Relaxation Oscillator Circuit Analysis

A relaxation oscillator is a type of non-linear electronic oscillator that produces a non-sinusoidal output waveform, such as a sawtooth or square wave. These oscillators are often built using a Unijunction Transistor (UJT) as the active switching element, along with a capacitor and a resistor that control the charging and discharging cycles, thus determining the oscillation frequency.

The Unijunction Transistor (UJT) is a three-terminal semiconductor device. It is unique because it exhibits a negative resistance characteristic, meaning its voltage across the emitter-base1 junction decreases as the current through it increases in a certain region. This characteristic makes it ideal for timing circuits, trigger circuits, and, as in this case, relaxation oscillators.

UJT Parameters Provided

We are given the following parameters for the Unijunction Transistor (UJT) in the relaxation oscillator circuit:

• Interbase Resistance (\(R_{BB}\)): This is the total resistance between the two base terminals (\(B_1\) and \(B_2\)) of the UJT. For this problem, \(R_{BB} = 5 \text{ k}\Omega\).
• Intrinsic Standoff Ratio (\(\eta\)): This is a crucial characteristic parameter of the UJT. It represents the ratio of the internal resistance \(R_{B1}\) (the resistance between the emitter and base 1) to the total interbase resistance \(R_{BB}\). Here, \(\eta = 0.6\).
• Valley Voltage (\(V_v\)): This is the voltage at the valley point on the UJT's emitter characteristic curve, where the UJT transitions from its negative resistance region to its saturation region. We are given \(V_v = 1 \text{ V}\).
• Valley Current (\(I_v\)): This is the current at the valley point on the UJT's emitter characteristic curve. For this problem, \(I_v = 10 \text{ mA}\).
• Peak Point Current (\(I_p\)): This is the current at the peak point on the UJT's emitter characteristic curve, where the UJT switches from its cutoff region to its negative resistance region. It is given as \(I_p = 10 \text{ \mu A}\).

The question specifically asks for the value of \(R_{B1}\), which is the internal resistance of the UJT between its emitter and base 1 terminals.

Calculating \(R_{B1}\) for the UJT

The intrinsic standoff ratio (\(\eta\)) of a Unijunction Transistor (UJT) is fundamentally defined by the ratio of its internal resistances. Specifically, it is the ratio of \(R_{B1}\) (the resistance from the emitter junction to base 1) to the total interbase resistance \(R_{BB}\).

The mathematical relationship is given by the formula:

\[ \eta = \frac{R_{B1}}{R_{BB}} \]

To find \(R_{B1}\), we can rearrange this formula:

\[ R_{B1} = \eta \times R_{BB} \]

Step-by-Step Calculation of \(R_{B1}\)

Let's substitute the given values into the derived formula:

• The intrinsic standoff ratio \(\eta = 0.6\).
• The interbase resistance \(R_{BB} = 5 \text{ k}\Omega\).

Now, perform the calculation:

\[ R_{B1} = 0.6 \times 5 \text{ k}\Omega \]

\[ R_{B1} = 3 \text{ k}\Omega \]

It's important to recognize that while other parameters like \(V_v\), \(I_v\), and \(I_p\) are vital for understanding the complete operating characteristics and design of a relaxation oscillator circuit, they are not needed for this specific calculation of \(R_{B1}\) when \(\eta\) and \(R_{BB}\) are provided.

Conclusion on \(R_{B1}\) Value

Based on the intrinsic standoff ratio (\(\eta\)) and the interbase resistance (\(R_{BB}\)) provided for the UJT in the relaxation oscillator circuit, the calculated value of \(R_{B1}\) is \(3 \text{ k}\Omega\).