frac {1}{R_{i}}}={\frac {1}{R_{1}}}+{\frac {1}{R_{L}}}+g_{m}}$

At the amplifier output (drain) the resistors and the amplifier output resistance are parallel. The amplifier output resistance is high and is therefore neglected. The resistance stands for the resonance circuit losses and depends on the resonance frequency , the inductance and the resonance circuit quality factor . With is ${\displaystyle R_{P}}$ ${\displaystyle R_{o}}$ ${\displaystyle R_{P}}$ ${\displaystyle f}$ ${\displaystyle L}$ ${\displaystyle Q}$ ${\displaystyle R_{P}=2\pi fLQ}$

${\displaystyle {\frac {1}{R_{A}}}={\frac {1}{R_{P}}}={\frac {1}{2\pi fLQ}}}$

At the amplifier input, the effect is lower by a factor . The converted output resistance is ${\displaystyle R_{A}}$ ${\displaystyle N^{2}}$ ${\displaystyle R_{A}'}$

${\displaystyle {\frac {1}{R_{A}'}}={\frac {N^{2}}{R_{A}}}={\frac {N^{2}}{2\pi fLQ}}}$

The amplitude condition is fulfilled if is. It follows ${\displaystyle Ng_{m}={\frac {1}{R_{E}}}+{\frac {1}{R_{A}'}}}$

${\displaystyle N={\frac {1}{g_{m}}}\left({\frac {1}{R_{E}}}+{\frac {1}{R_{A}'}}\right)={\frac {1}{g_{m}}}\left({\frac {1}{R_{E}}}+{\frac {N^{2}}{R_{A}}}\right)}$

For the quadratic formula the equation is rearranged according to

${\displaystyle 0=N^{2}-Ng_{m}R_{A}+{\frac {R_{A}}{R_{E}}}}$

The gear ratio is ${\displaystyle N}$

${\displaystyle N_{1,2}={\frac {g_{m}R_{A}}{2}}\pm {\sqrt {\left({\frac {g_{m}R_{A}}{2}}\right)^{2}-{\frac {R_{A}}{R_{E}}}}}}$

The smaller of the two solutions is used. The larger it is, the more harmonics the oscillator produces. In the circuit should be revised. An increase in and , a higher one through another JFET or a higher one through another inductor helps, as does a lowering of . Finally, the resonant circuit capacity is calculated and divided into and . ${\displaystyle N_{1,2}}$ ${\displaystyle N}$ ${\displaystyle N>10}$ ${\displaystyle R_{1}}$ ${\displaystyle R_{L}}$ ${\displaystyle g_{m}}$ ${\displaystyle Q}$ ${\displaystyle L}$ ${\displaystyle C}$ ${\displaystyle C_{1}}$ ${\displaystyle C_{2}}$

${\displaystyle C={\frac {1}{\left({2\pi f}\right)^{2}L}}}$

${\displaystyle C_{1}=C\left({\frac {N+1}{N}}\right)}$

${\displaystyle C_{2}=NC_{1}}$

Often, something larger is chosen for safe oscillation. After is increased by 2 dB to 4 dB, i.e. H. multiplied by a factor of 1.2 to 1.6. The method shown here can also be used to calculate other oscillator circuits such as Clapp circuits , Seiler oscillators , Hartley circuits or Meissner circuits . ${\displaystyle N}$ ${\displaystyle N}$

Calculation example

The slope of the JFET 2N5484 or MMBF5484 is between and . The desired resonance frequency is , the inductance is, and the resistances are and . The calculation results , , , , , , and . The capacitor is not required in this example. ${\displaystyle g_{m}=3{\frac {mA}{V}}}$ ${\displaystyle g_{m}=6{\frac {mA}{V}}}$ ${\displaystyle f=30MHz}$ ${\displaystyle L=470{nH}}$ ${\displaystyle R_{1}=220\Omega }$ ${\displaystyle R_{L}=200\Omega }$ ${\displaystyle g_{m}=3{\frac {mA}{V}}}$ ${\displaystyle R_{i}=333\Omega }$ ${\displaystyle R_{E}=79{,}7\Omega }$ ${\displaystyle R_{A}=8{,}86k\Omega }$ ${\displaystyle N_{1}=24{,}4}$ ${\displaystyle N_{2}=5{,}20}$ ${\displaystyle C=59{,}9{pF}}$ ${\displaystyle C_{1}=71{,}4{pF}}$ ${\displaystyle C_{2}=371{pF}}$ ${\displaystyle C_{3}}$

