Clapp circuit

Fig. 1: Clapp oscillator with tube

The Clapp oscillator was developed by James K. Clapp and published in 1948. According to an article by Vackář, the principle was developed independently by other engineers; a variant of Gouriet had been in operation with the BBC since 1938 . It can be seen as an improvement on the Colpitts circuit .

An electron tube was used as an amplifier (Fig. 1). The frequency-determining resonant circuit consists of the coil and the three capacitors connected in series. The frequency-determining capacitor C _{1 is} not included in the positive feedback. As in the Colpitts circuit, the other two capacitors C ₂ and C ₃ form a voltage divider at which part of the resonant circuit voltage is fed back to the cathode and thus amplified.

The circuit is suitable for high frequencies, where high frequency stability is necessary and coil tapping, as in the Hartley oscillator, is not practical.

For a tuning oscillator in the superhet receiver, the Clapp oscillator is better suited for higher frequencies than the Colpitts oscillator. The tuning capacitor C1 has one connection to ground. In addition, the overall gain between the low oscillator frequency and the high oscillator frequency does not change as much as with the Colpitts oscillator. The Hartley circuit is also suitable as a tuning oscillator if coil tapping is justifiable.

The data from the coil and capacitor of the resonant circuit essentially define the generated frequency using Thomson's resonance formula . The additional capacities of the remaining components reduce this calculated frequency.

Transistor circuit

Fig. 2: Clapp oscillator with JFET in gate circuit

The frequency-determining components in the Clapp oscillator circuit in FIG. 2 are the two capacitors C ₁ , C ₂ and the inductance L ₁ , which are known from the Colpitts circuit . Additional frequency-determining components are the variable capacitor C ₃ for frequency setting and the HF choke L ₂ . 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 amplifier output (JFET drain connection) is divided by the capacitive voltage divider C ₁ , C ₂ and fed into the amplifier input (JFET source connection). The gain of J ₁ is adjusted by R ₁ . Due to the component tolerances of J ₁ , it is often necessary to make R ₁ adjustable in order to achieve both goals, safe oscillation and low harmonics . With C ₄ the output signal of the oscillator is decoupled. The RC element R ₂ , C ₅ sifts the operating voltage . The operating voltage is fed to the JFET drain connection via the HF choke L ₂ .

The load resistance R _L does not belong to the oscillator, but is a substitute element for the input resistance of the following stage. The parallel resistance R _P1 reduces the quality factor of the resonant circuit to Q = 100. The quality of the HF choke is set to Q = 65 with R _P2 . The values ​​of load resistance and quality factor are important for the dimensioning or the circuit simulation .

Equivalent circuit

The equivalent circuit of the Clapp oscillator is calculated in two steps. First the reactances are calculated, then the real resistances . The reactances from to , and determine the generated frequency. After calculating the effective resistances, which also include , and , the voltage transmission ratio of and can be calculated. ${\displaystyle C_{1}}$ ${\displaystyle C_{3}}$ ${\displaystyle L_{1}}$ ${\displaystyle L_{2}}$ ${\displaystyle R_{P_{1}}}$ ${\displaystyle R_{P_{2}}}$ ${\displaystyle R_{i}}$ ${\displaystyle N}$ ${\displaystyle C_{1}}$ ${\displaystyle C_{2}}$

Calculation of reactances

The circuit oscillates at the frequency for which the sum of the reactances becomes zero. In Thomson's oscillation equation with two frequency-determining components, the approach is . Inductive reactances are positive and capacitive reactances are negative . If reactances are in series, such as and , the reactances are added. The total reactance of reactances in parallel is calculated with: ${\displaystyle 0=X_{L}+X_{C}}$ ${\displaystyle \left(X_{L}>0\right)}$ ${\displaystyle \left(X_{C}<0\right)}$ ${\displaystyle C_{3}}$ ${\displaystyle L_{1}}$ ${\displaystyle X_{G}}$

${\displaystyle {\frac {1}{X_{G}}}={\frac {1}{X_{1}}}+{\frac {1}{X_{2}}}+{\frac {1}{X_{3}}}}$

