Difference between revisions of "Analog Tutorial Lesson 10: Designing High Frequency BJT Colpitts Oscillators"

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|All versions|{{download|http://www.emagtech.com/content/project-file-download-repository|EM.Tempo Lesson 1|[[EM.Cube]] 14.8}} }}
 
|All versions|{{download|http://www.emagtech.com/content/project-file-download-repository|EM.Tempo Lesson 1|[[EM.Cube]] 14.8}} }}
  
<b>Designing Low and High Frequency Oscillator Circuits</b>
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=== What You Will Learn ===
 
+
=== Objective ===
+
  
 
[[File:TUT12-1.png|thumb|400px| The Wien Bridge Oscillator.]]  
 
[[File:TUT12-1.png|thumb|400px| The Wien Bridge Oscillator.]]  
 
In the first part of this tutorial lesson, you will build a Wien Bridge Oscillator using an LM741 Op-Amp and will analyze its oscillatory behavior. In the second part, you will build and test a high frequency Colpitts oscillator using a parallel resonant LC circuit. The primary objective of this tutorial lesson is to underline the challenges of analyzing oscillator circuits.     
 
In the first part of this tutorial lesson, you will build a Wien Bridge Oscillator using an LM741 Op-Amp and will analyze its oscillatory behavior. In the second part, you will build and test a high frequency Colpitts oscillator using a parallel resonant LC circuit. The primary objective of this tutorial lesson is to underline the challenges of analyzing oscillator circuits.     
 
 
 
=== Designing and Testing a Wien Bridge Oscillator===
 
 
The following is a list of parts needed for this part of the tutorial lesson:
 
 
----
 
 
Voltage Source VCC: 15V
 
 
Voltage Source VEE: -15V
 
 
LM741 Op-Amp: Accessible form "Parts > Integrated Circuits" menu
 
 
Four Resistors: R1, R2, R3 and R4
 
 
Two Capacitors: C1 and C2
 
 
----
 
 
The Wien Bridge Oscillator comprises an Op-Amp, four resistors and two capacitors. The oscillator can also be viewed as a positive gain amplifier combined with a bandpass filter that provides positive feedback. At the resonant frequency, the reactance of the series R2–C2 arm will be an exact multiple of the shunt R1–C1 arm. If the two R3 and R4 arms are adjusted to the same ratio, then the bridge is balanced. These conditions can be written as:
 
 
<math>\omega^2 = \frac {1}{R_1 R_2 C_1 C_2}</math>
 
 
and
 
 
<math> \frac {C_1}{C_2} = \frac {R_4}{R_3} - \frac {R_2}{R_1}</math>
 
 
 
This can be further simplified by setting R1 = R2 = R and C1 = C2 = C. In that case, setting R4 = 2 R3 will satisfy the above conditions and will lead to the following simple equation for the oscillation frequency:
 
 
<math>f_o = \frac {1}{2 \pi RC}</math>
 
 
For this project, you will initially choose R1 = R2 = 10k, R3 = 10k, R3 = 2 R3 = 20k, and C1 = C3 = 100pF. Place and connect all the parts as shown in the above figure. Place a voltage probe marker at the output of the Op-Amp. The oscillation frequency of this circuit must be f<sub>o</sub> = 1 / (2&pi; . 1e+4 . 1e-9) = 15.9kHz. 
 
Run a Transient Test of this circuit with start and stop times set to 0 and 25ms and a Step Ceiling of 1&mu;s. You will get a graph like the one shown below.
 
 
<table>
 
<tr>
 
<td>
 
[[File:TUT12-2.png|thumb|800px|The output voltage of the Wien Bridge Oscillator when R4 = 20k.]]
 
</td>
 
</tr>
 
</table>
 
 
The circuit is certainly not oscillating in a sustainable way as the output voltage fluctuates around 3.3mV. Next, change the value of R4 to 21k and run a new Transient Test. This time you will get a fairly large oscillation between -5V and +5V as show below.
 
 
<table>
 
<tr>
 
<td>
 
[[File:TUT12-3.png|thumb|800px|The output voltage of the Wien Bridge Oscillator when R4 = 21k.]]
 
</td>
 
</tr>
 
</table>
 
 
In order to calculate the oscillation frequency, first zoom in the graph window by clicking the "Zoom In" button of the [[Graph toolbar|Graph Toolbar]]. Then use the "Delta Tool" of the [[Graph toolbar|Graph Toolbar]] to measure the distance between two successive peaks of the sinusoidal signal. The period is about 78.5&mu;s, which gives an oscillation frequency of 12.75kHz.     
 
 
<table>
 
<tr>
 
<td>
 
[[File:TUT12-4.png|thumb|800px|Measuring the signal period on a close-up of the output voltage of the Wien Bridge Oscillator when R4 = 21k.]]
 
</td>
 
</tr>
 
</table>
 
 
Next, reduce the value of R4 further to 20.25k and run a new Transient Test again, but this time with a stop time of 50ms. You will notice that the sustainable oscillations start at much later time around 30ms with a reduced peak-to-peak level. If you zoom in the graph and measure the signal period, you will note that it has reduced to 71.5&mu;s, which gives an oscillation frequency of about 14kHz, fairly close to the design frequency.     
 
