Understanding the Resistance Reflection Rule

Key Takeaways

• Discover what the resistance reflection rule is.

• Learn how to calculate the resistance reflection rule.

• Understand the significance of the resistance reflection rule when designing an amplifier with a BJT transistor.

The resistance reflection rule helps designers choose the right resistor values

Growing up, I was an avid fan of FIFA games. Even now, in my late 30s, I still enjoy battling other players in a game of 11 vs. 11. In these games, I relish the moments of greatness when I can easily defeat my opponent. However, with these moments of greatness also come moments of frustration, when I lose a game for reasons out of my control. When such instances happen, I try to accept the outcome and move on, as there isn’t much point in worrying about things that aren’t in my control. 

When designing an amplifier with a BJT transistor, luckily, designers have more variables in their control than when playing a FIFA game. The resistance reflection rule provides insight into how an amplifier will perform in a given configuration. Applying this rule correctly ensures that designing amplifiers is far more predictable and controllable than playing a FIFA game. 

What Is the Resistance Reflection Rule?

The resistance reflection is an essential characteristic of BJT amplifiers 

If you’re designing an amplifier with a bipolar junction transistor (BJT), you need to understand the significance of the resistance reflection rule. This formula determines the characteristics and performance of an amplifier when set up in a particular configuration. To better understand this formula, let’s first take a look at the BJT. 

Bipolar Junction Transistors

The BJT is an electronic component made up of 2 P-N junctions. BJTs have 3 terminals, known as the collector (C), base (B), and emitter (E) terminals. There are two types of BJTs: NPN transistors and PNP transistors. Both types are determined by the order of how the terminals are arranged. 

BJTs can operate in the cut-off, saturated, and active regions. The resistance reflection rule comes into play when a transistor is in an active region. When driven in an active region, the transistor operates as an amplifier, which either amplifies the voltage, current, or both. 

The resistance reflection rule refers to the relationship between the input resistance and output resistance of a transistor. It is derived by solving simple equations of the transistor amplifier circuit. The resulting equation provides a picture of how altering the resistance of the output affects the resistance seen from the input.

Calculating Resistance Reflection for a BJT 

When it comes to amplifiers, the transistor can be configured as a common-emitter, common-based, or common-collector to different effects. The common-emitter amplifier is popular due to its ability to amplify both current and voltage. 

Let’s review a common-emitter configuration of an NPN transistor:

A common-emitter amplifier circuit

In the above circuit, the input resistance from the base is given by:

Expressing the relationship of i_b and i_e  gives:

Also, v_i can be expressed by the following equation, where r_e is the input resistance looking into the emitter: 

Replace both v_i and i_b in the first and second equations, which gives you: 

Equation 4 is the resistance reflection rule for the common-emitter transistor amplifier. From the equation, it can be seen that any changes in the emitter resistance are multiplied by the amplification factor, β. As β averages around 100 in a multi-purpose transistor, the input resistance is significantly large. 

For common-base configurations, you’ll have very low input resistance. As the input is formed by the emitter, the input resistance is as follows:

R_ib = r_e

What about the common-collector configuration? 

The resistance reflection rule for a common-collector configuration can be found through the same method used to solve the same parameter for a common-emitter amplifier.

You’ll get a low input resistance for the common-collector configuration, as follows:

Why Does the Resistance Reflection Rule Matter?

From the resistance reflection rule, you’ll get a good idea of how changes in the output resistance could influence the input resistance. This can help you to choose the right value of the output resistor to get the desired input resistance.

You’re also able to decide the type of transistor amplifier to use in your design. Common-emitter transistors, which have a high input impedance, are usually used for Class A amplifiers. Meanwhile, the common-base transistor’s low input impedance is useful in amplifying high-frequency signals on a coaxial cable. 

Regardless of the application, you’ll need to determine the resistance reflection rule during the design process. Instead of wasting time with tedious calculations, use SPICE software to save time. Additionally, Cadence’s PSpice tool can help simulate circuit parameters, enabling you to easily derive the value.