The parallel and series connection of the reactances in the Clapp oscillator result in the following:

${\displaystyle 0={\frac {1}{X_{L_{2}}}}+{\frac {1}{X_{C_{3}}+X_{L_{1}}}}+{\frac {1}{X_{C_{1}}+X_{C_{2}}}}}$

Usually the values ​​from to are searched for for a given frequency and a given “Colpitts inductance” . The Clapp oscillator uses larger inductances than the Colpitts oscillator. It is and . There is , and . The values and cannot yet be calculated. With is the new approach: ${\displaystyle f}$ ${\displaystyle L_{0}}$ ${\displaystyle C_{1}}$ ${\displaystyle C_{3}}$ ${\displaystyle L_{1}=PL_{0}}$ ${\displaystyle L_{2}=AL_{0}}$ ${\displaystyle P>1}$ ${\displaystyle A>P}$ ${\displaystyle A\gg 1}$ ${\displaystyle X_{C_{1}}}$ ${\displaystyle X_{C_{2}}}$ ${\displaystyle X_{C_{0}}=X_{C_{1}}+X_{C_{2}}}$

${\displaystyle 0={\frac {1}{AX_{L_{0}}}}+{\frac {1}{X_{C_{3}}+PX_{L_{0}}}}+{\frac {1}{X_{C_{0}}}}}$

The switch to delivers ${\displaystyle X_{C_{3}}}$

${\displaystyle X_{C_{3}}={\dfrac {1}{-{\dfrac {1}{AX_{L_{0}}}}-{\dfrac {1}{X_{C_{0}}}}}}-PX_{L_{0}}}$

With the definitions of the angular frequency , the inductive reactance and the capacitive reactance becomes ${\displaystyle \omega =2\pi f}$ ${\displaystyle X_{L}=\omega L}$ ${\displaystyle X_{C}=-{\frac {1}{\omega C}}}$

${\displaystyle C_{3}=-{\dfrac {1}{\omega \left({\dfrac {1}{\omega C_{0}-{\dfrac {1}{A\omega L_{0}}}}}-P\omega L_{0}\right)}}}$

The conversion of the resonant circuit formula allows the calculation of and from given values of , , and . ${\displaystyle C_{0}={\frac {1}{\omega ^{2}L_{0}}}}$ ${\displaystyle C_{0}}$ ${\displaystyle C_{3}}$ ${\displaystyle P}$ ${\displaystyle A}$ ${\displaystyle f}$ ${\displaystyle L_{0}}$

Calculation example

Are given , , and . It follows , , and . When is set and the values of , , and remain the same, then . ${\displaystyle P=6}$ ${\displaystyle A=20}$ ${\displaystyle f=30\,\mathrm {MHz} }$ ${\displaystyle L_{0}=500\,\mathrm {nH} }$ ${\displaystyle L_{1}=3\,\mathrm {\mu H} }$ ${\displaystyle L_{2}=10\,\mathrm {\mu H} }$ ${\displaystyle C_{0}=53{,}5\,\mathrm {pF} }$ ${\displaystyle C_{3}=11{,}5\,\mathrm {pF} }$ ${\displaystyle f=15\,\mathrm {MHz} }$ ${\displaystyle P}$ ${\displaystyle A}$ ${\displaystyle C_{0}}$ ${\displaystyle L_{0}}$ ${\displaystyle C_{3}=338\,\mathrm {pF} }$

Calculation of effective resistances

The effective resistances are calculated according to the Colpitts circuit . First, all effective resistances at the amplifier input (source) are combined into a substitute element and all effective resistances at the amplifier output (drain) in . The equation must be fulfilled for the amplitude condition with the voltage-transmission ratio and the amplifier slope . The solution to this quadratic equation is ${\displaystyle R_{E}}$ ${\displaystyle R_{A}}$ ${\displaystyle N}$ ${\displaystyle g_{m}}$ ${\displaystyle N\,g_{m}={\frac {1}{R_{E}}}+{\frac {N^{2}}{R_{A}}}}$