 
 
<table>
 
<tr>
 
<td>
 
[[File:TUT12-5.png|thumb|800px|The output voltage of the Wien Bridge Oscillator when R4 = 20.25k.]]
 
</td>
 
</tr>
 
</table>
 
 
=== Analyzing the Wien Bridge Oscillator and Explaining Its Behavior ===
 
 
The above behavior of the circuit can be explain using the feedback theory. The Wien Bridge Oscillator is indeed an non-inverting Op-Amp amplifier with positive feedback provided using two series and shunt RC impedances: 
 
 
 
<math>Z_1(s) = \frac {R . \frac{1}{sC}}{R + \frac{1}{sC}}  </math>
 
 
 
<math>Z_2(s) = R + \frac{1}{sC}  </math>
 
 
 
The gain of the non-inverting amplifier is given by:
 
 
 
<math>A = 1 + \frac{R_4}{R_3}  </math>
 
 
 
The feedback gain can be found from the voltage divider:
 
 
 
<math> \beta (s) = \frac{Z_1(s)}{Z_1(s) + Z_2(s)} = \frac {sRC} {s^2 R^2 C^2 + 3sRC + 1} </math>
 
 
 
The Barkhausen criterion for oscillation requires that T(s) = A&beta;(s) &ge; 1. Substituting s = j&omega;, one can write:
 
 
 
<math> T(j\omega) = A \beta(j\omega) = \frac {j\omega RC} {(1-\omega ^2 R^2 C^2)+ 3j\omega RC} </math>
 
 
 
A zero phase shift can be achieved only if 
 
 
 
<math> 1-\omega ^2 R^2 C^2 = 0 </math>
 
 
 
which lead to the oscillation frequency &omega;<sub>o</sub> = 1/(RC). This further simplifies the Barkhausen criterion to
 
 
 
<math> T(j\omega) = \frac {A}{3} \ge 1</math>
 
 
 
which means that A = 1 + R<sub>4</sub>/R<sub>3</sub> &ge; 3 or R<sub>4</sub> &ge; 2R<sub>3</sub>. This shows that setting R<sub>4</sub> = 2R<sub>3</sub> provides the threshold of oscillation. For R<sub>4</sub> &gt; 2R<sub>3</sub>, positive feedback causes the oscillations to grow indefinitely. 
 
 
  
=== Designing a BJT Colpitts Oscillator ===
+
== Designing a BJT Colpitts Oscillator ==
  
 
[[File:TUT12-6.png|thumb|400px| The Colpitts Oscillator.]]  
 
[[File:TUT12-6.png|thumb|400px| The Colpitts Oscillator.]]  
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<math>A \beta(s) = \left( \frac{C_3}{C_3 + C_4} \right). \left( \frac{I_C}{V_T} \right). R_3 \ge  1</math>
 
<math>A \beta(s) = \left( \frac{C_3}{C_3 + C_4} \right). \left( \frac{I_C}{V_T} \right). R_3 \ge  1</math>
  
=== Building and Testing the Colpitts Oscillator ===
+
== Building & Testing the Colpitts Oscillator ==
  
 
For this project, you will choose L1 = 27&mu;H, C1 = 100nF, C2 = 1nF, C3 = 1nF, C4 = 15nF, R1 = 22k, R2 = 10k, R3 = 2k and R4 = 1k. Place and connect all the parts as shown in the above figure. Place a voltage probe marker at the output of the oscillator circuit at the collector of Q1. For the given inductance and capacitance value, the oscillation frequency of this Colpitts circuit is found to be f<sub>o</sub> = 1MHz.  
 
For this project, you will choose L1 = 27&mu;H, C1 = 100nF, C2 = 1nF, C3 = 1nF, C4 = 15nF, R1 = 22k, R2 = 10k, R3 = 2k and R4 = 1k. Place and connect all the parts as shown in the above figure. Place a voltage probe marker at the output of the oscillator circuit at the collector of Q1. For the given inductance and capacitance value, the oscillation frequency of this Colpitts circuit is found to be f<sub>o</sub> = 1MHz.  
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</table>
 
</table>
  
=== Changing the Tuning of the Colpitts Oscillator ===
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== Changing the Tuning of the Colpitts Oscillator ==
  
 
In this part, let's change the tuning of the parallel LC circuit to get an oscillation frequency of 4MHz. Due to the presence of the square root in the denominator of the formula for f<sub>o</sub>, you need to make the product of L1 and (C3 || C4) 16 times smaller. To do so, set C3 to 0.25nF and L1 to 6.75&mu;H. Run a new transient test of your modified oscillator with the stop time set to 50&mu;s. As you can see from the figure below, the output voltage this time oscillates between 3V and 11V with a period of about 260ns, which corresponds to an oscillation frequency of 3.85MHz.     
 