The calculation with delivers the results and . The gear ratio increases when it is done. The large component tolerances of transistors often make adjustable resistors necessary. Alternatively, an amplitude control replaces the amplitude limitation. ${\displaystyle g_{m}=6{\frac {mA}{V}}}$ ${\displaystyle N_{1}=50{,}4}$ ${\displaystyle N_{2}=2{,}73}$ ${\displaystyle N=5{,}15}$ ${\displaystyle R_{1}=59\Omega }$

poll

The Colpitts oscillator is well suited for a tuning oscillator in the superhet receiver if the inductance is varied ( variometer tuning). It is less suitable if C ₁ or C _{2 are used} as the tuning capacitor , because this changes the divider ratio and thus the loop gain or the tuning range is restricted by the other capacitor. However, you can make C ₁ and C ₂ much smaller than necessary and connect the tuning capacitor C _{3 in} parallel, as done in the JFET circuit in Figure 3. Alternatives for capacitive tuning are the Clapp circuit , Seiler oscillator , Hartley circuit or the Meißner circuit .

Frequency of the generated vibration

The generated frequency is determined by the inductance of the coil and the series connection of the capacitances of the capacitors C ₁ and C ₂ ( Thomson's resonance formula ):

${\displaystyle f_{\mathrm {res} }={1 \over 2\pi {\sqrt {L_{1}\cdot \left({C_{1}\cdot C_{2} \over C_{1}+C_{2}}\right)}}}}$

The additional capacities of the remaining components reduce this calculated frequency.

literature

• JE Brittain: Edwin H. Colpitts: A pioneer in communications engineering . 6th edition. No. 85 . Proceedings of the IEEE, June 1997, ISSN  0018-9219 , pp. 1020-1021 , doi : 10.1109 / JPROC.1997.598423 .

• Wes Hayward: Radio Frequency Design . In: ARRL (Ed.): Radio Amateur's Library . 1st edition. tape 191 . American Radio Relay League, 1994, ISBN 0-87259-492-0 .

• Ulrich Tietze, Christoph Schenk: Semiconductor circuit technology . 14th edition. Springer, Berlin 2012, ISBN 978-3-642-31025-6 .

Individual evidence

1. ↑ ^{a b} Patent drawing CA 203986 , Patent US1624537 : Oscillation Generator. Applied February 1, 1918 , published April 12, 1927 , Applicant: Western Electric Company, Inventor: EH Colpitts. ‌
2. ^ Wes Hayward: Radio Frequency Design . In: ARRL (Ed.): Radio Amateur's Library . 1st edition. tape 191 . American Radio Relay League, 1994, ISBN 0-87259-492-0 , Chapter 7.2 The Colpitts Oscillator, p. 265-273 .
3. ^ Paul Falstad: Circuit Simulator Applet. Retrieved July 8, 2016 . 
4. ↑ Dennis Melikjan, Prof. Geißler: Chapter 4 Oscillators. (No longer available online.) Archived from the original on September 22, 2015 ; accessed on July 13, 2016 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
5. ↑ Prof. Mark Rodwell: Transistor amplifier crib sheet. Retrieved July 13, 2016 . 
6. ↑ Ulrich Tietze, Christoph Schenk: Semiconductor circuit technology . 14th edition. Springer, Berlin 2012, ISBN 978-3-642-31025-6 , Chapter 26.1.3.1 Calculation for amplifiers without feedback.