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

The parallel connection of the resistors , and , the input resistance of the amplifier is connected to the amplifier input. For a JFET is . So that ${\displaystyle R_{1}}$ ${\displaystyle R_{L}}$ ${\displaystyle R_{i}}$ ${\displaystyle R_{i}={\frac {1}{g_{m}}}}$

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

The parallel connection of the resistors , and , the output resistance of the amplifier is connected to the amplifier output. The quality factor is for the series connection of and and thus is the effective resistance equivalent element ${\displaystyle R_{P_{1}}}$ ${\displaystyle R_{P_{2}}}$ ${\displaystyle R_{o}}$ ${\displaystyle Q_{1}}$ ${\displaystyle C_{3}}$ ${\displaystyle L_{1}}$

${\displaystyle R_{P_{1}}=Q_{1}\left(\omega L_{1}-{\frac {1}{\omega C_{3}}}\right)}$

The HF choke has the quality factor . The effective resistance replacement element is ${\displaystyle L_{2}}$ ${\displaystyle Q_{2}}$

${\displaystyle R_{P_{2}}=Q_{2}\omega L_{2}}$

The output resistance of the amplifier is very high and is ignored. It will ${\displaystyle R_{o}}$

${\displaystyle {\frac {1}{R_{A}}}={\frac {1}{R_{P_{1}}}}+{\frac {1}{R_{P_{2}}}}}$

Calculation example

Are given , , , , , , , and . It follows and . Next follows and . The smaller value is used . Now you can split into and . ${\displaystyle f=30\,\mathrm {MHz} }$ ${\displaystyle L_{1}=3\,\mathrm {\mu H} }$ ${\displaystyle L_{2}=10\,\mathrm {\mu H} }$ ${\displaystyle C_{0}=53{,}5\,\mathrm {pF} }$ ${\displaystyle R_{1}=220\,\Omega }$ ${\displaystyle R_{L}=200\,\Omega }$ ${\displaystyle g_{m}=3{\frac {\mathrm {mA} }{V}}}$ ${\displaystyle Q_{1}=100}$ ${\displaystyle Q_{2}=65}$ ${\displaystyle R_{E}=79{,}7\,\Omega }$ ${\displaystyle R_{A}=17{,}8\,\mathrm {k\Omega } }$ ${\displaystyle N_{1}=4{,}57}$ ${\displaystyle N_{2}=48{,}9}$ ${\displaystyle N_{1}}$ ${\displaystyle C_{0}}$ ${\displaystyle C_{1}}$ ${\displaystyle C_{2}}$

${\displaystyle C_{1}=C_{0}\,\left({\frac {N+1}{N}}\right)}$

${\displaystyle C_{2}=N\,C_{1}}$

There are and . The calculation of the Clapp oscillator is now complete. ${\displaystyle C_{1}=65{,}2\,\mathrm {pF} }$ ${\displaystyle C_{2}=298\,\mathrm {pF} }$

literature

• H. Ward Silver: The ARRL Handbook for Radio Communications 2013 . 90th edition. American Radio Relay League, 2012, ISBN 0-87259-405-X .
• Wes Hayward: Radio Frequency Design . American Radio Relay League, 1994, ISBN 0-87259-492-0 .
• Tietze, Schenk: semiconductor circuit technology . 14th edition. Springer, 2012, ISBN 3-642-31025-7 .

Individual evidence

1. ^ JK Clapp, "An inductance-capacitance oscillator of unusual frequency stability", Proc. IRE, vol. 367, pp. 356-358, Mar. 1948.
2. ↑ Jiří Vackář , LC Oscillators and their Frequency Stability , TESLA Report 1949, ch. 4 ( Memento from August 13, 2012 on WebCite )
3. ^ Wes Hayward: Radio Frequency Design . ARRL, 1994, ISBN 0-87259-492-0 , Chapter 7.2 The Colpitts Oscillator, p. 274 .
4. ^ Paul Falstad: Circuit Simulator Applet. Retrieved July 8, 2016 .