In this part, let's change the tuning of the parallel LC circuit to get an oscillation frequency of 4MHz. Due to the presence of the square root in the denominator of the formula for f<sub>o</sub>, you need to make the product of L1 and (C3 || C4) 16 times smaller. To do so, set C3 to 0.25nF and L1 to 6.75&mu;H. Run a new transient test of your modified oscillator with the stop time set to 50&mu;s. As you can see from the figure below, the output voltage this time oscillates between 3V and 11V with a period of about 260ns, which corresponds to an oscillation frequency of 3.85MHz.     

Revision as of 04:27, 21 September 2015

Tutorial Project: Designing Low and High Frequency Oscillator Circuits
TUT12-8.png

Objective: In this project, the basic concepts of RF.Spice A/D are demonstrated, and a simple voltage divider is modeled and examined.

Concepts/Features:

Minimum Version Required: All versions

'Download2x.png Download Link: [1]

What You Will Learn

The Wien Bridge Oscillator.

In the first part of this tutorial lesson, you will build a Wien Bridge Oscillator using an LM741 Op-Amp and will analyze its oscillatory behavior. In the second part, you will build and test a high frequency Colpitts oscillator using a parallel resonant LC circuit. The primary objective of this tutorial lesson is to underline the challenges of analyzing oscillator circuits.

Designing a BJT Colpitts Oscillator

The Colpitts Oscillator.

The following is a list of parts needed for this part of the tutorial lesson:


Voltage Source VCC: 12V

NPN BJT: 2N2222

Four Resistors: R1, R2, R3 and R4

Three Capacitors: C1, C2 and C3

Inductor: L1


The opposite figure shows a Colpitts oscillator. The parallel resonant LC circuit consisting of L1 and capacitors C3 and C4 is connected between the base and the collector of transistor Q1, and partial feedback voltage is fed to its emitter through the voltage divider constituted by C3 and C4. The oscillating frequency of Colpitts oscillator can be calculated from:

[math]f_o = \frac {1}{2 \pi \sqrt{ L_1 \left( \frac{C_3 C_4}{C_3 + C_4} \right) } }[/math]

The operating point results obtained through DC Bias Test of the Colpitts Oscillator.

Note that C1 and C2 are bypass and coupling capacitors, respectively. In this Colpitts oscillator circuit, the feedback factor β(s) is C3/(C3 + C4) ≅ C3/C4. The voltage gain A is given by:

[math]A = g_m R = \frac{I_C}{V_T} R_3 = \frac{kI_C}{qT} R_3[/math]

Therefore, the Barkausen criterion can be written as:

[math]A \beta(s) = \left( \frac{C_3}{C_3 + C_4} \right). \left( \frac{I_C}{V_T} \right). R_3 \ge 1[/math]

Building & Testing the Colpitts Oscillator

For this project, you will choose L1 = 27μH, C1 = 100nF, C2 = 1nF, C3 = 1nF, C4 = 15nF, R1 = 22k, R2 = 10k, R3 = 2k and R4 = 1k. Place and connect all the parts as shown in the above figure. Place a voltage probe marker at the output of the oscillator circuit at the collector of Q1. For the given inductance and capacitance value, the oscillation frequency of this Colpitts circuit is found to be fo = 1MHz.

Before running a Transient Test of your Colpitts oscillator, first run a DC Bias Test to find the DC operating point of the BJT. The results of the DC bias test are shown in the opposite figure. According to this table, the quiescent collector current IC is 2.985mA. The Barkhausen criterion in this case is thus satisfied:

[math]A \beta(s) = \left( \frac{1nF}{16nF} \right). \left( \frac{2.985e-3}{26e-3} \right). 2e3 = 14.351 \ge 1[/math]

Now run a Transient Test of your oscillator circuit with start and stop times set at 0 and 100μs, respectively, and a Step Ceiling equal to 1ns. The output voltage graph is shown in the figure below. The output signal oscillates between 2V and 14V. A signal period of almost 1μs can be measured, which corresponds to an oscillation frequency of 1MHz.

The output voltage of the Colpitts Oscillator.

Changing the Tuning of the Colpitts Oscillator

In this part, let's change the tuning of the parallel LC circuit to get an oscillation frequency of 4MHz. Due to the presence of the square root in the denominator of the formula for fo, you need to make the product of L1 and (C3 || C4) 16 times smaller. To do so, set C3 to 0.25nF and L1 to 6.75μH. Run a new transient test of your modified oscillator with the stop time set to 50μs. As you can see from the figure below, the output voltage this time oscillates between 3V and 11V with a period of about 260ns, which corresponds to an oscillation frequency of 3.85MHz.

The output voltage of the modified Colpitts Oscillator with C3 = 0.25nF and L1 = 6.75μH.

Let's see what happen if you try to push the oscillation frequency even higher to 8MHz. For this purpose, let's reduce the value of C3 four times to 62.5pF. Run a new transient test of your oscillator with the stop time set to 50μs. The graph of the output voltage is shown in the figure blow. As you can see, the oscillation breaks down in this case.

The output voltage of the modified Colpitts Oscillator with C3 = 62.5pF and L1 = 6.75μH.

 

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