# What is DC small-signal transfer function?

Can someone please explain to me what is the DC small-signal transfer function? I found this analysis type in LTSpice and I have no idea what it does!

My guess: It linearizes the circuit around the operating point and then basically computes the small signal transfer function, neglecting AC voltage/current sources and plugs in the frequency 0 Hz?

A transfer function is a mathematical relationship linking an injected stimulus $$\U \$$ with a response $$\Y\$$ observed on the output of the network under study. The ratio Y/U defines the transfer function of the circuit. Because U and Y are complex variables - defined by a magnitude and a phase - we can express the transfer function - let's call it $$\H\$$ - in the Laplace domain by $$\H(s)=\frac{Y(s)}{U(s)}\$$.
A transfer function can be written in a low-entropy form - see my book on the subject for details - in which a leading term precedes a polynomial form representative of the poles-zeroes found in the network. In general, the leading term dimension is that of the transfer function, e.g. a resistance for an impedance, a unitless number for a gain and so on. For instance, a filter featuring a pole and a zero could be described by the following transfer function linking its output to its input: $$\H(s)=H_0\frac{1+\frac{s}{\omega_z}}{1+\frac{s}{\omega_p}}\$$. In this expression, $$\H_0\$$ is called the quasi-static gain also often found under the designation of dc gain in which "dc" designates the gain obtain for $$\s=0\$$. This term refers to a dynamic gain obtained after two dc measurements, very close to each other during which the system under study remains linear, hence the term small-signal. Assume an amplifier biased at 3 V from a 1-V input. Bias it to 1.1 V and measure 3.3 V for instance. Then, the quasi-static gain would be defined as $$\H_0=\frac{3.3-3}{1.1-1}=23\$$ or 27.2 dB.
If you run the .TF directive, then SPICE determines a dc output resistance $$\R_0\$$ made of the resistors in parallel and a dc insertion loss or a small-signal dc gain of -6 dB considering the divide-by-two configuration. During this calculation process, SPICE open-circuits all capacitors and short-circuits all inductors. Please note that it is not a bias point calculation but rather a dynamic measurement to determine a gain for $$\s=0\$$. Specifically to LTspice, I have found this well-documented link.