# Single Tuned Amplifier : Working and Its Applications

The tuned amplifier is one kind of amplifier that can be used for selecting or tuning. The selection process can be done between a set of available frequencies if any frequency to be selected at an exact frequency. The process of selection can be possible using a tuned circuit. When a load of an amplifier circuit is changed with a tuned circuit, then this amplifier is named as a Tuned amplifier circuit. This circuit is nothing but an LC circuit or tank circuit or resonant circuit. This circuit is mainly used for amplifying a signal over a slight band of frequencies that are located at the resonant frequency. As the inductor’s reactance balances the capacitor’s reactance within the tuned circuit at a specific frequency, then this is called resonant frequency, and it can be denoted with ‘fr’. The resonance formula is 2πfL=1/2πfc & fr=1/2π√LC. The tuned amplifier can be classified into three type’s namely single tuned amplifier, double-tuned amplifier and stager tuned the amplifier.

## What is a Single Tuned Amplifier?

The single tuned amplifier is a multistage amplifier, which uses a parallel tuned circuit like a load. But, the LC circuit and tuned circuit in every stage are necessary to be selected to the same frequencies. The configuration used in this amplifier is CE amplifier configurations which contain the parallel tuned circuit. In wireless communication, the RF stage requires a tuned voltage amplifier to choose the preferred carrier frequency as well as to change the passband signal which is allowed.

### Construction

The single tuned amplifier circuit diagram using capacitive coupling is shown below. It is important to notice that for an LC circuit, the value of inductance (L) and capacitance (C) should be chosen that the resonance frequency of resonance must be equal to the frequency signal which is applied.

The output of this circuit can be attained by using inductive and capacitive coupling. But, this circuit uses capacitive coupling. The common emitter capacitor used within the circuit can be a bypass capacitor while the circuits like stabilization & biasing follow by these resistors like R1, R2, and RE The LC circuit used within the collector region acts likes a load. The capacitor is changeable in order to contain a changeable resonant frequency. Huge signal amplification can be attained if the input signal frequency is comparable to the resonance frequency of the tuned circuit.

### Single Tuned Amplifier Operation

The single tuned amplifier operation mainly starts with the high-frequency signal application which can be improved at the transistor’s BE terminal shown in the above circuit. By changing the capacitor used within the LC circuit, the circuit’s resonant frequency is made equal to the given input signal’s frequency.

Here, the higher impedance can be given to the frequency of the signal through the LC circuit. Therefore, a huge o/p can be attained. For an i/p signal with various frequencies, simply the frequency communicates with resonant frequency so that it will get amplified. Whereas other types of frequencies will discard the tuned circuit.

Therefore, merely the preferred frequency signal will be selected & therefore this can be amplified through the LC circuit.

### Voltage Gain and Frequency Response

The voltage gain for the LC circuit can be given by the following equation.

**Av = β Rac/rin**

Here Rac is the LC circuit’s impedance (Rac = L/CR), so the above equation will become

The frequency response of this amplifier is shown below.

We know that the circuit’s impedance is extremely high & completely resistive within nature at the resonance frequency.

As a result, the utmost voltage is attained across RL for an LC circuit at the frequency of resonant.

The tuned amplifier bandwidth is given below.

**BW = f2-f1 => fr/Q**

Here, the amplifier amplifies any frequency in this range.

### Cascading Effect

Basically, cascading of several stages within a tuned amplifier can be done for enhancing the overall system gain. As the entire system gain is the outcome of the product’s gain for every stage within the amplifier.

In a tuned amplifier, when the voltage gain increases, then the bandwidth will decrease. So let’s have a look at how the cascading will affect the entire system’s bandwidth.

Consider an n-stages cascade connection in a single tuned amplifier. The amplifier’s relative gain is equivalent to the system’s gain at the resonant frequency can be represented with the following equation

** |A/A resonance| = 1/√ 1 + (2𝛿 Qe) ^{2}**

In the above equation, Qe denotes an efficient quality factor

𝛿 denotes fractional differences within the frequency.

The overall gain can be obtained by merging the gain of numerous stages in the tuned amplifier

**|A/A resonance| = [1/√ 1 + (2𝛿 Qe) ^{2}]^{n }= 1/ [1 + (2𝛿 Qe)^{2}]n/2**

By comparing the total gain to 1/√2 then we can terminate the 3dB frequencies to this amplifier.

Therefore we will have

**1/[√ 1 + (2𝛿Qe) ^{2}]^{n }= 1/√ 2**

The above equation can be written as

**1 + (2𝛿Qe) ^{2 }= 2^{1/n}**

From the above equation

**2 𝛿 Qe = + or – √21/n -1**

It is a fractional difference within frequency, so it can be written like the following.

**𝛿 = ω – ωr/ ωr = f – fr/fr**

Substitute this into the above equation so we can get

**2 (f – fr/fr ) Qe = + or – √2 ^{1/n} -1**

**2 (f – fr) Qe = + or – fr√2 ^{1/n} -1**

** f – fr = +fr / 2Qe √2 ^{1/n} -1**

Now, **f2 – fr = + fr/2Qe √2 ^{1/n} -1 and fr-f1 = + fr/2Qe √2^{1/n} -1**

The amplifier’s BW using number of cascaded stages can be written as

**B12 = f2 –f1 = (f2 – fr) + (fr-f1)**

Substitute the values in the above equation we can get the following equation.

**B12 = f2 –f1 = fr/2Qe √2 ^{1/n} -1 + fr/2Qe √2^{1/n} -1**

From the above equation

**B12 = 2fr/2Qe √2 ^{1/n} -1 = > fr/Qe √2^{1/n} -1**

**B1 = fr/Qe**

**B12 = B1 fr/Qe √2 ^{1/n} -1**

From the above B12 equation, we can conclude that basically n-stages BW is equal to the sum of a factor & single stage BW.

If the digit of stages can be two, then

**√2 ^{1/n} -1 = √2^{1/2} -1 = 0.643**

If the digit of stages can be three, then

**√2 ^{1/n} -1 = √2^{1/3} -1 = 051**

Therefore, from the above information, it is understandable that when the number of stages increases then BW will be decreased.

### Advantages and Disadvantages

The advantages of a single tuned amplifier include the following.

- The power loss is less due to the lack of collector resistance.
- Selectivity is high.
- The voltage supply of the collector is small due to the lack of Rc.

The disadvantages of a single tuned amplifier include the following.

- The product of gain bandwidth is small

### Applications of Single Tuned Amplifier

The applications of a single tuned amplifier include the following.

- This amplifier is used in the primary internal stage of the radio receiver wherever the selection of the front end can be done using an RF amplifier.
- This amplifier can be used in television circuits.

Thus, this is all about a single tuned amplifier which uses a parallel tank circuit as a load. But, the tank circuit in every stage can be needed to be tuned for the same frequencies. Here is a question for you, which configuration is used in a single tuned amplifier?