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# Tuned Amplifiers

 Posted Date: 21-Feb-2008 Last Updated: 21-Feb-2008 Category: General Author: satish Member Level: Gold Points: 5

Tuned Amplifiers

Tuned amplifiers can be constructed from either discrete components (FETs and BJTs) or op-amps. Discrete tuned amplifiers normally employ LC (inductive-capacitive) circuits to determine frequency response. Op-amps are normally tuned with RC (resistive-capacitive) circuits
Tuned Amplifier Characteristics
There are many types of tuned amplifiers. A tuned amplifier may have a lower cutoff frequency ( ), an upper cutoff frequency ( ), or both. An ideal tuned amplifier would have zero ( ) gain up to . Then the gain would instantly jump to until it reaches , when it would instantly drop back to zero. All the frequencies between and are passed by the amplifier. All others are effectively stopped. This is where the terms pass band and stop band come from. The gain of the practical tuned amplifier does not change instantaneously, as shown in Figure 17-1. Note that the value of shown in the figure corresponds to a value of .

FIGURE 17-1 Ideal versus practical pass band characteristics.
There are two basic principles we need to establish:
• The closer a tuned amplifier comes to the ideal, the better.
• In many applications, the narrower the bandwidth, the better.
How close a tuned amplifier comes to having the characteristics of an ideal circuit depends on the quality (Q) of the circuit. The Q of a tuned amplifier is a figure of merit that equals the ratio of its geometric center frequency to its bandwidth. By formula:

The relationship between Q, , and BW is illustrated in Figure 17-2. Note that the lower the Q of an amplifier:
• The lower its value of when operated at .
• The wider its bandwidth.
The equation in Figure 17-2 is somewhat misleading as it implies that Q is dependent upon the circuit’s center frequency and bandwidth. In fact, both Q and are dependent on circuit component values. Once Q and are calculated, BW can be found from

FIGURE 17-2 Bandwidth versus roll-off rate.

is the geometric average of and , found as

If the Q of a tuned amplifier is greater than or equal to 2, then approaches the algebraic average of and , designated as . The value of is found as

Discrete Tuned Amplifiers
Some applications exceed the power handling and/or high-frequency limits of op-amps. In these applications, discrete tuned amplifiers are commonly used. Discrete amplifiers are typically tuned using LC (inductive-capacitive) resonant circuits in place of their collector (or drain) resistors. One such circuit is shown in Figure 17-12.

FIGURE 17-12 Typical BJT tuned amplifier.
The parallel LC (or tank) circuit determines the frequency response of the amplifier. There is a frequency at which . This frequency, called the resonant frequency, is calculated using:

In an ideal resonant circuit, inductor current lags the capacitor current by 180° and the net circuit current is zero. As a result:
• The impedance of a parallel resonant circuit is extremely high.
• The amplifier voltage gain reaches its maximum value when the circuit is operated at .
Figure 17-13 shows the frequency response of an LC tank circuit. When the input frequency ( ) is lower than , the circuit impedance decreases from its maximum value, and is inductive. When is higher than , the circuit impedance drops again, but is capacitive. When operated at , the impedance of the tank circuit reaches its maximum value. As a result, the gain of the tuned amplifier (Figure 17-12) is also at its maximum value.

FIGURE 17-13 Frequency response of an LC tank circuit.
As stated earlier, the Q of a tuned amplifier equals the ratio of to BW. In a discrete tuned amplifier, it is the Q of the parallel LC circuit that determines the amplifier Q. A more accurate definition of Q is the ratio of energy stored in the circuit to the energy lost per cycle by the circuit, which equals the ratio of reactive power (energy stored per second) to resistive power (energy lost per second). Since inductor Q is much lower than capacitor Q, the overall Q of the tank circuit is determined by the inductor. By formula:

where is the winding resistance of the coil.

the procedure used to calculate loaded Q. Once the value of is known, the circuit bandwidth is found using:

Once the values of , BW, and are known, we can then calculate the cutoff frequencies using the following equations:
When : and
When :
and

Discrete Tuned Amplifiers: Practical Considerations and Troubleshooting
It is common to see a significant difference between the calculated and measured center frequencies of a tuned amplifier. Two of the reasons for the difference are as follows:
1. Inductors and capacitors tend to have large tolerances.
2. Amplifiers tend to have many "natural" or stray capacitances that are not accounted for in the frequency calculations. The higher the operating frequency of the circuit, the greater the impact of stray capacitance.
One method to overcome these problems is to include a variable inductor or capacitor in the circuit. The other technique is referred to as electronic or varactor tuning. You may recall that a varactor is a diode that acts as an electronically variable capacitor. It is used to tune the circuit by changing the voltage applied to the varactor (and thus its capacitance).
Applications:
2) In filter design :--Band Pass, low pass, High pass and band reject filter design

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Responses to "Tuned Amplifiers"
Author: Maryam Saeed    26 Apr 2010Member Level: Bronze   Points : 1

Guest Author: Rakesh P     27 Jan 2013
I was searching Tuned amplifiers theory where I got it here, an ideal resonant circuit, inductor current lags the capacitor current by 180° and the net circuit current is zero and its result helpful for my project, good job done by providing article as such in this site which helps student to get their subject online - thanks

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